1、Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.1,Chapter 27Credit Derivatives,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.2,Credit Default Swap,Company A buys default protection from B to protect against default on a reference bond issue
2、d by the reference entity, C.A makes periodic payments to BIn the event of a default by CA has the right to sell the reference bond to B for its face value, orB pays A the difference between the market value and the face value,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull
3、,27.3,CDS Structure,Default Protection Buyer, A,Default Protection Seller, B,90 bps per year,Payment if default by reference entity,C,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.4,CDS Final Payments,Notation:L:Face value of bond, notional value of CDSA(t):Accrued int
4、erest on bond per $ of principal at time tR:Recovery rate, market price as a percent of face value plus accrued interests:CDS payment rate per year. Annual payment = sL:Time since last CDS paymentA pays sL and B pays L - RL1 + A(t),Options, Futures, and Other Derivatives, 5th edition 2002 by John C.
5、 Hull,27.5,Sample Quotes (Jan 2001),Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.6,CDS Valuation,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.7,PV of CDS Payments per $1 of Notional,If default event occurs at t T, PV of payments isIf no
6、 default event, PV of payments isExpected PV is,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.8,PV of CDS Costs per $1 of Notional Principal,If default event occurs at t Interest Rate Swaps,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.40
7、,Convertibles,A convertible bond is a corporate bond that can be exchanged for equity at certain times in the future at a predetermined exchange ratio (shares per bond),Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.41,Convertibles continued,One of the problems in valui
8、ng convertibles is that, in order to value the corporate bond correctly, it is necessary to take account of the chance of default in some wayOtherwise we are implicitly assuming it is a no-default Treasury bond,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.42,Valuing C
9、onvertible Bonds,The value at a node isMAX MIN(Q 1, Q 2), Q 3 where Q 1 is the value given by the rollback Q 2 is the call price, &Q 3 is the value if conversion takes place.,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.43,Valuing Convertible Bonds(continued),We divid
10、e the value of the bond at each node into two componentsa component that arises from situations where the bond ultimately ends up as equitya component that arises from situations where the bond ultimately ends up as debt,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.44
11、,Example 27.6,9-month zero-coupon bond with face value of $100Convertible into 2 sharesCallable for $115 at any timeInitial share price = $50, volatility = 30%, no dividendsRisk-free rates all 10%Yields on issuers non-convertible bonds = 15%,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,27.45,The Tree,(Numbers at each node in descending order are the stock price, equity component, debt component & total value),
