The formula for the price of a European call futures option in terms of the futures price, F 0 ,
The formula for the price of a European call futures option in terms of the futures price, F0, is given in Chapter 18 as
and K, r, T, and Ïƒ are the strike price, interest rate, time to maturity, and volatility, respectively.
(a) Prove that F0N'(d1) = KN'(d2)
(b) Prove that the delta of the call price with respect to the futures price is e-rTN(d1).
(c) Prove that the vega of the call price is F0 √T N'(d1)e-rT
(d) Prove the formula for the rho of a call futures option given in Section 19.12.
The delta, gamma, theta, and vega of a call futures option are the same as those for a call option on a stock paying dividends at rate q with q replaced by r and S0 replaced by F0. Explain why the same is not true of the rho of a call futures option.
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