Calculate numerically (by trial-and-error, not in Excel) the implied volatility of Corp Inc. stock on April 5, 2021 using an European call option on the stock with a strike price of 315 and an expiration date of 15 March 2023. The bid and ask prices of the call on April 5, 2021 are USD 130 and USD 134, respectively, the stock price is USD 420, and the risk-free rate is 1% per annum.

Using the data and results from above:

a) What is the probability of exercise for this call option in a risk-neutral world?

b) What would the call option value be after four weeks (May 5, 2021), holding the other parameters constant?

c) Estimate the call value if the implied volatility went up to 50%.

d) Suppose the expected return of the stock is 25% per annum. Estimate the expected value of the stock price and standard deviation after two years.