DOCSLIB.ORG

Valuation Models of Inflation Derivatives Using Pricing Kernel

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Valuation Models of Inflation Derivatives Using Pricing Kernel Valuation Models of Inflation Derivatives using Pricing Kernel Workshop "Finance and Insurance", Jena (Germany) March 16-20, 2009 Koichi Miyazaki (with Sho Ito) University of Electro-Communications, Dept. of Systems Engineering 1 1. Introduction (Background, Basics and Purpose) 1-1. Origin of the corporate-debt valuation model: Merton (1974), the structural model. Time t Time T (Maturity ) S Case of F T F = K t T Default St WT = 0 Wt Equity : FT = K W = max()S − K ,0 Case of T T S Bond : T Non Default FT = min()ST , K WT The firm’s asset-value process St under physical probability measure P dS = µS dt +σ S dzS S 2 1-2. Extension of the Merton model and our model -Black and Cox (1976) and Geske (1977): incorporate the effects of the coupons and covenants of corporate bonds. Extension in terms of “Cash Flow” -Shimuko, Tejima, and Deventer (1993): incorporate the stochastic interest rate proposed by Vasicek (1977). R dR = κ R − R dt +σ dz Instantaneous nominal interest-rate f : f ( f f ) Rf Rf Extension in terms of “Modeling of nominal interest rate” -Longstaff and Schwarz (1995): incorporating the Vasicek (1977) model into the Black and Cox (1976) model. Extension in terms of “Cash Flow” and “Modeling of nominal interest rate” -Zhou (1997): applies the jump-diffusion process in Merton (1976) to the valuation of corporate debt. dS ω+ηε Nominal company-asset S : = µS dt +σ S dzS + (e −1)dNt . Extension in terms of “Firm Value Process” S z However, to best of our knowledge, no valuation model of inflation derivatives in the structural model. Our Extension is in terms of “Modeling of real interest rate” and “Modeling of inflation” 3 z Inflation-linked government bonds - The U.S.A. in mid 1990s, Japan since 2004, Germany and Italy at much the same time as in Japan. - In the U.K. (since 1982) and Canada, the history of such bonds is much longer. US TIPS (Anual Issuance and Ratio of UK Index-Linked Gilt (Ratio of Outstanding) Outstanding 35 800 10.00% 30 8.00% 600 25 6.00% 400 20 4.00% (%) 15 Oku-Dollar 200 2.00% 10 0 0.00% 5 8 2 6 0 997 9 001 0 005 0 1 19 1999 20002 20 2003 2004 2 20 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Year Year Fig1: US TIPS Fig2: UK LINKER z From now on, the active issuance of inflation-linked financial product may become feasible. - Thus, it is very useful to introduce a model that evaluates inflation related products. 