Question

Consider continuous-time model and five-month European call option on a non- dividend stock which a stock price of $200 and premium (c=40) when the strike price is $190, the risk-free rate per annum of a year is 3%. Find implied volatility. The implied volatility must be calculated using an iterative proce

Answer 1

Here, the S0 = 200; X = 190; r = 3%, t = 5/12 = 0.42. q = 0%, C = 40. Using this information, implied volatility is determined by applying Black-Scholes' option pricing model.

os_ Ing&) ++(1+9+ ovt

da = d; -ovt

C = S, e-qt + N(d,)-Xe-rt + N(d))

using these equations in excel, when sigma = 50%, C = 31.51 & when sigma = 100%, C = 55.47. Therefore, sigma should be between 50% & 100%. Similarly checking, we can find that 60%<sigma<70%. Iterating this process further, C = 40 when sigma = 67.59%.