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1. Solving the Black-Scholes equation, we calculate the European call option price on a non-dividend-paying stock as
c=SN(d1)-Ke- r TN(d2)
where the K is the strike price and T is the time for the option to mature, and
d1=(ln(S/K)+((r+σ 2 )/2)×T)/(σ√T)
d2=d1-σ√T
Problem 1) Derive gamma of a European call option on a dividend-paying stock. Please show your calculations and reasoning
Problem 2) Please discuss / explain the sign of gamma and its significance.
Problem 3) Is it possible to set up a position in the stock and the option that remains riskless for the whole of the life of the option? Please explain your reasoning
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