4 1.3 Risk-neutral valuation and Pricing kernel valuation under the Merton model - Risk-neutral valuation (Valuation under Risk-neutral measure) dS Q ⎛⎛ 1 2 ⎞ Q ⎞ = R f dt + σ S dzS , ST = St exp⎜⎜ R f − σ S ⎟()T − t +σ S zS ()T − t ⎟ S ⎝⎝ 2 ⎠ ⎠ −Rf ()T −t Q + Equity value: W (t,T ) = e E [(ST − K ) ], Bond value: F()t,T = St −W (t,T ) - Pricing kernel valuation (Valuation under Physical measure) dM = −R dt +φ dz +φ dz dz dz Pricing kernel (Stochastic Discount Factor): M f S S u u , where u ⊥ S dS ⎛ dM ⎞ Nominal firm-asset S : = (R f + σ S λS )dt + σ S dzS , where λS dt = −Cov⎜ ,dzS ⎟ = −φS dt S ⎝ M ⎠ ⎡M T ⎤ Risk-free Bond value: P()t,T = Et ⎢ ⋅1⎥ ⎣ M t ⎦ ⎡M ⎤ W ()t,T = E T ()S − K + Equity value: t ⎢ T ⎥ , Bond value: F(t,T ) = St −W (t,T ) ⎣ M t ⎦ 5 1.4 Computational Method of Expectation in the Pricing kernel valuation Utilize moment generating function (m.g.f.) 2 2 When stochastic variable ()X ,Y ~ N 2 (µ1 , µ 2 ,σ 1 ,σ 2 , ρ ), its m.g.f. mXY (u,v)is given by ⎛ σ 2u 2 + 2ρσ σ uv +σ 2v2 ⎞ m u,v = exp ux + vy f x, y dxdy = exp⎜µ u + µ v + 1 1 2 2 ⎟ XY ()∫∫ ( )() ⎜ 1 2 ⎟ . ⎝ 2 ⎠ ⎡M T ⎤ −R f ()T −t MT ⎛⎛ 1 2 2 ⎞ ⎞ Risk-free Bond value: P()t,T = Et ⎢ ⋅1⎥ = e , = exp⎜⎜− R f − ()φS +φu ⎟()T − t +φS zS ()T − t +φu zu ()T − t ⎟ ⎣ M t ⎦ M t ⎝⎝ 2 ⎠ ⎠ ⎡M + ⎤ x ⎛ M ⎞ ⎛ S ⎞ + W ()t,T = E T ()S − K = e g ()()y f x, y dxdy X = ln⎜ T ⎟ Y = ln⎜ T ⎟ y Equity value: t ⎢ T ⎥ ∫∫ , ⎜ ⎟ , ⎜ ⎟ and g()y = (St e − K ) . ⎣ M t ⎦ ⎝ M t ⎠ ⎝ St ⎠ ⎛ 1 2 2 ⎞ 2 2 ⎛ 1 2 ⎞ 2 E[]X = ⎜− R f − ()φS + φu ⎟()T − t , V []X = (φS + φu )(T − t), E[]Y = ⎜ R f + σ S λS − σ S ⎟()T − t , V [Y ] = σ S (T − t), Cov(X ,Y ) = φSσ S (T − t). ⎝ 2 ⎠ ⎝ 2 ⎠ ∞ x Define f ()y ≡ e f (x, y )dx ， ∫−∞ ∞ ∞ ∞ ∞ ∞ evy f ()y dy = evy e x f ()x, y dxdy = e x+vy f ()x, y dxdy = m ()1, v ∫−∞ ∫−∞ ∫−∞ ∫∫−∞ −∞ 2 ⎧ ⎛ 1 ⎞ ⎫ 2 2 ⎛ 2 ⎞ ⎛ σ ⎞ ⎛ σ ⎞ ⎪ ⎜ y − ⎜ R f − σ s ⎟()T − t ⎟ ⎪ = exp⎜ µ + 1 ⎟ exp⎜()µ + ρσ σ v + 2 v2 ⎟ 1 ⎪ ⎝ ⎝ 2 ⎠ ⎠ ⎪ ⎜ 1 ⎟ ⎜ 2 1 2 ⎟ f ()y = P (t,T ) exp⎨− ⎬ ⎝ 2 ⎠ ⎝ 2 ⎠ 2 2πσ S T − t ⎪ 2σ S ()T − t ⎪ ⎛ 1 σ 2 ()T − t ⎞ ⎪ ⎪ ⎜⎛ 2 ⎞ S 2 ⎟ ⎩ ⎭ = P()t,T exp⎜⎜ R f − σ S + ()λS + φS σ S ⎟v + v ⎟ ⎝⎝ 2 ⎠ 2 ⎠ 6 1.5 Equity value formula in the Merton model Equity value formula: ∞ ⎡M T + ⎤ x W ()t,T = Et (ST − K )= e g ()(y f x, y )dxdy = g ()()y f y dy We have only to evaluate ⎢ ⎥ ∫∫ ∫−∞ using the probability ⎣ M t ⎦ ⎧ 2 ⎫ ⎛ ⎛ 1 2 ⎞ ⎞ ⎪ ⎜ y − ⎜ R f − σ s ⎟()T − t ⎟ ⎪ 1 ⎪ ⎝ 2 ⎠ ⎪ ⎝ ⎠ . density function f ()y = P (t,T ) exp⎨− 2 ⎬ 2πσ S T − t ⎪ 2σ S ()T − t ⎪ ⎪ ⎪ ⎩ ⎭ ⎧ 2 ⎫ ⎛ ⎛ 1 2 ⎞ ⎞ ⎪ ⎜ y − ⎜ R f − σ s ⎟()T − t ⎟ ⎪ ∞ 1 ⎪ ⎝ ⎝ 2 ⎠ ⎠ ⎪ W ()t,T = g ()()y P t,T exp − dy ∫−∞ ⎨ 2 ⎬ 2πσ S T − t ⎪ 2σ S ()T − t ⎪ ⎪ ⎪ ⎩ ⎭ ⎧ 2 ⎫ ⎛ ⎛ 1 2 ⎞ ⎞ ⎪ ⎜ y − ⎜ R f − σ s ⎟()T − t ⎟ ⎪ ∞ ⎜ ⎟ y + 1 ⎪ ⎝ ⎝ 2 ⎠ ⎠ ⎪ = P()t,T ()St e − K exp − dy ∫−∞ ⎨ 2 ⎬ 2πσ S T − t ⎪ 2σ S ()T − t ⎪ ⎪ ⎪ ⎩ ⎭ ⎛ ⎛ 1 2 ⎞ ⎞ ⎛ ⎛ 1 2 ⎞ ⎞ ⎜ ln()St K + ⎜ R f + σ S ⎟()T − t ⎟ ⎜ ln()St K + ⎜ R f − σ S ⎟()T − t ⎟ ⎜ ⎝ 2 ⎠ ⎟ ⎜ ⎝ 2 ⎠ ⎟ = St Φ − KP()t,T Φ ⎜ σ T − t ⎟ ⎜ σ T − t ⎟ ⎜ S ⎟ ⎜ S ⎟ ⎝ ⎠ ⎝ ⎠ 7 1.6 Purpose of Our Research Using Pricing Kernel, (1-A) we derive closed-form valuation formulas of nominal and real (inflation-linked) corporate bonds. (1-B) we examine the