Cosmos Coinage Code

Cosmos Coinage Code Jamila Awad

The Cosmos Coinage Code: The Multicurrency Suitcase Hedging Protocol

Author Jamila Awad

Rights Reserved JAW Group

Date August 2013

Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

Executive Summary

The international financial stability sphere reclaims a global coinage code in conjunction with imminent economic reforms. The research paper strives to deliver a coherent and impartial multicurrency hedging protocol. The paper is partitioned in three sections. Section 1 articulates the environmental asymmetric monetary regimes. Section 2 integrates the mathematical, theoretical and atmospheric components of inward-looking and global fiscal cooperation schemes into the engineered prototype. Section 3 exemplifies the implementation of the brainstorm with a combined devise investment portfolio. In brief, the universal economic system shall be immunized from divergent monetary policies and abrasive exchange-rate practices.

Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 2 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

Introduction

The international monetary cooperation phenomena depicts a predominant foundation in cementing a stable global coinage environment immune from liquidity crises, market collapses, credit-based instruments and fiscal regime divergences. Nations adopt inward- looking monetary guidelines however ponder interest in universal flexible exchange-rate arrangements to safeguard their economic system from perilous downturns. Ergo, the dissertation aspires to deliver a coherent and impartial multicurrency hedging protocol in line with forthcoming financial reforms.

Financial market meltdowns condemn abrasive practices and force rejuvenated fund infrastructures to shield the confidence of common-man economic participant as well as to armor the health of economic frames. Therefore, engineered financial risk management designs shall minimize the ever-present risks involved in financial markets.

The copulae regime analyzes the interdependencies of investment instruments in the cosmos of financial markets. The copula approach portrays a modeling strategy whereby a joint distribution is induced by specifying marginal distributions and a copula function that binds them together. The copula parameterizes the dependence structure of random variables thereby captures all the joint behavior. In addition, the copula function executes multidimensional frameworks and enables the evaluation of extreme events. The investigation of contagion and interconnectedness between currencies deriving from divergent monetary policies is performed with D-vine as well as Archimedean copula families. The selected copula classes unravel tail and asymmetric dependencies to overcome limitations engendered by standardized model risk techniques. They also strengthen the hedging prototype by encapsulating multivariate parameterization distributions and by facilitating a docile dependency analysis.

The Value-at-Risk (VaR) quantum metric portrays a widespread financial risk management tool that is complemented with the expected shortfall to determine the capital required to buffer unanticipated losses. The VaR is not considered coherent: It fails to comply with the subadditivity axiom whereas the summed risk of subportfolios fails to generate an inferior result compared to the sum of individual subportfolio risks and it neglects to estimate the size of losses when the VaR threshold is exceeded (Artzner & al., 1999). Thus, a multivariate setting customized with a copula credit risk frame provides an alternative solution to remedy VaR drawbacks.

The research paper is partitioned in three sections. Section 1 formulates the various concepts about inward-looking and international monetary policies. Section 2 amalgamates the mathematical, theoretical and atmospheric components of inward- looking and global fiscal cooperation schemes into the engineered prototype. Section 3 exemplifies the implementation of the hedging technique with a multicurrency investment portfolio.

In brief, coherent and transparent exchange-rate transactions in line with harmonized monetary policies shall secure the commencement of an unprecedented epoch in prudential financial risk management.

1. The Universal Monetary Cooperation and the Inward- Looking Economic Policies.

Section 1 describes the international monetary collaboration regime based on considerations of structural asymmetries across countries as well as the inward-looking fiscal policy. In precise terms, the first section articulates the environmental components that secure the enforcement of a sound global coinage framework.

The universal monetary cooperation depicts a theory widely analyzed during periods of economic meltdowns as well during episodes of market booms. Nations generally adopt for domestic policies however consider multi-country devise models to optimize their home country’s macroeconomic performance. Money holds a strong symbolic content whereas a coinage portrays a traditional attribute of sovereignty and economic power. The process of securitization and other financial innovations have engineered new financing routes for the non-financial sector. In addition, the prices and risk spreads across all types of financial products encapsulate relevant information to brainstorm as well as administer monetary policies.

The silent yet ever-present fear of currency wars and competitive devaluations upsurge a widespread disquietude for all nations regardless their ruling proxy power over the global economic system.

Central banks meddle during episodes of market disruptions by executing dynamic policy measures that engender an environment whereas the tacit conventional monetary actions are constrained and come close to the domain of fiscal governance. Thus, the methodology to separate untraditional monetary from fiscal activism requisites to examine the nature of the assets acquired. A second technique demands to investigate the character of the liabilities that finance the operations. In precise terms, exercises financed with monetary base are considered monetary and those furnished with debt are esteemed fiscal. Moreover, practices that involve government debt exclusively are regarded as debt management. Central banks generally succeed in administrating operations to steer short-term interest rates in vision to stimulate economic activity as well as to oversee inflation. Nonetheless, interventions during shock absorption episodes quest for drastic balance sheet expansions and significant alterations in asset composition. For example, central banks intervened to cushion the adverse effects of the past financial crisis by enforcing conventional and tailored actions to manage consequences derived from distant party operations such as investment banks as well as insurance firms. The confinement of risk in monetary policy independence is complex due to the entanglement between central banks’ balance sheet assets placed with national treasuries and its operations in relation to traditional as well as unconventional methods.

