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    CREDIT DEFAULT SWAPTIONS

    Alan L. Tucker, Ph.D. 1 Associate Professor of Finance

    Lubin School of BusinessPace University

    Jason Z. WeiAssociate Professor of FinanceRotman School of Management

    University of Toronto

    April 26, 2005

    1Contact author: Alan L. Tucker, Department of Finance, Lubin School of Business, Pace University, 1Pace Plaza, New York, NY 10038, 212-618-6524 (voice), 212-346-1673 (fax), atucker@pace.edu .

    mailto:atucker@pace.edumailto:atucker@pace.edu
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    CREDIT DEFAULT SWAPTIONS

    Abstract

    Credit derivatives were arguably invented by Bankers Trust (now part of Deutsche Bank)in 1991, with the product market not taking off until 1996 due to a period of tight creditspreads and generally favorable credit market conditions witnessed during the first half ofthe 1990s. Product education, advances in pricing, and more adverse credit events duringthe last decade have served to accelerate market growth. Indeed, the credit derivativesmarket is widely regarded as the fastest growing sector of the derivatives industry andnow exhibits over $5 trillion in average outstanding notional principal worldwide. Creditdefault swaps (CDSs) account for approximately 72.5% of the marketplace, with theremaining 27.5% spread mostly across credit spread swaps, total rate of return swaps, andcredit spread options. Options on credit default swaps known as CDS swaptions have

    only recently become popular among end users. CDS swaptions come in two generalvarieties: Calls and puts written on CDSs, and cancelable CDSs. A cancelable CDScontains an embedded option to terminate an existing CDS (an embedded CDSswaption). This paper describes credit default swaptions, provides illustrations of theiruses, for example, in creating synthetic collateralized debt obligations, and presents andillustrates valuation models. The pricing models offered here are more accessible thanthose presented in the working papers of Sch nbucher (2000), Jamshidian (2002) and

    Schmidt (2004).

    Keywords: Credit default swaps, swaptions, option pricing

    JEL Classifications: G13

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    CREDIT DEFAULT SWAPTIONS

    1. Introduction

    Credit derivatives have been traded since 1991 and credit default swaps (CDSs) account

    for the vast majority of trading. Only recently have end users begun to take interest in

    options on CDSs. Analogous to interest rate swaptions for the interest rate marketplace,

    credit default swaptions represent a potentially important derivative product for credit

    markets. Indeed, a CDS that is cancelable contains an embedded credit default swaption.

    A cancelable long CDS position (where long means that the CDS trader is paying a

    fixed swap rate and is thus the buyer of credit protection) is simply a package of a

    straight (read non-cancelable) long CDS plus a put-style CDS swaption an option to

    enter a CDS short and thus close the already outstanding long position. 2 A cancelable

    short CDS represents a combination of a short position in a straight CDS plus a call-style

    CDS swaption. To the extent that existing CDSs are cancelable and most are in

    practice then ignoring the value of the embedded CDS swaption can lead to pricing

    errors and thus arbitrage opportunities. 3 In fact, we opine that methods used to establish

    initial swap rates on cancelable CDSs, as well as methods used to value seasoned CDSs

    2 See, for example, Hull (2003, Chapter 27), for a discussion of straight credit default swaps.3 CDSs are commonly cancelable because they are written on a particular reference credit asset, forexample, a junk bond. To reverse-trade a CDS without an embedded option to cancel, the trader wouldhave to find another counterparty willing to execute a CDS on the particular reference credit asset. This is

    plausible, but may not be realistic depending on the nature (read liquidity) of said asset. This contrastswith say, an interest rate swap, wherein a trader can readily reverse trade and close an outstanding position

    because the underlying is a generic variable, for example, the s.a. $LIBOR.

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    that are cancelable, typically ignore the embedded swaption to terminate the position, and

    thus these CDSs may be mis-priced. 4

    The purpose of this paper is three-fold: to describe CDS swaptions; to illustrate some of

    their applications; and, most importantly, to present valuation models which are

    accessible to the reader. Sections 2, 3 and 4 address these goals, respectively. Section 5

    offers a brief conclusion and suggestions for future research.