sensitivity of nominal and real credit spreads on company parameters related to inflation. (2-A) we derive closed-form valuation formula of the non-defaultable inflation derivatives. (2-B) we examine the sensitivity of the non-defaultable inflation derivative prices. (3-A) we derive semi-closed-form valuation formula of the defaultable inflation derivatives. (3-B) we examine the sensitivity of the default premium in the inflation derivative prices. to attain some useful implication for corporate finance. 8 2 The setting and the valuation of the nominal government bond 2.1 Setting (Replacing the equity process with company value process in Brennan and Xia (2002)) dΠ z Price level Π : = πdt + σ Π dz Π (1) Π z Instantaneous expected inflation π : dπ = α(π − π )dt + σ π dzπ (2) dM M = −rdt + φS dz S + φr dzr + φπ dzπ + φu dzu = −rdt + φ′dz + φu dzu z Real-pricing kernel : M , (3) where φi (i = S,r,π ,u ) are constants and determine the corresponding market price of risks λS , λr , λπ and λu . z Instantaneous real interest-rate r : dr = κ(r − r)dt +σ rdzr (4) dS z Nominal firm-asset S : = (R f + σ S λS )dt + σ S dzS (5) S where λS is the constant unit-risk premium associated with the innovation, dzS , and Rf is the nominal interest rate. ′ z Price level Π process can be written by the innovations dz = []dzS ,dzr ,dzπ and the projection residualξudzu . dΠ = πdt + σ Π dzΠ = πdt + ξ S dz S + ξ r dz r + ξπ dzπ + ξ u dzu ≡ πdt + ξ ′dz + ξ u dzu (6) Π 9 2.2 Nominal government-bond price (Brennan and Xia (2002)) z The nominal-pricing kernel: M Π z The price of the nominal government bond that pays $1 at the maturity T , as follows: ⎡M T M t ⎤ P()t,T = Et ⎢ ⋅1⎥ (7) ⎣ ΠT Π t ⎦ T ⎛ 1 ⎞ T T ln()M T M t = ⎜− r ()s − VM ⎟ds + φ′dz + φu dzu (8) ∫t ⎝ 2 ⎠ ∫t ∫t T T T ⎛ 1 2 ⎞ ln()()Π T Π t = ⎜π s − VΠ ⎟ds + ξ ′dz + ξ u dzu (9) ∫t ⎝ 2 ⎠ ∫t ∫t ⎡ ⎤ ⎧ ⎫ ⎡M T M t ⎤ ⎧ ⎛ M T ⎞ ⎛ Π T ⎞⎫ ⎪ ⎡ ⎛ M T ⎞ ⎛ Π T ⎞⎤ 1 ⎡ ⎛ M T ⎞ ⎛ ΠT ⎞⎤⎪ (Proof) P()t,T = Et ⎢ ⋅1⎥ = Et ⎢exp⎨ln⎜ ⎟ − ln⎜ ⎟⎬⎥ = exp⎨Et ⎢ln⎜ ⎟ − ln⎜ ⎟⎥ + Vart ⎢ln⎜ ⎟ − ln⎜ ⎟⎥⎬ ⎜ M ⎟ ⎜ ⎟ ⎜ M ⎟ ⎜ ⎟ 2 ⎜ M ⎟ ⎜ ⎟ ⎣ ΠT Π t ⎦ ⎣⎢ ⎩ ⎝ t ⎠ ⎝ Π t ⎠⎭⎦⎥ ⎩⎪ ⎣ ⎝ t ⎠ ⎝ Π t ⎠⎦ ⎣ ⎝ t ⎠ ⎝ Π t ⎠⎦⎭⎪ ⎛ M ⎞ ⎛ Π ⎞ X = ln⎜ T ⎟ − ln⎜ T ⎟ E [exp X ] m ()1 m (t) Putting T ⎜ ⎟ ⎜ ⎟ , t T is equivalent to X T , where X T is moment generation function ⎝ M t ⎠ ⎝ Π t ⎠ ⎧ 1 2 ⎫ of X T and is given by exp⎨Et ()X T t + Vart ()X T t ⎬ . Therefore, we have only to evaluate Et [X T ] and Vart []X T . ⎩ 2 ⎭ ■ 10 3 Valuation of corporate bond and inflation-linked corporate bond (1-A) 3.1 Corporate bond (The discount bond that has maturity T and face amount K ) value F(t,T ) - First, find out the equity value by evaluating equation (10), then subtract it from the firm value to derive F()t,T .
Load more

Recommended publications
  • Derivatives: a Twenty-First Century Understanding Timothy E
