How Much Do Banks Use Credit Derivatives to Reduce Risk?
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Implied Volatility Modeling
Implied Volatility Modeling Sarves Verma, Gunhan Mehmet Ertosun, Wei Wang, Benjamin Ambruster, Kay Giesecke I Introduction Although Black-Scholes formula is very popular among market practitioners, when applied to call and put options, it often reduces to a means of quoting options in terms of another parameter, the implied volatility. Further, the function σ BS TK ),(: ⎯⎯→ σ BS TK ),( t t ………………………………(1) is called the implied volatility surface. Two significant features of the surface is worth mentioning”: a) the non-flat profile of the surface which is often called the ‘smile’or the ‘skew’ suggests that the Black-Scholes formula is inefficient to price options b) the level of implied volatilities changes with time thus deforming it continuously. Since, the black- scholes model fails to model volatility, modeling implied volatility has become an active area of research. At present, volatility is modeled in primarily four different ways which are : a) The stochastic volatility model which assumes a stochastic nature of volatility [1]. The problem with this approach often lies in finding the market price of volatility risk which can’t be observed in the market. b) The deterministic volatility function (DVF) which assumes that volatility is a function of time alone and is completely deterministic [2,3]. This fails because as mentioned before the implied volatility surface changes with time continuously and is unpredictable at a given point of time. Ergo, the lattice model [2] & the Dupire approach [3] often fail[4] c) a factor based approach which assumes that implied volatility can be constructed by forming basis vectors. Further, one can use implied volatility as a mean reverting Ornstein-Ulhenbeck process for estimating implied volatility[5]. -
Tax Treatment of Derivatives
United States Viva Hammer* Tax Treatment of Derivatives 1. Introduction instruments, as well as principles of general applicability. Often, the nature of the derivative instrument will dictate The US federal income taxation of derivative instruments whether it is taxed as a capital asset or an ordinary asset is determined under numerous tax rules set forth in the US (see discussion of section 1256 contracts, below). In other tax code, the regulations thereunder (and supplemented instances, the nature of the taxpayer will dictate whether it by various forms of published and unpublished guidance is taxed as a capital asset or an ordinary asset (see discus- from the US tax authorities and by the case law).1 These tax sion of dealers versus traders, below). rules dictate the US federal income taxation of derivative instruments without regard to applicable accounting rules. Generally, the starting point will be to determine whether the instrument is a “capital asset” or an “ordinary asset” The tax rules applicable to derivative instruments have in the hands of the taxpayer. Section 1221 defines “capital developed over time in piecemeal fashion. There are no assets” by exclusion – unless an asset falls within one of general principles governing the taxation of derivatives eight enumerated exceptions, it is viewed as a capital asset. in the United States. Every transaction must be examined Exceptions to capital asset treatment relevant to taxpayers in light of these piecemeal rules. Key considerations for transacting in derivative instruments include the excep- issuers and holders of derivative instruments under US tions for (1) hedging transactions3 and (2) “commodities tax principles will include the character of income, gain, derivative financial instruments” held by a “commodities loss and deduction related to the instrument (ordinary derivatives dealer”.4 vs. -
Credit Derivative Handbook 2003 – 16 April 2003
16 April 2003 Credit Derivative CREDIT Chris Francis (44) 20 7995-4445 [email protected] Handbook 2003 Atish Kakodkar (44) 20 7995-8542 A Guide to Products, Valuation, Strategies and Risks [email protected] Barnaby Martin (44) 20 7995-0458 [email protected] Europe The Key Piece In The Puzzle V ol a Risk til t ity Managemen rate rpo Co ds Bon Capital Structure CreditCredit DerivativesDerivatives Arbitrage F irst D To efa dit ult Cre ed Link tes No Convertible Bonds Derivatives Refer to important disclosures at the end of this report. Merrill Lynch Global Securities Research & Economics Group Investors should assume that Merrill Lynch is Global Fundamental Equity Research Department seeking or will seek investment banking or other business relationships with the companies in this report. RC#60910601 Credit Derivative Handbook 2003 – 16 April 2003 CONTENTS n Section Page Market Evolution: Going 1. Market growth, importance and prospects 3 Mainstream? Credit Default Swap Basics 2. The basic concepts 10 Valuation of Credit Default 3. Arbitrage relationship and an introduction to survival probabilities 13 Swaps Unwinding Default Swaps 4. Mechanics for terminating contracts 19 Valuing the CDS Basis 5. Comparing CDS with the cash market 29 What Drives the Basis? 6. Why do cash and default market yields diverge? 35 CDS Investor Strategies 7. Using CDS to enhance returns 44 CDS Structural Roadmap 8. Key structural considerations 60 What Price Restructuring? 9. How to value the Restructuring Credit Event 73 First-to-Default Baskets 10. A guide to usage and valuation 84 Synthetic CDO Valuation 11. Mechanics and investment rationale 95 Counterparty Risk 12. -