In game theory, a nation’s macroeconomic fulfillment can be accomplished by implementing a harmonized multinational coinage plan or by executing a Nash non- collaborative monetary doctrine. For example, central banks shift towards rules-based protocols with enhanced emphasis on domestic price stability and deflate their activism towards international monetary guidelines to ameliorate international economic conditions following financial collapses. Precisely, the entanglement of the past global economic plunge with the infectious liquidity crisis has exhibited the complexity of a universal economic system whereas emerging entities as well as developing countries had experienced a latent recovery. The forthcoming new epoch in prudential financial risk management has commenced by foreign affairs and central banks closely examining adverse spillover and contagion effects derived from host countries’ discretionary fiscal stratagems in order to buffer hazardous repercussions in home soil and to shield the health of the global financial system.

The upcoming financial reforms reclaim a revision of the policy assumptions behind the theories and models enforced in rule-like monetary doctrines. The timeframe whereas interest rates are frozen to a certain benchmark level depicts an example of a deviation conducted by central banks in a rule-like fiscal regime (Ahrend, 2010). In addition, the monetary conduit bifurcation is enhanced when countries synchronize their currency policies with other jurisdictions.

The collaboration of nations in transparent coinage frame of references can therefore deflate contagion effects induced from host monetary arrangements and inward-looking currency approaches.

Central banks adopt open market operations to promote capital mobility and to cushion arbitrage forces that align the rate of return in different currencies. The central banks policies on interest and funds rate aim to encompass future coinage depreciation or appreciation as well as to mitigate risk appetite. For example, entities in foreign countries borrow host currency to finance their ventures even though the anticipated returns are denominated in local devise. However, the debt carried remains subject to counterparty, default, exchange-rate and credit risk. Financial institutions acting as liquidity intermediaries therefore examine crusade projects with a Value-at-Risk (VaR) protocol whereas the following parameters are infused in the equation: the probability of insolvency, the interest rate, and finally, the size of the loan. Hence, a prolonged duration in low interest rates may lead to more risk bearing endeavors in various geographical locations. The effect might also be magnified when a dynamic interaction occurs between the lending cycle and the exchange-rates. The conformism behavior must also be integrated in the picture frame to diagnose the interdependencies between the actions of reacting institutions to the maneuvers of central banks (Hofmann and Bogdanova, 2012). The universal equilibrium of interest rates absorbs collisions such a financial meltdowns or liquidity razes and shall therefore be immunized from divergent monetary policy rules.

The magnifying contagion and adverse spillover apparatus between two distinct nations (a primary nation and a reacting nation) is summarized with the mathematical frame:

Rr = β + (γ*σ) Definition of variables:

Rr: The interest rate of the reacting nation denominated in their distinctive currency (domestic currency for the primary nation and foreign devise for the reacting nation). β: The domestic parameters established by central banks and that are incorporated to set the interest rate (such as Real Gross Domestic Product and the inflation) for the primary nation. σ: The standard deviation that represents variations in monetary policies between the primary and the reacting nation transposed in their distinctive devise. γ: The homogeneity level of similarities in monetary policies between the primary nation and the reacting country transposed in their distinctive currencies.

The mathematical formula demonstrates that central banks of reacting countries adjust their interest rates following the behavior of a primary nation. The inflammation propaganda occurs from infectious spillovers effects induced and thus shifts the international equilibrium of interest rates following the cascade reactions triggered by host countries in response to alterations in monetary strategies of the primary nation. Consequently, the cosmos of coinage is impacted by the asymmetric shocks and the global equilibrium of interest rates absorbs the described magnified mechanism.

On the other hand, central banks also complement monetary approaches with capital controls to deflate enhanced scales of volatile risk borrowing levels and to moderate devise appreciation. The currency intervention can however engender drawbacks such as an accumulation of international reserves that requisite safe and sound investment techniques in a globally amplified contagion monetary policy atmosphere (Bordo and Lane, 2012). In brief, central banks and foreign affairs are bound to thwart unrestrained exchange-rate fluctuations and disproportionate risk bearing schemes to bulwark divergence in monetary doctrines.

In a floating exchange-rate economic atmosphere, coinage and non-interest bearing deposits at central banks motion roles in a similar fashion to capital. Central banks apply stress-tests to balance sheet items to ascertain the capital requirements. In precise terms, they measure the total capital to be chambered in order to buffer anticipated losses by determining the level of coinage plus the capital necessary to sustain their operational expenditures. In light, the size of the central bank’s balance sheet predominates to weigh extra-budgetary financial market intervention. In essence, unconventional monetary stratagems shall facilitate economic recoveries following traumatic episodes and enhance global growth in a harmonious bona fide mindset. Nations considered individually or collectively portray entities that can distort Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 7 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad optimal universal equilibrium levels through unilateral activism (Gagnon and Henderson, 2002). The analysis of cross-country strategies to recoup from depressed economic periods unravels a correlation relationship between the timing of monetary policy initiatives and the timing of economic rehabilitation. In specific terms, central banks engaged in forward-looking governance such as preserving interest rates at target levels as well as expanding money and credit supplies are held responsible for initiating permanent changes in monetary regimes. A macroprudential set of regulations destined to limit the capability of financial entities to lend foreign deposits can be counterbalanced by the array of foreign funds into nonbank channels in the presence of efficient international coordination. Furthermore, the frontward mode induces a positive impact on asset prices and consequently on investments as well as export expansions. Thus, the proactive alterations to monetary guidelines improve competitiveness and moderate cross-border spillover effects. The undesirable externalities from the absence of international fiscal harmonization engender the following consequences: artificially weak devise to attain a competitive advantage, aggressive policies to depreciate currencies in turbulent periods that trigger competitive devaluations, and finally, spurious strong coinage that trigger a contagion crisis and meltdown the global financial system.