    Loyola University Chicago Law Journal Volume 43 Article 3 Issue 1 Fall 2011 2011 Derivatives: A Twenty-First Century Understanding Timothy E. Lynch University of Missouri-Kansas City School of Law Follow this and additional works at: http://lawecommons.luc.edu/luclj Part of the Banking and Finance Law Commons Recommended Citation Timothy E. Lynch, Derivatives: A Twenty-First Century Understanding, 43 Loy. U. Chi. L. J. 1 (2011). Available at: http://lawecommons.luc.edu/luclj/vol43/iss1/3 This Article is brought to you for free and open access by LAW eCommons. It has been accepted for inclusion in Loyola University Chicago Law Journal by an authorized administrator of LAW eCommons. For more information, please contact [email protected]. Derivatives: A Twenty-First Century Understanding Timothy E. Lynch* Derivatives are commonly defined as some variationof the following: financial instruments whose value is derivedfrom the performance of a secondary source such as an underlying bond, commodity, or index. This definition is both over-inclusive and under-inclusive. Thus, not surprisingly, even many policy makers, regulators, and legal analysts misunderstand them. It is important for interested parties such as policy makers to understand derivatives because the types and uses of derivatives have exploded in the last few decades and because these financial instruments can provide both social benefits and cause social harms. This Article presents a framework for understanding modern derivatives by identifying the characteristicsthat all derivatives share. All derivatives are contracts between two counterparties in which the payoffs to andfrom each counterparty depend on the outcome of one or more extrinsic, future, uncertain event or metric and in which each counterparty expects (or takes) such outcome to be opposite to that expected (or taken) by the other counterparty.
    [Show full text]
  • Liquidity Premiums in Inflation-Indexed Markets
    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Driessen, Joost; Nijman, Theo E.; Simon, Zorka Working Paper The missing piece of the puzzle: Liquidity premiums in inflation-indexed markets SAFE Working Paper, No. 183 Provided in Cooperation with: Leibniz Institute for Financial Research SAFE Suggested Citation: Driessen, Joost; Nijman, Theo E.; Simon, Zorka (2017) : The missing piece of the puzzle: Liquidity premiums in inflation-indexed markets, SAFE Working Paper, No. 183, Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe, Frankfurt a. M., http://dx.doi.org/10.2139/ssrn.3042506 This Version is available at: http://hdl.handle.net/10419/169388 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Electronic copy available at: https://ssrn.com/abstract=3042506 Non-Technical Summary Inflation-indexed products constitute a multitrillion dollar market segment worldwide.