Derivative Securities
2. DERIVATIVE SECURITIES Objectives: After reading this chapter, you will 1. Understand the reason for trading options. 2. Know the basic terminology of options. 2.1 Derivative Securities A derivative security is a financial instrument whose value depends upon the value of another asset. The main types of derivatives are futures, forwards, options, and swaps. An example of a derivative security is a convertible bond. Such a bond, at the discretion of the bondholder, may be converted into a fixed number of shares of the stock of the issuing corporation. The value of a convertible bond depends upon the value of the underlying stock, and thus, it is a derivative security. An investor would like to buy such a bond because he can make money if the stock market rises. The stock price, and hence the bond value, will rise. If the stock market falls, he can still make money by earning interest on the convertible bond. Another derivative security is a forward contract. Suppose you have decided to buy an ounce of gold for investment purposes. The price of gold for immediate delivery is, say, $345 an ounce. You would like to hold this gold for a year and then sell it at the prevailing rates. One possibility is to pay $345 to a seller and get immediate physical possession of the gold, hold it for a year, and then sell it. If the price of gold a year from now is $370 an ounce, you have clearly made a profit of $25. That is not the only way to invest in gold. -
Derivative Securities, Fall 2012 – Homework 3. Distributed 10/10
Derivative Securities, Fall 2012 { Homework 3. Distributed 10/10. This HW set is long, so I'm allowing 3 weeks: it is due by classtime on 10/31. Typos in pbm 3 (ambiguity in the payoff of a squared call) and pbm 6 (inconsistent notation for the dividend rate) have been corrected here. Problem 1 provides practice with lognormal statistics. Problems 2-6 explore the conse- quences of our formula for the value of an option as the discounted risk-neutral expected payoff. Problem 7 makes sure you have access to a numerical tool for playing with the Black-Scholes formula and the associated \Greeks." Problem 8 reinforces the notion of \implied volatility." Convention: when we say a process Xt is \lognormal with drift µ and volatility σ" we mean 2 ln Xt − ln Xs is Gaussian with mean µ(t − s) and variance σ (t − s) for all s < t; here µ and σ are constant. In this problem set, Xt will be either a stock price or a forward price. The interest rate is always r, assumed constant. (1) Suppose a stock price st is lognormal with drift µ and volatility σ, and the stock price now is s0. (a) Give a 95% confidence interval for sT , using the fact that with 95% confidence, a Gaussian random variable lies within 1:96 standard deviations of its mean. (b) Give the mean and variance of sT . (c) Give a formula for the likelihood that a call with strike K and maturity T will be in-the-money at maturity. -
Credit Derivatives
3 Credit Derivatives CHAPTER 7 Credit derivatives Collaterized debt obligation Credit default swap Credit spread options Credit linked notes Risks in credit derivatives Credit Derivatives •A credit derivative is a financial instrument whose value is determined by the default risk of the principal asset. •Financial assets like forward, options and swaps form a part of Credit derivatives •Borrowers can default and the lender will need protection against such default and in reality, a credit derivative is a way to insure such losses Credit Derivatives •Credit default swaps (CDS), total return swap, credit default swap options, collateralized debt obligations (CDO) and credit spread forwards are some examples of credit derivatives •The credit quality of the borrower as well as the third party plays an important role in determining the credit derivative’s value Credit Derivatives •Credit derivatives are fundamentally divided into two categories: funded credit derivatives and unfunded credit derivatives. •There is a contract between both the parties stating the responsibility of each party with regard to its payment without resorting to any asset class Credit Derivatives •The level of risk differs in different cases depending on the third party and a fee is decided based on the appropriate risk level by both the parties. •Financial assets like forward, options and swaps form a part of Credit derivatives •The price for these instruments changes with change in the credit risk of agents such as investors and government Credit derivatives Collaterized debt obligation Credit default swap Credit spread options Credit linked notes Risks in credit derivatives Collaterized Debt obligation •CDOs or Collateralized Debt Obligation are financial instruments that banks and other financial institutions use to repackage individual loans into a product sold to investors on the secondary market. -
Derivative Instruments and Hedging Activities