The rationale for harmonized international fiscal policies aims to buffer external counterproductive effects of independent domestic monetary stratagems and to stimulate a healthy global growth factor after collisions to the economic system. Nations shall opt for optimal balances between inward-looking guidelines and international coordination to sustain a sage position in the era of globalization. Coinage stability shall promote global economic exchanges and shall deflate adverse currency volatility. In light, exchange-rate misalignments depict a source of hefty disputes for all nations reacting to the fiscal plans of a primary country. For example, a depreciated devise can trigger competitive pressure on a nation’s trading partners and can stimulate protectionist sentiments in foreign soil. The sequel may lead to commercial discords between countries and disrupt trade accords. In fact, disordered exchange-rates may also engender the following events: contagion effects in neighboring countries, creation of conditions for speculative attacks, and lastly, large real appreciations that are reversed by nominal devaluations.

Banking institutions curtail their tendency to pass on lower interest rates to other participants in a morose economy especially when they are prone to absorb downturn shocks. Moreover, a lower elasticity of output growth in relation to real interest rates induces a pronounced incision in rate polices required to yield a predetermined increase in demand. The process of deleveraging is often initiated during downspin economic episodes however elicits significant benefits to enhance recoveries only after periods of traumatic events rather than after normal intervals of financial plunges. In fact, debt levels are not pushed to excessive levels in normal business cycles which boost lending habits with more leverage to finance profitable investment ventures and consumption. In brief, the leveraging parameter evaluates the effectiveness of monetary guidelines. Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 8 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

Therefore, the optimal timing of executing monetary policies in regards to deleveraging levels during periods of downturns depicts a primordial action to set in motion strong recoveries.

However, the collocation of the operational central banks’ policies and direct legislative control over traditional fiscal guidelines resorts to tailored balance sheet management in order to achieve monetary goals in periods of economic distress. In line, central banks play a prevalent intermediary role to secure conventional and emergency actions in order to stabilize the economic system during episodes of market crashes. Banking entities opt for target leverage ratios that derive from structural models to capture tradeoffs between constraints and resources and thus secure optimal operations. The deviations from predetermined leverage levels impact loan interest rates and provoke consequences in the blooming of real economy such as altering borrowing conditions. Banking institutions are constricted in maximizing profits when they face balance sheet restrictions. In light, the profit ratio of banking firms is measured by the net interest margin inferred from a loan whereas the deposit of interest payments and the bank’s deviation degree from its target ratio are deducted. The cost of a loan is extrapolated from a central bank’s monetary policy and from the reacting entity’s spread related to the degree of leverage.

The credit supply conduit is initiated by loan provision movements that alter the equilibrium level of loan financing and real output. Credit intermediaries administer supply requirements by proactively participating in lending spreads and in modifying leverage ratios. Therefore, banking entities adjust grant contributions in response to their balance sheet conditions. Precisely, banks tighten their credit requirements in presence of capital constraints and loosen their preconditions in absence of capitalization targets.

The credit reservoir channel induces a grant supply schedule that triggers the measurement of a loan rate demanded by a reacting banking firm:

3 Ir = Ic + [(σ*δr ) / (1 + Ic)]*Lr

Definition of variables:

Ir: The loan rate for the reacting banking firm towards a monetary policy set by a central bank. Ic: The interest rate derived from a monetary policy dictated by a central bank. σ: The reacting banking institution’s deviation degree from its target capital-to-asset ratio. δr: The reacting banking firm’s target capital-to-asset ratio. Lr: The reacting banking entity’s leverage ratio.

The elasticity of supply moves proportionally with the reacting bank’s target capital-to- asset ratio as well as with the cost derived from the deviation degree. The capital accumulation of a banking institution relies on its profits thus an increase in its profitability level triggers a reduction in its loan rate. Moreover, the provision supply that shifts with monetary policy adjustments is induced by central banks. In summary, credit supply alterations repercuss the equilibrium level of loan market interest rates. It also unravels the interaction between granting provision and the credit reservoir channels. The magnifying effect is therefore accentuated by lending rates whereas procyclical loan supply shifts impact consumption and investment projects.

In conclusion, the international currencies that play a benchmark role in the global financial bubble shall safeguard the coinage system from hazardous economic frames. The imminent reform in international monetary policies shall lay a foundation in securing stable value, rules-based and manageable devise. In light, the reconstitution of cosmos monetary arrangements strives to deflate the ever-present risks involved in financial markets. Moreover, the cosmos currency remodeling code shall complement sage liquidity management practices in line with credit-based transactions.

2. The Multicurrency Suitcase Hedging Prototype

The second chapter describes the logic inferred to model the multicurrency hedging prototype with a copula approach and delivers the cascade steps to implement the protocol. 2.1 The Copulae Framework The interlinkage between monetary policies and financial market transactions quest for sage risk management quantum methodologies that underpin all structural behaviors induced by the underlying traded instruments. Consequently, the adverse spillover and contagion effects arising from divergent fiscal as well as economic activism are then buffered by an impartial and transparent multicoinage suitcase hedging protocol. The copulae frame of reference apprehends the joint behavior of marginal pairs such as the combination of currencies in an investment portfolio. Moreover, the copula function executes multidimensional frameworks and evaluates extreme events.

The theorem of Sklar (1959) decomposes an n-dimensional joint distribution into its n- marginal distributions and a copula that describes the dependency between the n- variables. The copula theory sides the Gaussian assumption to facilitate financial modeling with a multifaceted approach. The copula function is generated from a random vector with a cumulative distribution function.