    [Show full text]
  • Inflation Derivatives
    Inflation Derivatives Graduation Thesis Financial Engineering and Management A research on the implementation of inflation derivatives within pension funds Supervisors: Dr. D.Y. Dupont Dr. R. A. M. G. Joosten Dr. B. Roorda Drs. P. Bajema Author: C.F.A.R. Wanningen Company: Blue Sky Group Date: July 2007 Preface his thesis about inflation derivatives is the result of a six-month research which started in February and ended in July at pension fund provider Blue TSky Group. During this period I conducted a literature research on inflation linked products and developed a pricing model. Moreover I visited investment banks in London and the Euromoney Inflation Linked Products Conference 2007 in Frankfurt. The visits provided me with valuable information insights and business experience. Furthermore conversations with specialists working at Blue Sky Group and investment banks helped me to understand how inflation linked products are traded in the marketplace. By writing this preface I would gladly grasp the opportunity to thank persons who made a contribution to this thesis. From the University of Twente I would like to thank Dr. D.Y. Dupont, Dr. R.A.M.G. Joosten and Dr. B. Roorda. Dr. Dupont supervised the research and gave information insights during the first months. Dr. Roorda supervised the research throughout the whole period and initiated useful discussions on inflation. Dr. Joosten supervised the research during the last months and gave supportive suggestions on writing a thesis. From Blue Sky Group I would like to give thanks to Drs. P. Bajema, Drs. J.F. van Halewijn and A.A.M.
    [Show full text]
  • Quantitative Easing: Entrance and Exit Strategies
    Quantitative Easing: Entrance and Exit Strategies Alan S. Blinder This article was originally presented as the Homer Jones Memorial Lecture, organized by the Federal Reserve Bank of St. Louis, St. Louis, Missouri, April 1, 2010. Federal Reserve Bank of St. Louis Review , November/December 2010, 92 (6), pp. 465-79. pparently, it can happen here. On easing is something aberrant. I adhere to that December 16, 2008, the Federal Open nomenclature here. Market Committee (FOMC), in an I begin by sketching the conceptual basis for effort to fight what was shaping up quantitative easing: why it might be appropriate Ato be the worst recession since 1937-38, reduced and how it is supposed to work. I then turn to the the federal funds rate to nearly zero. 1 From then Fed’s entrance strategy—which is presumably on, with all its conventional ammunition spent, in the past, and then to the Fed’s exit strategy— the Federal Reserve was squarely in the brave which is still mostly in the future. Both strate gies new world of quantitative easing . Chairman Ben invite some brief comparisons with the Japanese Bernanke tried to call the Fed’s new policies experience between 2001 and 2006. Finally, I “credit easing,” probably to differentiate them address some questions about central bank inde - from actions taken by the Bank of Japan (BOJ) pendence raised by quantitative easing before earlier in the decade, but the label did not stick. 2 briefly wrapping up. Roughly speaking, quantitative easing refers to changes in the composition and/or size of a central bank’s balance sheet that are designed to THE CONCEPTUAL BASIS ease liquidity and/or credit conditions.
