Sunday, April 5, 2009

Digital Call Option value = exp(-rt)N(d2)


Black Scholes says C= SN(d1) - Xexp(-rt)N(d2) = exp(-rt){SN(d1)exp(rt)-XN(d2)},
So for risk-neutral, N(d2)= Pr(Price end up above Strike).

Digital Call = Pay M if expired above X. So Digital Call Value =exp(-rt)MN(d2).

In general with Yield,

C=exp(Y-r)tMN(d2)
P=exp(Y-r)tMN(-d2)

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