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0) Denote by F=Se(rq)T the forward price corresponding to time T of an asset with spot price S at time t, paying dividends continuously at
0) Denote by F=Se(rq)T the forward price corresponding to time T of an asset with spot price S at time t, paying dividends continuously at the rate q. (i) Show that the Black-Scholes formulas can be written in terms of the forward price as follows: C(S,t)P(S,t)=KerT(KFN(d1)N(d2));=KerT(N(d2)KFN(d1)), where d1=Tln(KF)+2T;d2=Tln(KF)2T. (ii) Show that the values of the at the money forward call and put options are equal; an at the money forward option is struck at the forward price, i.e., K=F=Se(rq)(Tt). (iii) Find an approximation formula for the value of at the money forward call and put options
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