    [Show full text]
  • Essays in Modelling Mortality Rates
    SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES Colin O’HARE (MMath. D.A.T. C.F.I.) Essays in modelling mortality rates Subject SA0 Advisors: Dr Shane WHELAN (F.F.A., F.S.A., F.S.A.I.) James Joyce Library Building School of Mathematical Sciences Statistics and Actuarial Science University College Dublin Dr Youwei LI (BSc., MSc., PhD(Finance), PhD(Math)) Queen’s University Management School Queen’s University Belfast Riddel Hall Belfast prepared at Queens University Management School Declaration The work of this thesis is my own and where material submitted by me for another degree or work undertaken by me as part of a research group has been incorporated into the thesis, the extent of the work thus incorporated has been clearly indicated Signed ............................................................................... (Candidate) Date ............................................................................... iii Dedication This submission for SA0 of the Institute and Faculty of Actuaries is dedicated to my wife Diane and my daughter Lottie who have put up with my constant ramblings about research, mortality, statistics and data and never once asked me to explain myself. I would also like to dedicate this work to the late Professor William Parry F.R.S. (1934 - 2006), Professor of Dynamical Systems and Ergodic Theory at Warwick Uni- versity whom I knew well in the years between 1996 and 2004. During that very short period he instilled in me enough enthusiasm about the research process that 15 years after graduating from the University of Warwick School of Mathematics, and after a decade working and growing in the actuarial profession as a pension actuary I am able to return to my natural place in academia.
    [Show full text]
  • Valuation Adjustments 6 Ntnze
    0 0 ·~rf'J. ·~> ·~Q Q) 8 0 u 0 ~ ~ Q) ~ ·~ ~ t 0 ~ Q) ~ ~ 0 ~ ~ ~ 0 ~ u ~ ·s:t:::: .0 fJl Od 00 b ...... 0 ~ W,o c:: 0 0 co 0 ~ :iQ 0 :::. ·~ @ Ql ~ ~ .;:: ~ $: ~ ~ ~ ~ .D ~ ro Cl) > ~ ~ LBEX-WGM 002234 CONFIDENTIAL TREATMENT REQUESTED BY LEHMAN BROTHERS HOLDINGS, INC. t""'('l rn~ ~~ ~ti ~~ t:l:i>-l ~> Contents >-lt""" :::r:...., I [/).>~G; :::r:...., 1. Executive Summary 3-5 0~ t""'tn z....,oz @G; "!0 JL Valuation Adjustments 6 ntnze . [/)....., Significant Changes 7 0 Summary 8 ~ Regional Matrix 9 Americas 10- 11 Europe 12-13 Asia 14-15 Monthly Changes 16-17 UL Pricing Report 18 r Explanation of Significant Variances 19-23 m m >< Coverage 24-25 Projects 26-28 :s:~ 0 0 1\.) 1\.) (.,) 0'1 LEHlvfAN BROTHERS 2 t""'('l rn~ ~~ ~ti ~~ t:l:i>-l ~> Executive summary >-lt""" :::r:...., Complex Derivatives Transaction Review Committee [/).>~G; :::r:...., This committee, consisting of Capital Market Finance, Accounting Policy and Model Validation personnel, was set up in April 2005 and meets to 0~ t""'tn consider any significant derivative transactions undertaken. The committee considers whether the transactions are being booked, valued and z....,oz modeled appropriately. Furthermore, the committee determines whether the proper accounting treatment is being applied. During the month, the @G; following transactions were reviewed: "!0 ntnze . [/)....., -----+Emerging Market Loan with FX Call Spread- Lehman loaned ¥6 billion to Astana, a Kazakhstan quasi-sovereign entity. In addition, Lehman entered into a currency swap with Astana to convert the JPY loan into USD. Lehman also purchased a FX call spread from 0 Astana.
    [Show full text]
  • Wiley Finance : Derivatives Demystified : a Step-By-Step Guide
    Derivatives Demystified For other titles in the Wiley Finance series please see www.wiley.com/finance Derivatives Demystified A Step-by-Step Guide to Forwards, Futures, Swaps and Options Second Edition Andrew M. Chisholm A John Wiley and Sons, Ltd., Publication This edition first published 2010 C 2010 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered.
