August 8th, 2011, 1:09 pm
Hi,where can I find formulas for the analytical Greeks of a Spread Option valued using Black(1976) with Kirk?s Approximation?I have, I think, for F1=28, F2=20, K=7, v1=0.29, v2=0.36, R(correlation)=0.42, i=0.05, T=0.25AndF = F1/(F2+K) = 1.04v = ( v1^2 + [v2* F2/(F2+K) ]^2 ? 2*R*v1*v2* F2/(F2+K) ) ^0.5 = 0.30d1 = [ ln(F) + (v^2/2) * T ] / (v * T^0.5) = 0.32d2 = d1 ? v * T^0.5 = 0.17then (for a call)DeltaA = N(d1) = 0.62DeltaB = - N(d2) = -0.56GammaA = N(d2)/ (F1 * v * T^0.5) = 0.13GammaB = N(d2)/ [ (K*exp(-i*T) + F2) * v * T^0.5] = 0.14CrossGamma = N(d1)/ [ (K*exp(-i*T) + F2) * v * T^0.5] = - 0.13 VegaA=? = 3.10?VegaB=? = 1.87?CrossVegaGamma=? = 0.01?Chi (aka Riga, Correlation Vega etc.) =? = -1.35?Theta=? = 3.04?Rho=? = -0.54?