if the expected stock return is 20 what is the true probability that the call option 620231

Consider the valuation of a European call on stock XYZ with a strike price of $110 and a term to maturity of three months. Assume the stock price is $100 today and it has a lognormal distribution with volatility of 40% over the life of the option. In addition, the continuously compounded risk-free rate is 2% per year. Using the Black-Scholes formula, answer the questions below.

  1. What is the theoretical value of the call?
  2. If the stock will pay a $4 dividend next month, what should the theoretical call price be?
  3. What is the risk-neutral probability that you will exercise the option at maturity?
  4. If the expected stock return is 20%, what is the true probability that the call option will be exercised prior to maturity?