The Black-Scholes pricing problem for a European binary call option is given by the PDE and final condition

2. The Black-Scholes pricing problem for a European binary call option is given by the PDE and final condition av 1 a2V av 1 SE + trs - rV = 0, V (S, T) = at 2 as2 as 0 SE OS2 = { V (S,t) is the option value, S is the underlying asset price, t is time, T is expiry, r is the constant risk-free interest rate, o is the constant volatility and E is the strike price. a. By introducing the following change of variables x = log (6), v = 0"(T t), w(x, t') = V(S,t) show that the problem can be reduced to aw aw at' aw + (a - 1) ar2 aw, w(a,0) = { 1 2 > 0 0 0 02 0 0 2