    [Show full text]
  • © 2010 Thomas a Jacobs THREE ESSAYS in EMPIRICAL ASSET PRICING
    © 2010 Thomas A Jacobs THREE ESSAYS IN EMPIRICAL ASSET PRICING BY THOMAS A JACOBS DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Finance in the Graduate College of the University of Illinois at Urbana-Champaign, 2010 Urbana, Illinois Doctoral Committee: Professor George G Pennacchi, Chair and Director of Research Professor Charles M Kahn Professor Neil D Pearson Associate Professor Timothy C Johnson ABSTRACT The financial crisis of 2007-2008 led to extraordinary government intervention in firms and markets. The scope and depth of government action rivaled that of the Great Depression. Many traded markets experienced dramatic declines in liquidity leading to the existence of conditions normally assumed to be promptly removed via the actions of profit seeking arbitrageurs. These extreme events motivate the three essays in this work. The first essay seeks and fails to find evidence of investor behavior consistent with the broad 'Too Big To Fail' policies enacted during the crisis by government agents. Only in limited circumstances, where government guarantees such as deposit insurance or U.S. Treasury lending lines already existed, did investors impart a premium to the debt security prices of firms under stress. The second essay introduces the Inflation Indexed Swap Basis (IIS Basis) in examining the large differences between cash and derivative markets based upon future U.S. inflation as measured by the Consumer Price Index (CPI). It reports the consistent positive value of this measure as well as the very large positive values it reached in the fourth quarter of 2008 after Lehman Brothers went bankrupt.
    [Show full text]
  • Encouraging Growth in the US Inflation Derivatives Market
    US INFLATION DERIVATIVES SPONSOREDSPONSORED ROUNDTABLE FORUM Risk: To what extent is the market for US inflation contingent on the asset swap market? To what extent does that have an impact and what other sources are out there when you look at it compared with Europe? Alvaro Mucida, JP Morgan: Asset swaps are still the major source of supply of inflation derivatives. One relatively new development in the market is that a broader base of clients is getting involved on the sell side, paying inflation. That includes real money, hedge funds and even insurance companies and pension funds, which historically had been exclusively receivers. The low real-yield environment also helps by bringing in people interested in paying real yields, which works effectively as supply of inflation derivatives. Then there are the traditional textbook sources of inflation derivatives such as infrastructure and utilities, but the Street hasn’t Encouraging growth in the been very successful in sourcing from them so far. There are a number of initiatives that are trying to get more infrastructure projects going in the US, like the creation of an infrastructure Evan Guppy development bank. That could be very positive for the future of US inflation derivatives market inflation derivatives, but it is still further down the road. Risk: Is there still some interest in deflation hedges? Prabhat Arora: A number of equity hedge funds and portfolio Prabhat Arora, Bank of America Merrill Lynch: We have seen real- managers have shown an interest in deflation protection this year. There continues to be uncertainty about the direction of US inflation, particularly given the money players pay inflation, especially when forward inflation gets The bulk of their portfolio gets hurt significantly if there is a realised latest attempts by the Federal Reserve to stimulate growth, known as Operation Twist.
    [Show full text]
  • Take No Prisoners
    BOUDICA BPI WORDPRESS WEBLOG A BOUDICA POINT OF VIEW: Take No Prisoners! By Alexis Ainsworth JUNE 2012 Anecdotal repartee in the spirit of ‘been there, done that, know whence, whom, and of what is spoken’ Veni, Vidi, Vixi Diary by Alexis Ainsworth : The harvesting of notions that amuse - from people whose arrogance amuses. The dynamics of ‘thought- production’ determine the noumena of a word’s communication value. The arrogance of self-approbating intellectual ‘opinion’ is the measure of a mind incapable of thought-product of high-energy intelligence level . (NOTE: ‘A Boudica Point of View: Take No Prisoners’ postings from ‘Veni, Vidi, Vixi Diary’ by Alexis Ainsworth is copyrighted material ) ____________________________________________________________ “TREASON & SHROUD: Letters to the Dreamers, Schemers & Reamers” ************** “OPEN LETTER TO “THE ENVY CLASS”: ‘THE DREAMER-REAMERS’ INTRODUCTION: 1. THE DREAMER-REAMERS, THE ‘ENVY CLASS ’ 2. (‘OBAMA’S) SCHEMER-REAMER’, WARREN BUFFETT, 3. (MOHMAMMED’S) REAMER-SCHEMER, BARACK OBAMA NARCISSISM, SADISM, AND MASOCHISM, IN A HANDFUL OF DESPOTS: DREAMERS, SCHEMERS, AND REAMERS : (paraphrasing T. S. Eliot's 1922 poem The Waste Land : I will show you something different from either Your shadow at morning striding behind you Or your shadow at evening rising to meet you; I will show you madmen worshipping the dust of their own image on parade, Rising before them at evening and following behind them at morning, Each a silhouette of fear marching arrogantly one shadow at a time, pretending sanity. ************* January 2012; Comment: Veni, Vidi, Vixi Diary entries dated since 2008 – quoted in the series of articles “Treason & Shroud”, predicting Barack Obama’s intentions as U.S.
