Question: Hi, could you please help me solve. Consider a share S traded in the market. Let the current inter- est rate be 'r and the

Hi, could you please help me solve.

Consider a share S traded in the market. Let the current inter- est rate be 'r and the volatility (roughly speaking, the variance of the price) of the share be a. We suppose that 'r and o are constants. A EurOpean call option V(S, t) on S gives the holder the right to buy the share at a xed price K (the strike price) at some future time T. If the price of the share at T is greater than K , the Option holder can buy the share for K , then sell it for S , making a prot of S K dollars. If the price of the share at T is less than K , the option is worthless, because no one would buy a share for more than it is worth on an exchange. Problem: How much is European call option worth? Black and Scholes showed that if V(S,t) = u(S, T t), then u(S,t) satises the partial differential equation Bu 1 8211. Bu 2 02S2 + 'rS Tn, 673 2 ('9S2 6S with u(S,0) = {2 K\" 3:1; Scholes equation. The purpose of this question is to obtain the price of a call option. This is the famous Black

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