The following mathematical expression describes a copula function, noted as (X1,….,XN) Є RN, presented as a random vector with a cumulative distribution function (F) and marginal functions (Fn(xn)):

F (X1,….,XN) = P ( X1 ≤ x1,…..,XN ≤ xN) and

Fn(xn) = P (Xn ≤ xn), 1 ≤ n ≤ N

In addition, a copula function C of vector F is described as a cumulative distribution function of a probability measure bounded to [0,1]N such:

Cn(un) = C (1,….,1,un,1,….,1) = un whereas ≤ n ≤ N, 0 ≤ un ≤ 1 and

F(x1,….,xN) = C (F1(x1),….,Fn(xN)) for the interval (x1,….,xN) and whereas xn is a continuity point of Fn (1 ≤ n ≤ N).

The copula function is characterized with axioms: Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 11 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

 Every distribution function F holds at least one copula function that is uniquely defined in the dimension (F1(x1),….,FN(xN)) of the points (x1,….,xN), thus all

figures included in the interval ≤ n ≤ N become a continuity point of Fn. The copula function of F is unique when all the marginal functions are continuous.

 Every copula C is continuous and conforms to the following inequality: (

≤ n ≤ N, 0 ≤ un, vn ≤1): | C(u1,….,uN) – C( v1,….,vN) | | un – vn | .

 The ensemble C of all copula functions is convex and follows one set of convergence: punctual, uniform or weak.

 All copula functions of (X1,….,XN) are also copula functions of (h1(X1), ….,hN(XN)) when (h1,….,hN) that are monotone and non-decreasing mappings of R.

 If {F(m), m ≥1}is a sequence of probability cumulative distribution function in RN, (m) the convergence of F to a distribution function F with continuous margins Fn when m→∞ is equivalent to the following states:

(m) (a) Fn → Fn for all figures included in the interval ≤ n ≤ N.

(b) C(m) →C when C is a unique copula function associated to F and when C(m) illustrates a copula function linked to F(m).

The theory of the conditional copula states that the conditional distribution of (X,Y) given W, be denoted by the parameter H. Also, the conditional marginal distributions of X|W and Y|W are denoted F and G respectively. All previously stated variables are supposed continuous. The cumulative distribution functions of a random parameter as well as the corresponding probability density function are then schematized.

The copula approach facilitates the analysis of two random variables by unraveling the dependency between arbitrary variables in a general form. The copula contains information from the joint distribution that is not enclosed in the marginal distributions. Hence, the transformation of X and Y to u and v coordinates filters out information incorporated in the marginal distributions. In precise terms, the copula C contains all of the information on the dependency between X and Y, but disregards the univariate individual characteristics of X and Y.

A two-dimensional conditional copula depicts a function C that conforms with the following property; [0,1]* [0,1]*Z→[0,1] whereas Z Є Rk and k is a finite integer in line with the maxims: Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 12 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

The Sklar theorem for continuous conditional distributions is described with the parameters: F is the conditional distribution of X|Z, G is the conditional distribution of Y |Z, and finally H is the joint conditional distribution of (X,Y)|Z. If parameters F and G are continuous in x and y, then a unique conditional copula C is generated: H(x,y|Z) = ((C(F(x|Z),G(y|Z)|Z)).

Conversely, if the parameter F illustrates a conditional distribution of X|Z, G describes a conditional distribution of Y|Z and C portrays a conditional copula, then the function H becomes a conditional bivariate distribution function enclosing the conditional marginal distributions F and G.

The Archimedean class of copula encompasses many families due to its achievement in reducing dimensionality. It contains the following copula names: Ali-Mikhail-Haq (AMH), AP, Clayton, Frank, Gumbel and Joe. The mathematical properties of the Archimedean class are captured by an additive generator function φ: II → [ 0,∞] which is continuous, convex and a decreasing function (φ’(t) < 0 ). Moreover, the additive generator function may also be indexed by the association parameter θ enabling an entire family of copulas to be Archimedean. Therefore, any function φ that satisfies the above stated conditions can be utilized to generate a valid bivariate cumulative distribution function (cdf).

Table I: The general parameters of the Archimedean class of copulas

Definition of variables:

θ: The association parameter of the copula. u: The first coordinate density of the copula. v: The second coordinate density of the copula. φ: The additive generator function of the copula

Hence, the parameters of the copulas map the dependency structure of instruments incorporated in the investment portfolio. The contour scatter plots generated by the Archimedean class of copula trace the asymmetric and skewed distribution of products pooled in a multicurrency suitcase.

The rotated flexibility of the Archimedean family of copulas renders an appealing solution to investigate marginal distributions by surmounting standard dilemmas arising from the biased assumption that returns are normally distributed. In addition, financial engineering methodologies with Archimedean copula functions also enable to capture fat- tail features of the underlying and dependence structures. The D-Vine copula foundation magnifies the malleability to decapsulate pairs of marginals in the multicurrency investment suitcase. The combination of D-Vine and Archimedean copulas strengthens the model without imposing symmetric dependence on variables.

Tail dependence captures the behavior of random variables during extreme events. Precisely, it measures the probability of observing an extremely large positive or negative realization of one variable, given that the other variable also took on an extremely large positive or negative value. Therefore, the assembled copula design enables upper and lower tail dependency to range anywhere from zero to one. Clayton's copula illustrates an asymmetric copula, exhibiting greater dependence in the negative tail than in the positive tail. The generator of the Clayton copulae is determined by ΦC(u) = (u-α – 1) and hence Φ- 1(t) = ((t+1) -1/ α). The Clayton copula is suitable for describing dependencies in the left tail and during financial market meltdowns (Longin and Solnik, 2001). The relationship between Kendall’s tau (ρτ) and the Clayton copulae parameter α is computed by: 2 ρτ /(1- ρτ).

