【正文】 sets or liabilities ? What is the loss in each case? Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Example continued ? The probability of default is N(d2) or % ? The market value of the debt is ? The present value of the promised payment is ? The expected loss is about % ? The recovery rate is 91% Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Volatilities s ?? s sE V VE EV V N d V0 0 1 0? ? ( )This equation together with the option pricing relationship enables V0 and sV to be determined from E0 and sE Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Equity vs. Assets An option pricing model enables the value of the firm’s equity today, E0, to be related to the value of its assets today, V0, and the volatility of its assets, sV E V N d De N ddV D r TTd d TrTVVV0 0 1 21022 12? ??? ?? ??( ) ( )ln ( ) ( )。 20xx by John C. Hull Which World Should We Use? ? We should use riskneutral estimates for valuing credit derivatives and estimating the cost of default ? We should use real world estimates for calculating credit VaR and scenario analysis Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull RiskNeutral Probabilities The analysis based on bond prices assumes that ? The expected cash flow from the Arated bond is % less than that from the riskfree bond ? The discount rates for the two bonds are the same This is correct only in a riskneutral world Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Possible Reasons for These Results ? The liquidity of corporate bonds is less than that of Treasury bonds ? Bonds traders may be factoring into their pricing depression scenarios much worse than anything seen in the last 20 years Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Bond Prices vs. Historical Default Experience yp r o b a b i l i t h i st o r i ca l 0 . 5 7 % t h e t h a n g r e a t e r m u ch is T h i s 2 . 4 7 % . is d e f a u l t ofy p r o b a b i l i t yr5 T h e r a t e .r e co v e r y z e r o A ss u m ep e r i o d . ye a r5 a o v e r v a l u e sb o n d 39。 20xx by John C. Hull Do Default Probabilities Increase with Time? ? For a pany that starts with a good credit rating default probabilities tend to increase with time ? For a pany that starts with a poor credit rating default probabilities tend to decrease with time Options, Futures, and Other Derivatives, 5th edition 169。P Report, January 20xx) 1 2 3 4 5 7 10 AAA 0 0 4 7 2 2 7 AA 1 4 0 8 9 2 6 A 4 2 1 6 7 1 6 BBB 4 5 9 5 3 0 0 BB 8 8 5 1 12 .57 18 .09 23 .86 B 4 13 .49 20 .12 25 .36 29 .58 36 .34 43. 41 C C C 25 .26 34 .79 42 .16 48 .18 54 .65 58 .64 62 .58 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Cumulative Average Default Rates (%) (Table , page 619。 20xx by John C. Hull Theory and Practice ? In theory asset swap spreads should be slightly dependent on the bond’s coupon ? In practice it is assumed to be the same for all bonds with a particular maturity and the quoted asset swap spread is assume to apply to a bond selling for par ? This means that the spread would be quoted as bps in Example 2 and when calculating default probabilities we would assume Bj=100 and Gj= Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Asset Swaps: Example 1 ? An investor owns a 5year corporate bond worth par that pays a coupon of 6%. LIBOR is flat at %. An asset swap would enable the coupon to be exchanged for LIBOR plus 150bps ? In this case Bj=100 and Gj= (The value of 150 bps per year for 5 years is .) Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Value Additivity ? If claim amount equals nodefault value, value of a coupon bond is sum of values of constituent zerocoupon bonds ? The same is not true when claim amount equals face value plus accrued interest Options, Futures, and Other Derivatives, 5th edition 169。 Expected Recovery Rate=30%) Bond Life Coupon (%) Yield (%) 1 2 3 4 5 10 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull What Should We Use as the Claim Amount The best assumption seems to be that the claim amount for a bond equals the face value plus accrued interest not the nodefault value Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Relaxing Assumptions ? This analysis assumes constant interest rates, and known recovery rates and claim amounts