    2. Product description We describe CDS swaptions through an example. Assume that all counter parties

    (dealers and buy side) are AA-rated, either because they are already AA-rated or because

    they have been credit enhanced to AA through collateral agreements, mid-market

    agreements, netting agreements, and other well known credit enhancement techniques.

    Assume that the CDS which underlies the swaption has a 3-year maturity, semi-annual

    payment dates, and a swap rate (the strike rate on the swaption) of 150 basis points (bps).

    The strike rate assumes semi-annual compounding the same periodicity (or tenor) of the

    CDS. The credit default swaps underlying reference credit asset is a BB-rated 10-year,

    8%-coupon bond with $100 million par. The CDS swaption is a call, European-style,

    with a maturity of 6 months. Thus the CDS swaption owner has the right, in 6 months, to

    enter the underlying CDS long, that is, paying 150 bps.

    Suppose that in 6 months, when the swaption matures, the bid-offer swap rates on newly-

    minted 3-year credit default swaps (with semi-annual tenors) on the same reference

    4 However, see the discussion below regarding pari passu assets.

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    credit asset (or pari passu asset) are 200 bps by 220 bps. 5 So, the underlying bond has

    exhibited credit deterioration, for example, having been downgraded to a weak single B.

    The call swaption is exercised, meaning that its owner can now long the same swap

    paying just 150 bps. By engaging in a reversing trade, that is, entering a short CDS, the

    swaption owner locks into an annuity of 50 bps (the bid of 200 bps less the strike rate of

    150 bps) on $50 million for the next 6 semi-annual periods. This annuity is present

    valued (monetized) at the interest rate swap mid-rate on a newly-minted 3-year

    seminal annual (s.a.) $LIBOR swap since both counter parties are AA-rated.

    If the swaption is a put and at expiry newly-minted CDS rates are 100 bps by 110 bps

    (perhaps because the bond is now a weak single A), then the payoff to the CDS swaption

    would be the present value (again, discounted at the 3-year interest rate swap mid-rate) of

    six annuity payments of $50 million times 40 bps (the strike rate of 150 bps less the offer

    of 110 bps). 6

    CDS swaptions that are traded outright are likely to be European-style. However, a

    cancelable CDS will contain either an American- or, more likely, Bermudian-style

    5 Commonly, a CDS that is physically settled requires the long trader to deliver (read transfer ownership)to the short the reference credit asset, or an equivalent asset known as a pari passu asset. The short traderthen pays the long the face value of the reference credit asset (the notional on the CDS). A cash-settledCDS entails the short trader paying the long the difference between the face value and the post-defaultvalue of the reference credit asset, where said value is determined by a calculation agent. The agent

    typically ascribes a value by taking the mean of the bid and offer prices quoted by dealers of the referencecredit asset. CDS dealers tend to prefer physical settlement in order to work the reference credit asset,that is, because they feel they can obtain better value than indicated by the calculation agent. Importantly,notice that the ability to trade pari passu assets, and other CDSs on pari passu assets, tends to mitigate thevalue of the embedded swaption to terminate an existing CDS. In other words, to trade pari passu assetsserves to give the CDS greater secondary market liquidity, a la an interest rate swap written on a genericreference rate such as seminal annual $LIBOR.6 In these illustrations we ignore the day count convention, that is, we assume that markets operatecontinually and time can be carved into perfect one-half year intervals. The usual day count conventionfor a CDS or CDS swaption is Actual/360.

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    swaption. For example, consider a long CDS giving the buyer of credit protection the

    option to terminate the swap every six months. Assume that the CDSs underlying

    reference credit asset is unique, illiquid, and has no pari passu substitutes. Then this

    CDS represents a package of a straight CDS plus a potentially valuable Bermudian-style

    put swaption the ability to short the CDS, at six-month intervals, thus closing the

    original long position.

    Besides plain-vanilla CDS swaptions whether they are American, Bermudian,

    European, calls, puts, outright, or embedded in cancelable CDSs there can exist ofcourse a variety of more exotic CDS swaptions. For instance, there can be swaptions

    written on binary and basket CDSs. There can be barrier CDS swaptions. And so on. It

    should be interesting to witness changes in the market for CDS swaptions