From the practical point of view, the Archimedean copulas depict a highly malleable copulae family due to their capabilities to generate a number of copulas from interpolating between certain copulas and capture various dependency structures. The Archimedean copulas may be constructed by using a continuous, decreasing or convex generator function Φ: I →R+ such that Φ(0) = 1. The generator function is called strict whenever Φ(0) = + ∞.The pseudo inverse of the generator function, subtitled Φ-1, is continuous, does not increase in boundaries [0, ∞] and strictly decreases in interval [0, Φ(0)]. Given a generator and its inverse, an Archimedean copula entitled CArchimedean is -1 generated according to the Kimberling theorem such: C(u1,u2) = Φ (Φ(u1) + Φ(u2)) in interval [0,1]2 → [0,1] for quantiles of two random variables X and Y. Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 14 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

The generator of the Gumbel copulae is provided by ΦG(u) = ((-ln(u))α and therefore ΦG(u)-1(t) = exp(-t1/ α). The Gumbel copulas schematize multivariate extreme value distributions and they are often used to model extreme distributions. They depict asymmetric Archimedean copulas, exhibiting greater dependence in the positive tail than in the negative tail. The relationship between Kendall’s tau (ρτ) and the Gumbel copulae parameter α is illustrated by: 1/(1- ρτ).

A Vine copulae (V(n)) portrays a copula containing n variables that is nested in a set of trees (T1, ..., Tn−1) whereas the edges of the trees (j) represent the nodes of the trees ((j+1) where (j = 1,…,n-2)) and each tree contains a maximum number of edges. Thus, a conventional Vine on n variables in which two edges in a tree are joined by edges sharing a common node (Bedford and Cooke, 2001).

The Vine copulae conforms to the following axioms:

 A tree is characterized (T = (N,E)) with nodes (N) and edges (E) when the edges represent a subset of unordered pairs of nodes with no cycle. In addition, a sequence of elements surges for any variable a and b bounded in interval N.

 A regular Vine (V) on n elements is defined as: V(n) = (T1, ..., Tn−1) whereas T1 illustrates a tree with nodes (N1 = {1,…,n}) and edges E1.  The regular Vine complies with the proximity property whereas edges (E) consider the symmetric differences between the numbers of elements in a set.

A regular Vine copula is considered canonical if each tree Ti has a unique maximum node of degree n-1. A conventional Vine copula is pronounced D-Vine when all nodes in T1 hold a degree attaining a maximum of 2. There are [(n*(n-1))/2] edges in a regular Vine on n variables. Each edge in a conventional Vine is linked to a conditional copula that unravels the conditional bivariate distribution with uniform margins.

Conventional Vine copulas aim to pinpoint a set of conditional bivariate constraints associated with each edge. The process is initiated with variables that are attainable from a given edge via a bond known as the constraint set of that edge. Afterwards, when two edges are joined by the edge of the next tree, the intersection of the respective constraint sets is parameterized as the conditioning variables. The symmetric differences of the constraint sets are optimized as the conditioned variables. The order of an edge or of a node is defined by the cardinality of its conditioning set.

The use of copulas is however challenging in higher dimensions, therefore the implementation of Vine and Archimedean copula families surmount standard limitations arising from conventional financial risk regimes. In light, the engineered protocol designs a complex dependency structure pattern by benefiting from the abundant array of bivariate copulas as building blocks.

The Vine copula procedure depicts a flexible graphical technique to describe multivariate copulas modeled from a cascade of bivariate copulas entitled pair-copulas (PCC). The PCCs decompose a multivariate probability density into bivariate copulas whereas each pair-copula can be selected independently from the others and thus magnify the malleability in the dependency arrangement. In particular, the asymmetries and the tail dependency can be integrated in the conditional independence to inaugurate robust coherent hedging techniques. Lastly, the Vine copula frame combines the advantages of multivariate copulas and amplifies the docility of bivariate copulas.

Fitting a Vine copula frame is executed in steps. Primo, the first command identifies an appropriate Vine tree structure from examined sets of data or through expert knowledge. The second operation selects copula families for the isolated Vine structure. The third instruction estimates the parameters of the copula families selected for the given Vine copula fit. The final procedure evaluates and compares other potential copula pair family sets.

The copula values for a predetermined array of copula families are performed with the maximum likelihood estimation. Parametric estimation with the maximum likelihood portrays a sound methodology to prescribe the optimal copula choice by fitting the data into a copula and afterwards analyzing the parameters to pursue further investigation.

The maximum likelihood technique is derived from the following logic. The density of the joint distribution F for the copula C and the margins Fn is illustrated:

N f(x1,….,xn,….,xN) = c(F1(x1),….,Fn(xn),….,FN(xN))*Π fn(xn) whereas fn is the density of the margin Fn and c is the density of the copula described by: c(u1,….,un,….,uN) = [∂ C (u1,….,un,….,uN)] ÷ [∂u1,.... ,∂un,....,∂uN] .

The logarithm likelihood (l(θ)) estimator is schematized with the equation:

t t l(θ) = lnPr{(X1,….,XN) = (x 1,….,x N)}.

