Credit Default Swaptions ALAN L. TUCKER AND JASON Z. WEI ALAN L. TUCKER mong the credit derivatives traded I. PRODUCT DESCRIPTION is an associate professor of since 1991, credit default swaps finance in the Lubin School (CDS) account for the vast majority We describe CDS swaptions using an of Business at Pace University of trading. Like interest rate swap- example. Assume that all counterparties in New York City, A (dealers and buy side) are AA-rated, which [email protected] tions in the interest rate marketplace, credit default swaptions represent a potentially impor- could be through credit enhancements such JASON Z. WEI tant derivative product for credit markets, as collateral, midmarket, or netting agreements. is an associate professor A CDS that is cancelabie includes an Assume the CDS that underlies the of finance in the Rotman embedded credit default swaption, A cance- swaption has a three-year maturity, semian- School of Management at lable long CDS position (where long means nual payment dates, and a swap rate (the strike the University ofToronto rate on the swaption) of 150 basis points (bp). in Toronto, Ontario, that the CDS trader is paying a fixed swap rate and is thus the buyer of credit protection) is a The strike rate assumes semiannual com- package of a straight (non-cancelable) long pounding—the same periodicity (or tenor) of CDS plus a put-style CDS swaption—an the CDS, The credit default swap underlying option to enter a CDS short and thus close the reference credit asset is a BB-rated ten- the outstanding long position, A cancelable year 8% coupon bond with $100 lnillion par. short CDS represents a combination ofa short The CDS swaption is a call, European-style, position in a straight CDS plus a call-style CDS with a maturity of six months. Thus the CDS swaption,' swaption owner has the right, in six months, to enter the underlying CDS long, that is, To the extent that a CDS is cancelable— paying 150 bp. and most are in practice—ignoring the value of the embedded CDS swaption can lead to Suppose that in six months, when the pricing errors and thus arbitrage opportuni- swaption matures, the bid-offer swap rates on ties. We believe that methods used to establish newly minted three-year credit default swaps initial swap rates on cancelable CDS, as well (with semiannual tenors)—on the same refer- as methods used to value seasoned CDS that ence credit asset (or pari passu asset)—are 200 are cancelable, typically ignore the embedded bp by 220 bp,^ The underlying bond has thus swaption to terminate the position, so these exhibited credit deterioration, perhaps having CDS may be mispriced,^ been downgraded to a weak single B, The call Our purposes are threefold: to describe swaption is exercised, meaning that its owner CDS swaptions; to illustrate some of their can now long the same swap payingjust 150 bp. applications; and, most important, to present By engaging in a reversing trade (enter- accessible valuation models. ing a short CDS), the swaption owner locks in an annuity of 50 bp (the bid of 200 bp less 88 CREDIT DEFAULT SWAPTIONS JUNE 2005 the strike rate of 150 bp) on $50 million for the next six CDS does not eliminate the need for the call swaption semiannual periods. This annuity is present-valued (mon- owner to exercise in the event of default ofthe reference etized) at the interest rate swap midrate on a new three- credit asset. Finally, these circumstances do not affect can- year semi-annual (s,a,) dollar-LIBOR swap since both celable CDS, A default-triggering event terminates the CDS counterparties are AA-rated, and therefore the embedded option to cancel the CDS, lfthe swaption is a put and at expiration new CDS Besides plain vanilla CDS swaptions—whether rates are 100 bp by 110 bp (perhaps because the bond is American, Bermudan, European, calls, puts, outright, or now a weak single A), the payoff to the CDS swaption embedded in cancelable CDS—there are a variety of more would be the present value (again, discounted at the three- exotic CDS swaptions, such as swaptions written on binary year interest rate swap midrate) of six annuity payments and basket CDS, or barrier CDS swaptions. It will be of $50 million times 40 bp (the strike rate of 150 bp less interesting to watch changes in the market for CDS swap- the offer of 110 bp),-* tions as the market for credit derivatives in general con- CDS swaptions that are traded outright are likely to tinues to grow in size and innovation, be European, but a cancelable CDS will entail either an American or Bermudan swaption. For example, consider a II. PRODUCT APPLICATION long CDS giving the buyer of credit protection the option to terminate the swap every six months. Assume the