An investment bank has written a number, N, of European call options on a non-dividend paying stock with strike price R250, current stock price R185, time to expiry of 2 years and an assumed continuously - compounded interest rate of 6% p.a. The bank is delta-hedging the option position assuming the Black-Scholes framework holds and currently holds 125,000 shares of the stock and is short R 3,800 000 in cash.

(i) By using the hedging position and the Black-Scholes formula for the value of the option, derive two equations satisfied by N and volatility(stigma) , the banks assumed volatility.

(ii) Estimate by interpolation. [7]

(iii) Deduce the value of N