www.pwc.com 2015 Derivative instruments and hedging activities www.pwc.com Derivative instruments and hedging activities 2013 Second edition, July 2015 Copyright © 2013-2015 PricewaterhouseCoopers LLP, a Delaware limited liability partnership. All rights reserved. PwC refers to the United States member firm, and may sometimes refer to the PwC network. Each member firm is a separate legal entity. Please see www.pwc.com/structure for further details. This publication has been prepared for general information on matters of interest only, and does not constitute professional advice on facts and circumstances specific to any person or entity. You should not act upon the information contained in this publication without obtaining specific professional advice. No representation or warranty (express or implied) is given as to the accuracy or completeness of the information contained in this publication. The information contained in this material was not intended or written to be used, and cannot be used, for purposes of avoiding penalties or sanctions imposed by any government or other regulatory body. PricewaterhouseCoopers LLP, its members, employees and agents shall not be responsible for any loss sustained by any person or entity who relies on this publication. The content of this publication is based on information available as of March 31, 2013. Accordingly, certain aspects of this publication may be superseded as new guidance or interpretations emerge. Financial statement preparers and other users of this publication are therefore cautioned to stay abreast of and carefully evaluate subsequent authoritative and interpretative guidance that is issued. This publication has been updated to reflect new and updated authoritative and interpretative guidance since the 2012 edition. -
Credit Derivatives: Capital Requirements and Strategic Contracting∗
Credit Derivatives: Capital Requirements and Strategic Contracting∗ Antonio Nicol`o Loriana Pelizzon Department of Economics Department of Economics University of Padova University of Venice and SSAV [email protected] [email protected] Abstract How do non-publicly observable credit derivatives affect the design contracts that buyers may offer to signal their own types? When credit derivative contracts are private, how do the different rules of capital adequacy affect these contracts? In this paper we address these issues and show that, under Basel I, high-quality banks can use CDO contracts to signal their own type, even when credit derivatives are private contracts. However, with the introduction of Basel II the presence of private credit derivative contracts prevents the use of CDO as signalling device if the cost of capital is large. We also show that a menu of contracts based on a basket of loans characterized by different maturities and a credit default swap conditioned on the default of the short term loans can be used as a signalling device. Moreover, this last menu generates larger profits for high-quality banks than the CDO contract if the cost of capital and the loan interest rates are sufficiently high. JEL Classification: G21, D82 Keywords: Credit derivatives, Signalling contracts, Capital requirements. ∗We gratefully acknowledge conversations with Franklin Allen, Viral Acharya, Andrea Beltratti, Mark Carey, Ottorino Chillemi, Francesco Corielli, Marcello Esposito, Mark Flannery, Anke Gerber, Michel Gordy, Gary Gorton, Piero Gottardi, John Hull, Patricia Jackson, Fabio Manenti, Giovanna Nicodano, Bruno Parigi, Stephen Schaefer, Walter Torous, Elu vonThadden, Guglielmo Weber, seminar audiences at University of Padua, University of Bologna seminars and participants at Centro Baffi Workshop, Milan, EFMA 2004, Basel, La Sapienza University Workshop, Rome, CERF Conference on Financial Innovation, Cambridge, FMA 2005, Siena, CREDIT 2005, Venice. -
Introduction Section 4000.1
Introduction Section 4000.1 This section contains product profiles of finan- Each product profile contains a general cial instruments that examiners may encounter description of the product, its basic character- during the course of their review of capital- istics and features, a depiction of the market- markets and trading activities. Knowledge of place, market transparency, and the product’s specific financial instruments is essential for uses. The profiles also discuss pricing conven- examiners’ successful review of these activities. tions, hedging issues, risks, accounting, risk- These product profiles are intended as a general based capital treatments, and legal limitations. reference for examiners; they are not intended to Finally, each profile contains references for be independently comprehensive but are struc- more information. tured to give a basic overview of the instruments. Trading and Capital-Markets Activities Manual February 1998 Page 1 Federal Funds Section 4005.1 GENERAL DESCRIPTION commonly used to transfer funds between depository institutions: Federal funds (fed funds) are reserves held in a bank’s Federal Reserve Bank account. If a bank • The selling institution authorizes its district holds more fed funds than is required to cover Federal Reserve Bank to debit its reserve its Regulation D reserve requirement, those account and credit the reserve account of the excess reserves may be lent to another financial buying institution. Fedwire, the Federal institution with an account at a Federal Reserve Reserve’s electronic funds and securities trans- Bank. To the borrowing institution, these funds fer network, is used to complete the transfer are fed funds purchased. To the lending institu- with immediate settlement. -