Sklar's theorem decomposes a bivariate distribution, Ht, into three components: the two marginal distributions, Ft and Gt, and finally the copula, Ct. The maximum likelihood analysis is generated with the differentiation of Ft and Gt as well as the double differentiation of Ct.: ht(x,y|z) ≡ ft(x|z)*gt(y|z)*ct(u,v|z) where u ≡ Ft(x|z) and v ≡ Gt(y|z). Reformatting the equation on both sides with the logarithm results: LXY = LX + LY + LC.

The joint log-likelihood is equal to the sum of the marginal log-likelihoods and the copula log-likelihood. For the purposes of multivariate density design, the copula representation enhances greater flexibility in the specification by modeling individual variables using whichever marginal distributions with best fitting properties. In addition, the maximum likelihood estimator is the most efficient estimator because it attains the minimum asymptotic variance bound.

In conclusion, the copula function stands an attractive loop computing tool in financial risk management due to its flexibility to divulgate information relating to the structure of dependence.

2.2 Risk Statistic Techniques

Risk statistic methodologies are generated from parametric simulations. Prudential risk management is favored to encompass statistic test flaws whereas a framework of risk statistic tools enhances an accurate setting to quantify the total risk. The Basel guidelines emphasize on accurate and robust risk mapping instruments such as the Value-at-Risk (VaR) and the Expected Shortfall (ES). Ergo, the following sub-division describes the selected financial quantum management tools.

2.2.1 The Value-at-Risk

The VaR estimates the likelihood of recognizing a monetary loss exceeding a specific amount for a determined time horizon and at a stated confidence interval. It depicts a percentile of a profit & loss portfolio distribution enumerated either as a potential loss from current portfolio value or as an expected loss in the forecast horizon. However, the VaR does not conform to the subadditivity axiom and it is consequently complemented by the coherent risk measure entitled the expected shortfall (Artzner & al., 1999).

In light, a coherent risk statistic instrument must satisfy four distinct properties:

 Monotonicity: The risk of a portfolio will sequently oscillate with the gravity of losses in a portfolio.  Positive Homogeneity Degree 1: A size amendment of a position in a portfolio will uniformly impact the portfolio risk.  Subadditivity: The risk summing subportfolios stands inferior or equal to the addition conglomeration of their distinct risks.  Translation Invariance: A cash supplement to a portfolio will reduce its risk by an identical proportion.

2.2.2 The Expected Shortfall

The VaR is therefore shepherd by the coherent expected shortfall statistic to remedy its incompatibility with the subadditivity maxim. In consequence, the expected shortfall illustrates the deepness of losses to overstep the VaR benchmark. It also delivers relevant information about the tail traced from the profit & loss distribution. The expected shortfall mathematically expresses the conditional expectation of a portfolio loss greater than a VaR level. In brief, the expected shortfall instrument complies with the subadditivity postulate and complements the VaR approach due to its convex function of portfolio weights. It thus enhances optimization while minimizing uncertainty related to specific restraints.

2.3 The Cascade Steps to Execute the Cosmos Coinage Hedging Protocol

The engineered protocol aspires to deliver market participants an impartial and robust multicurrency hedging framework.

The R and the Matlab software depict efficient programs for statistical computing and graphics. The R program runs on all platforms and provides excellent interfaces with codes. In addition, the R software offers a one-directional communication channel with the Matlab software. The Archimedean and the Vine copulae cosmos coinage hedging technique was designed from the above stated programs. In brief, the archetype has been modeled with docility to enable participants to scissor the protocol rather than emulate the prototype to genuinely comprehend the brainstorm.

The prototype is executed in eight cascade commands:

1- The first step requisites to gather the following data: The spot exchange-rate currencies pooled in the investment portfolio, the data interval length and the weights attributed to each devise.

2-The second operation transforms the spot exchange-rate into logarithm returns.

3-The third procedure examines the data with statistical tests: the mean, the median, the standard deviation, the minima, the maxima, kurtosis and the Jarque-Bera test.

4-The fourth command traces the QQ-plots to visually investigate dependency structures and behavior in the tails of the distribution.

5-The fifth step migrates the pairs of marginals obtained from the logarithm spot exchange-rate returns into the D-Vine copula procedure with an optimization restriction to Archimedean copulas. The D-Vine copula methodology examines the sequences of marginal pairs and selects the best suited Archimedean copula with the maximum logarithm likelihood. Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 18 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

6-The sixth operation analyses currency pairs of marginals from the D-Vine copula optimization then investigates the currency pairs of marginals with the selected Archimedean copulas.

7-The seventh step incorporates the parameters for the pairs of marginals and the currency weights into an engineered loss distribution simulation script. The simulation is repeated 10,000 times with loop computing to retrieve the quantum risk metrics: the Value-at-Risk and the Expected Shortfall for a 95% confidence level.

8-The final command repeats step 7 for a 99% confidence level.

3. The Implementation of the Pioneered Hedging Protocol with a Multicurrency Investment Suitcase.

The final chapter delivers an example of the engineered cosmos coinage hedging protocol. A random devise investment suitcase has been assembled: The portfolio contains four currencies of equal weights for the period from January 1st 2000 to January 1st 2010. The timeframe sample therefore includes a shock absorption event such as the financial crisis of 2008. The spot exchange-rates for the coinage combination are denominated against the U.S. dollar (USD): the Euro (EUR), the Swiss franc (CHF), the Japanese yen (JPY) and finally the pound sterling (GBP).

Table II: The summary of statistic tests for logarithm spot exchange- rate returns.

