Assume the Black-Scholes model applies. An at the money European call option on a stock has an exercise date one year away and a strike price of R118.57. The option is priced at R10. The continuously compounded risk-free rate is 1% per annum.

(i) (a) Estimate the implied volatility to within 1% per annum.

(b) Calculate the corresponding hedging portfolio in shares and cash for 1000 options on the share, quoting any results that you use.

3 (c) Calculate the option's Vega. (10)

(ii) Price a put on the same stock with the same expiry date and a strike price of R110. (2) The hedging portfolio of the call option has the same value, the same Delta and the same Vega as the option. The Delta of the put option is 0.29975 and its Vega is 39.435. (

iii) Determine the hedging portfolio of the call option in terms of shares, cash and the put option.