Credit Default Swaps and Their Application
CREDIT DEFAULT SWAPS AND THEIR APPLICATION Dr Ewelina Sokołowska, Dr Justyna Łapi Lska Nicolaus Copernicus University Torun, Faculty of Economic Sciences and Management, ul. Gagarina 11, 87-100 Toru L, e-mail: [email protected] Abstract The market of credit derivatives has experienced enormous growth in recent years. One of the instruments, which play dominant role on the market are Credit Default Swaps. This paper examines the role of Credit Defaults Swaps on this marker and describes their possible application in separating and transferring credit risk. Key words Credit Default Swap, Credit Derivatives, risk management, credit risk 1 Introduction Credit Default Swap is like other credit derivatives an interesting innovation on the financial market. Until recently, credit remained one of the major components of business risk for which no tailored risk-management products existed. Credit derivatives have completed the process by allowing the independent management of default or credit spread risk. These instruments enable to separate the ownership and management of credit risk from other qualitative and quantitative aspects of ownership of financial assets. Fixed income derivatives introduced the ability to manage duration, convexity, and callability independently of security positions. By separating specific aspects of credit risk from other kinds of risk, credit derivatives allow even the most illiquid credit exposures to be transferred from portfolios that have, but don’t want the risk to those that want but don’t have that risk, even when the underlying asset itself could not have been transferred in the same way. These features of credit derivatives have helped them to attract many investors. -
Credit Derivatives Handbook
Corporate Quantitative Research New York, London December, 2006 Credit Derivatives Handbook Detailing credit default swap products, markets and trading strategies About this handbook This handbook reviews both the basic concepts and more advanced Corporate Quantitative Research trading strategies made possible by the credit derivatives market. Readers AC seeking an overview should consider Sections 1.1 - 1.3, and 8.1. Eric Beinstein (1-212) 834-4211 There are four parts to this handbook: [email protected] Andrew Scott, CFA Part I: Credit default swap fundamentals 5 (1-212) 834-3843 [email protected] Part I introduces the CDS market, its participants, and the mechanics of the credit default swap. This section provides intuition about the CDS Ben Graves, CFA valuation theory and reviews how CDS is valued in practice. Nuances of (1-212) 622-4195 [email protected] the standard ISDA documentation are discussed, as are developments in documentation to facilitate settlement following credit events. Alex Sbityakov (1-212) 834-3896 Part II: Valuation and trading strategies 43 [email protected] Katy Le Part II provides a comparison of bonds and credit default swaps and (1-212) 834-4276 discusses why CDS to bond basis exists. The theory behind CDS curve [email protected] trading is analyzed, and equal-notional, duration-weighted, and carry- neutral trading strategies are reviewed. Credit versus equity trading European Credit Derivatives Research strategies, including stock and CDS, and equity derivatives and CDS, are analyzed. Jonny Goulden (44-20) 7325-9582 Part III: Index products 111 [email protected] The CDX and iTraxx products are introduced, valued and analyzed. -
Optimal Structuring of Collateralized Debt Obligation Contracts: an Optimization Approach
Journal of Credit Risk Volume 8/Number 4, Winter 2012/13 (133–155) Optimal structuring of collateralized debt obligation contracts: an optimization approach Alexander Veremyev Risk Management and Financial Engineering Lab, Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA; email: [email protected] Peter Tsyurmasto Risk Management and Financial Engineering Lab, Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA; email: [email protected] Stan Uryasev Risk Management and Financial Engineering Lab, Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA; email: [email protected] The objective of this paper is to help a bank originator of a collateralized debt obligation (CDO) to build a maximally profitable CDO. We consider an opti- mization framework for structuring CDOs. The objective is to select attachment/ detachment points and underlying instruments in the CDO pool. In addition to “standard” CDOs we study so-called “step-up” CDOs. In a standard CDO con- tract the attachment/detachment points are constant over the life of a CDO. In a step-up CDO the attachment/detachment points may change over time. We show that step-up CDOs can save about 25–35% of tranche spread payments (ie, prof- itability of CDOs can be boosted by about 25–35%). Several optimization mod- els are developed from the bank originator perspective. We consider a synthetic CDO where the goal is to minimize payments for the credit risk protection (pre- mium leg), while maintaining a specific credit rating (assuring the credit spread) of each tranche and maintaining the total incoming credit default swap spread payments.