Q2) (15marks) An investment bank has written a number, N, of European call options on a non-dividend paying stock with strike price R200, current stock price R120, time to expiry of 2 years and an assumed continuously - compounded interest rate of 5% p.a. The bank is delta-hedging the option position assuming the Black-Scholes framework holds and currently holds 150,000 shares of the stock and is short R 12, 500 000 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 o, the bank's assumed volatility. [4] (ii) Estimate by interpolation. [8] (iii) Deduce the value of N. [3] Q2) (15marks) An investment bank has written a number, N, of European call options on a non-dividend paying stock with strike price R200, current stock price R120, time to expiry of 2 years and an assumed continuously - compounded interest rate of 5% p.a. The bank is delta-hedging the option position assuming the Black-Scholes framework holds and currently holds 150,000 shares of the stock and is short R 12, 500 000 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 o, the bank's assumed volatility. [4] (ii) Estimate by interpolation. [8] (iii) Deduce the value of N. [3]