Question

The underlying stock for a European exchange option has S = $27.15, div = 2.0%, and σ = 0.18. The strike stock has S = $30.00, div = 0.0%, and σ = 0.22. The two stocks have a correlation coefficient of 0.73. If the exchange option expires in 2 years, what is the price of the call using a Black-Scholes formula?

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Answer 1

Price of call =S* N(d1) - K * N(d2)

effective     =(.18^2+.22^2-  2*.18*.22*.73)^(1/2) =.1516 (Margrabes formula which is a modification for blackscholes formula for exchange options)

d1 = [ln(27.15/30) + ((.1516^2)/2)*2 ]/(.1516*(2)^(1/2)) =-.3584

= -.3584- .1516*(2^(1/2)) =-.5727

N(d1)= .36 ; N(d2) =.283 ( from standard normal table)

Hence;  Price of call = 27.15*.36- 30*.283 =1.284$