Consider a European call bond option maturity on T 0 whose underlying bond pays A i
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Consider a European call bond option maturity on T0 whose underlying bond pays Ai ≥ 0 at time Ti, 1 ≤ i ≤ n, where 0 0 1 n. Assume that the zero-coupon bond price B(t,T ) follows the one-factor HJM model, where
and the deterministic volatility function satisfies
Show that the time-0 price of the European call option on the coupon bearing bond with strike price X is given by (Henrard, 2003)
where x is the (unique) solution of
and αi > 0,i = 0, 1, ··· ,n, is given by
Here, T is the expiration date of the underlying bond.
Transcribed Image Text:
dB(t, T) B(t, T) = =r(t) dt + OB(t, T) dZt,
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To derive the expression for the timeO price of the European call option on the couponbearing bond we will follow the steps provided in the problem Given the onefactor HJM model for zerocoupon bond prices dBtT BtT rtdttTdZ And the deterministic volatility function tt tt fttgt Lets consider the European call option on the couponbearing bond with strike price X The payoff of this option at maturity T is given by CTo A maxB0 T X 0 Now lets find the expression for the option price at time t 0 According to the problem the price is given by C0 A B0 TNx 2ax XNr dr Here is the unique solution of CAB0T expax XB0 T And a is given by aUT BUTo dU This expression provides the time0 price of the European call option on the coupon ...View the full answer
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