A stock's current price S is $100.Its return has a volatility of $\sigma$ = 25 percent per year.European call and put options trading on the stock have a strike price of K = $105 and mature after T = 0.5 years.The continuously compounded risk-free interest rate r is 5 percent per year.
-The Black-Scholes-Merton model gives the price of the European call as:

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The Black-Scholes-Merton model gives the price of the European call as:C = S*N(d1) - Ke^(-rT)*N(d2)where:d1 = (ln(S/K) + (r + (sigma^2)/2)*T) / (sigma*sqrt(T))d2 = d1 - sigma*sqrt(T)Plugging in the given values, we get:d1 = (ln(100/105) + (0.05 + (0.25^2)/2)*0.5) / (0.25*sqrt(0.5)) = 0.5d2 = 0.5 - 0.25*sqrt(0.5) = -0.125N(d1) = 0.6915N(d2) = 0.4207Therefore, the price of the European call is:C = 100*0.6915 - 105*e^(-0.05*0.5)*0.4207 = $5.99

A Stock's Current Price S Is $100 σ\sigmaσ = 25 Percent Per Year

A Stock's Current Price S Is $100 $\sigma$ = 25 Percent Per Year