    [Show full text]
  • Confidential Treatment Requested by Lehman Brothers Holdings, Inc
    CONFIDENTIAL TREATMENT REQUESTED BY LEHMAN BROTHERS HOLDINGS, INC. LBEX-WGM 763319 Valuation & Control Report - Fixed Income Division June 2008 • r mOJ >< LEHMAN BROTHERS ~ G) Where vision built. s" ~ gets --....1 (J) w w 1\.) 0 CONFIDENTIAL TREATMENT REQUESTED BY LEHMAN BROTHERS HOLDINGS, INC. Contents I I. Executive Summary 3-5 II. Valuation Adjustments 6 Significant Changes 7 Summary 8 Regional Matrix 9 Americas 10-11 Europe 12-13 Asia 14-15 Monthly Changes 16-17 III. Pricing Report 18 Explanation of Significant Variances 19-24 Coverage 25-26 r mOJ Projects 27-30 >< ~ G) ~ --....1 (J) w LEHMAN BROTHERS 2 w 1\.) .....lo. CONFIDENTIAL TREATMENT REQUESTED BY LEHMAN BROTHERS HOLDINGS, INC. CONFIDENTIAL TREATMENT REQUESTED BY LEHMAN BROTHERS HOLDINGS, INC. LBEX-WGM 763322 Executive summary Complex Derivatives Transaction Review Committee This committee, consisting of Capital Market Finance, Accounting Policy and Model Validation personnel, was set up in April2005 and meets to consider any significant derivative transactions undertaken. The committee considers whether the transactions are being booked, valued and modeled appropriately. Furthermore, the committee determines whether the proper accounting treatment is being applied. During the month, the following transactions were reviewed: -+Callable Credit Default Swap- Lehman sold $50 million of credit protection on Rio Tinto. The trade matures in October 2009. The premium that Lehman receives on the trade will be the greater of: 1) 105 bps per annum and 2) 105 bps per annum plus the change in the spread of the on-the-run iTraxx index. Furthermore, the counterparty can call the trade on specified dates with the first call date in October 2008.
    [Show full text]
  • EQF 11/036: Inflation Products and Inflation Models
    EQF 11/036: Inflation products and inflation models Peter J¨ackel∗ and Jerome Bonnetony First version: 23rd July 2008 This version: 2nd November 2009 Abstract We give an outline of the inflation market, the most common products, and the most frequently used models. 1 Introduction The market for financial inflation products started with public sector bonds linked to some measure for inflation of prices of (mainly) goods and services. This dates back as early as the first half of the 18th century when the state of Massachusetts issued bonds linked to the price of silver on the London Exchange [DDM04]. Over time, and particularly in the last twenty years or so, the dominant index used for inflation-linked bonds has become the Consumer Price Index. A notable exception is the UK inflation indexed gilt market which is linked to the Retail Price Index 1. The actual cashflow structure of inflation indexed bonds varies from issue to issue, including Capital Indexed Bonds, Interest Indexed Bonds, Current Pay Bonds, Indexed Annuity Bonds, Indexed Zero-Coupon Bonds, and others. By far the most common cashflow structure is the Capital Indexed Bond (CIB) on which we shall focus in the remainder of this article. 2 Bonds, asset swaps, and the breakeven curve Inflation indexed bonds (of CIB type) are defined by: • N | a notional. • Ti : f1 ≤ i ≤ ng | coupon dates. • I | the inflation index. • ci : f1 ≤ i ≤ ng | coupon at date Ti (usually all ci are equal). • L | a lag (often three months). • I(T0 − L) | the bond's base index value. The bond pays the regular coupon payments I(Ti − L) N · ci · (2.1) I(T0 − L) plus the inflation-adjusted final redemption which often contains a capital guarantee according to I(T − L) N · max n ; 1 : (2.2) I(T0 − L) Asset swap packages swapping the inflation bond for a floating leg are liquid in some markets such as for bonds linked to the CPTFEMU (aka HICP) index.
    [Show full text]