under- To illustrate the use of CDS swaptions, we consider lying reference credit asset is unique and illiquid, and has three product applications: to reduce a bank's regulatory no pari passu substitutes. Then this CDS represents a package capital; to create a synthetic credit-linked note; and to ofa straight CDS plus a potentially valuable Bermudan put create a synthetic collateralized debt obligation. swaption—the ability to short the CDS, at six-month inter- vals, thus closing the original long position, Reducing Bank Regulatory Capital lfthe reference credit asset (our 8% coupon bond) has a default-triggering event (such as a missed coupon date) Suppose a bank is carrying so many commercial before the six-month maturity ofthe swaption, the CDS loans as to compromise its regulatory capital. The bank would be terminated by physical or cash settlement, which cannot sell all the loans because most are not assignable; means we have a CDS swaption with no underlying, lfthe it needs to reduce its regulatory capital requirements. CDS swaption is a put, the issue is moot; the put swaption The bank can sell one loan and use the proceeds to owner would not want to exercise, because the credit spread purchase a call credit default swaption whose underlying on the defaulted bond would presumably explode to some- reference credit asset is a portfolio ofthe remaining loans thing well above the original (150 bp) strike rate. (or a highly correlated basket of them). By purchasing this If it is a call swaption, the owner would want to exer- basket CDS call swaption, the bank should obtain regu- cise. The call owner therefore needs a mechanism to cap- latory capital relief much like being long a basket CDS, ture value, European-style CDS call swaptions permit early The principal advantage of buying the CDS call exercise in the event of a default-triggering event for the swaption (versus entering a long position in a basket CDS) reference credit asset before maturity ofthe CDS swaption,' is the returns earned on the loans should their credit lfthe CDS call swaption is exercised early because of quality improve. The principal disadvantage ofthe swap- default of the reference credit asset, the swaption owner tion is its cost. ought to be required to make a payment to the writer. Such a payment represents a type of premium accrual on a default Creating a Synthetic Credit-Linked Note insurance policy written on the reference credit asset. In our illustration, if at inception of the swaption there is a Suppose a hedge fund buys a four-year floating-rate six-month bond insurance policy costing 10 bp of face value note issued by a highly rated bank sponsor. The note pays that pays the difference between the face value and the s,a, dollar-LIBOR plus 5 bp. The fund manager can recovery value of the bond, then, assuming the reference enhance the coupon to s,a, $LIBOR plus 45 bp if she credit asset defaults midway through the life ofthe swap- agrees to bear the default risk associated with an alto- tion, the CDS call swaption owner (or its bond insurance gether different bond (in addition to the credit risk ofthe company) would be required to pay 5 bp of $100 million. note she is buying). This is a common credit-linked note Note that a pari passu provision on the underlying (representing a way dealers lay off their credit risk from JUNE 2005 THE JOURNAL OF FIXED INCOME 89 engaging in short CDS positions). European CDS Swaption Pricing Instead, the manager can effectively enhance the coupon on the note by writing a put CDS swaption on If the forward credit default swap midrate is log- the same/second bond. By purchasing the floating-rate normal, European CDS swaptions can be priced using a note and writing the put CDS swaption, the hedge fund straightforward modification of Black's [1976] model,^ manager is long a synthetic credit-linked note. That is, the CDS swaption can be priced using a model that prices interest rate swaptions. The notation is as follows: Creating a Synthetic Collateralized Debt Obligation Rg = relevant forward CDS swap rate, expressed Suppose an asset manager wants to create a synthetic with compounding of m periods per year, collateralized debt obligation (CDO), so he issues or spon- at time 0; sors a $200 million CDO (through a special-purpose vehicle) Rj, = strike rate on the CDS swaption, also expressed with four debt tranches and one equity tranche, $175 mil- with compounding of m periods per year; lion represents the debt tranches and $25 million represents T = maturity ofthe CDS swaption; the equity tranche, which the sponsor keeps. The $200 mil- O = standard deviation ofthe change in the nat- lion is then invested in high-quality agency securities.