Test statistic EUR CHF JPY GBP currency currency currency currency

Number of 2516 2516 2516 2516 observations

Mean 5,94701E-05 -7,29734E-05 -1,5288E-05 -1,09623E-06

Median 3,12193E-05 0,0000000 1,79557E-05 4,84126E-05

Maximum 0,020067846 0,015647629 0,011762278 0,019260342

Minimum -0,013042301 -0,021623582 -0,022651271 -0,021568149

Standard 0,002856582 0,003039597 0,002908287 0,002741144 deviation

Kurtosis 2,554672881 2,374487908 4,141374211 6,022398799

Jarque-Bera 2,2E-16 2,E-16 1,317E-12 2,2E-16 p-value

The Jarque-Bera p-values confirm the rejection of the null hypothesis at 95% level of confidence. Therefore, the logarithm spot exchange-rates are not normally distributed. Ergo, a copula framework is enforced to unravel the behavior of multicurrency interdependencies between each other and in global financial markets. The QQ-plots are examined to determine the distribution sampling between logarithm spot exchange-rate returns. The scatter plots support the inference of non-normal distributions. The schematizations confirm the inferred asymmetric distribution and tail behavior in the coinage cosmos. In conclusion, a copula approach is retained to encapsulate multifaceted dependency structures for all instruments pooled in the investment suitcase.

Figure 1: The QQ-plot for the logarithm returns for EUR/USD and CHF/USD.

The figure 1 illustrates the deviations in the tails of the distribution for the logarithm returns for EUR/USD and CHF/USD sample.

Figure 2: The QQ-plot for the logarithm returns for EUR/USD and JPY/USD.

The figure 2 exhibits the driftage in the tails of the distribution for the logarithm returns for EUR/USD and JPY/USD sample. Figure 3: The QQ-plot for the logarithm returns for EUR/USD and GBP/USD.

The figure 3 exemplifies the deflection in the tails of the distribution for the logarithm returns for EUR/USD and GBP/USD sample. Figure 4: The QQ-plot for the logarithm returns for JPY/USD and CHF/USD.

The figure 4 demonstrates the deviations in the tails of the distribution for the logarithm returns for JPY/USD and CHF/USD sample.

Figure 5: The QQ-plot for the logarithm returns for JPY/USD and GBP/USD.

The figure 5 illustrates the driftage in the tails of the distribution for the logarithm returns for JPY/USD and GBP/USD sample. Figure 6: The QQ-plot for the logarithm returns for GBP/USD and CHF/USD.

The figure 6 unravels the deflections in the tails of the distribution for the logarithm returns for GBP/USD and CHF/USD sample. In brief, the test statistics and the QQ-plots converge to an identical conclusion; the distribution of logarithm spot exchange-rate returns of the currencies pooled in the investment suitcase is non-normal, asymptomatic and heavily tailed. Therefore, a copula strategy delivers a flexible arrangement to unravel the structural dependency in line with divergent monetary policies and with the interlinkage behavior of currencies in global financial markets. The D-Vine copula optimization restricted to Archimedean copula enabled to underpin the best suited Archimedean copulas for the pairs of marginals examined. Table III: The D-Vine copula optimization results for the six pairs of marginals examined.

Pairs of EUR CHF JPY GBP marginals

EUR -----

CHF Clayton ------

JPY Frank Clayton -----

GBP Gumbel Frank Clayton -----

The D-Vine optimization examined the maximum logarithm likelihood for the sequences of marginal pairs to select the best suited Archimedean copula: EUR+JPY → EUR,JPY|CHF CHF+GBP → CHF,GBP|EUR JPY+GBP → JPY,GBP|EUR,CHF

Table IV: The risk quantum results

Risk quantum VaR 95% ES 95% VaR 99% ES 99% metric

Cosmos Coinage 0.00167758 0.002118918 0.002367995 0.002783725 Suitcase

The results were obtained by integrating the devise parameters with their respective selected Archimedean copula following the D-Vine optimization into a loss distribution script with equal weights for all currencies and then loop computed 10,000 times. The cosmos coinage hedging technique enabled to reduce the VaR and ES results comparatively to conventional methods without compromising the adroitness in execution.

Conclusion In conclusion, the hedging multicurrency suitcase protocol delivers a flexible and docile framework to buffer omnipresent risks involved in transacting coinage in line with divergent monetary strategies and global financial markets. Vine and Archimedean copulas model malleable multivariate dependency arrangements. They also construct joint distributions by specifying second order structures without imposing any algebraic constraints. Nations are deemed to reckon international monetary coordination and exponential caution about self-interest policies to enhance best outcomes in a macroeconomic standpoint. In brief, countries shall harmonize the paradoxical nature of the coinage complexion: On one side, the currency armors a nation’s economic power in the global financial playground, and on the other side, it secrets a nation’s fear of threat of damage.

References Aas K., Czado C., Frigessi A., Bakken H. (2009), Pair-Copula Constructions of Multiple Dependence, Insurance: Mathematics and Economics, 44(2), 182-198.

Ahrend, Rudiger (2010), Monetary Ease: A Factor Behind Financial Crises? Some Evidence from OECD Countries, Economics: The Open Access, Open Assessment E- Journal, 4.

Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999), Coherent Measures of Risk, Mathematical Finance.

Basel Committee on Banking Supervision (2001), The new Basel Capital Accord, Consultative document, Bank of International Settlements, Basel, Switzerland.

Basel Committee on Banking Supervision (2012), Basel III counterparty credit risk and exposures to central counterparties-FAQ, Bank of International Settlements, Basel, Switzerland.

