4/27 call settlement=56 expiration(in years)=13/252

4/28 call settlement=83 expiration(in years)=12/252

Use the Black-Scholes formula to compute the value of the following index call option on 2023/4/28. Exercise price =15500 Index level =15,579.18 Interest rate =1.1% Expiration month= May 2023 Assume average dividend yield =0 and there are 252 trading days. Please use the settlement price during the regular trading session as the market value of the option. (i) (12%) Using the Black-Scholes formula, what is the estimate the implied volatility of the same contract on the previous trading day (2023/4/27). The closing index of TAIEX on 2023/4/27 is 15,411.49. (ii) (10%) Use the implied volatility in (i) as the estimate of the volatility. What is the theoretical value of this call option on 2023/4/28 ? (iii) (10%) Compared the market value to theoretical value of this call. What are the market value, time value and intrinsic value of this option on 2023/4/27 and 2023/4/28. Explain your findings