Basel Committee on Banking Supervision (2010), Basel III: International framework for liquidity risk measurement, standards and monitoring, Bank of International Settlements, Basel, Switzerland.

Basel Committee on Banking Supervision (2013), Margin requirements for non-centrally cleared derivatives, Bank of International Settlements, Basel, Switzerland.

Bedford, T. J., Cooke, R. M. (2001), Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32, 245-268.

Bordo, Michael and John Landon Lane (2012), Does Expansionary Monetary Policy Cause Asset Price Booms: Some Historical and Empirical Evidence, Rutgers University.

Butler, J. and Schachter, B. (1998), Estimating Value-at-Risk with a Precision Measure by Combining Kernel Estimation with Historical Simulation, Review of Derivatives Research.

Cherubini U., E. Luciano, W.Vecchiato (2004), Copula methods in Finance, John Wiley Finance Series.

Chollete L., Heinen A., Valdesogo A. (2009), Modeling International Financial Returns with a Multivariate Regime Switching Copula, Journal of Financial Econometrics, 7, 437-480.

Clayton, D.G., (1978), A Model for Association in Bivariate Life Tables and its Application in Epidemiological Studies of Familial Tendency in Chronic Disease Incidence, Biometrika, 65(1), 141-151.

CreditRisk+ (1997), A credit risk management framework, Credit Suisse First Boston, London. Dibmann J., Brechmann EC., Czado C., Kurowicka D. (2013), Selecting and Estimating Regular Vine Copulae and Application to Financial Returns, Computational Statistics & Data Analysis, 59, 52-69.

Eichengreen Barry and Douglas Irwin (2010), The Slide to Protectionism in the Great Depression: Who Succumbed and Why?, Journal of Economic History 70, pp.871-897. F. Longin, B. Solnik (2001), Extreme Correlations of International Equity Markets, The Journal of Finance, Vol. 56, pages 649-676.

Frees, E.W. and E.A. Valdez (1998), Understanding relationships using copulas, North American Actuarial Journal, 2, 1-25.

Frees EW, Wang P. (2005), Credibility Using Copulas, North American Actuarial Journal, 9(2), 31–48.

G.Wei, T. Hu (2002), Supermodular dependence ordering on a class of multivariate copulas, Statistics and Probability Letters 57(4), 375-385.

Genest, C. and J. MacKay (1986), The joy of copulas: Bivariate distributions with uniform marginals, American Statistician, 40, 280-283.

Goldstein, Morris (2006), Exchange Rates, Fair Play, and the “Grand Bargain” Financial Times, April 21.

Harry Joe (1997), Multivariate Models and Dependence Concepts, Monographs on Statistics and Applied Probability 73, Chapman & Hall.

Hobaek Haff I., Aas K, Frigessi A. (2010), On the Simplified Pair-Copula Construction- Simply Useful or Too Simplistic?, Journal of Multivariate Analysis, 101(5), 1296-1310.

Hofmann, Boris and Bilyana Bogdanova (2012), Taylor Rules and Monetary Policy: A Global Great Deviation?, BIS Quarterly Review.

Hull J. (1997), Options, Futures, and Other Derivatives, 4th edition, Princeton-Hall, Princeton, NJ. Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 29 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected] Cosmos Coinage Code Jamila Awad

International Monetary Fund (2011), Spillover Report, Washington, D.C.: IMF. International Monetary Fund (2012), The Liberalization and Management of Capital Flows: An Institutional View, Washington, D.C.: IMF. Issing, Otmar (1999), The ECB and Its Watchers, speech at the ECB Watchers Conference, Frankfurt, Germany.

J.P. Morgan (1997), CreditMetrics, Technical Document, New York, U.S.A. Kurowicka, D., Cooke, R. M. (2003), A parameterization of positive definite metrics in terms of partial correlation vines. Linear Algebra and its Applications, 372, 225-251.

Meyer Laurence, Brian Doyle, Joseph Gagnon and Dale Henderson (2002), International Coordination of Macroeconomic Policies: Still Alive in the New Millennium?, International Finance Discussion Paper no. 723, Washington, D.C.: Board of Governors of the Federal Reserve System. Nikoloulopoulos AK., Joe H., Li H. (2012), Vine Copulas with Asymmetric Tail Dependence and Applications to Financial Return Data, Computational Statistics & Data Analysis, 56(11), 3659-3673.

R Development Core Team (2007), Writing R Extensions, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.

Sklar, A. (1959), Fonctions de répartition à n dimensions et leurs marges, Publications de l'Institut de Statistique de L'Université de Paris 8: 229–231.

Vines, David (2006), Comments on Global Imbalances and Emerging Markets, in Alan Ahearne, European and Asian Perspectives on Global Imbalances, Asia Europe Economic Forum, 40-51.

Von Hagen, J. (1999), Co-ordination of economic policies and employment, in A. Lamfalussy, L. D. Bernard and A. Cabral (eds.), The Euro-Zone: A New Economic Entity?, Bruylant, Brussels.

Wurtz D (2004), Rmetrics: An Environment for Teaching Financial Engineering and Computational Finance with R. Rmetrics, ITP, ETH Zurich, Zurich, Switzerland. URL http://www.Rmetrics.org/

Paper: “The Cosmos Coinage Code” (2013) Rights Reserved: JAW Group 30 Author: Jamila Awad JAW Group, 3440 Durocher # 1109 Date: August, 2013 Montreal, Quebec, H2X 2E2, Canada Mobile: (1) 514 799-4565 E-mail: [email protected]