Assume the following set of baseline parameters: The initial stock price (S0) is 45, the stock volatility is 0.30 (30% per annum), and the risk-free rate is 0.02 (2% per annum). Consider a European put option whose strike price is equal to 40, with a time-to-maturity of two years. The dividend yield is 0.04 (4% per annum). In some later tasks, you also encounter the “equivalent” American option.
Use the finite difference method to value the (plain-vanilla) American put option. I leave it up to you to decide whether you want to use the implicit or explicit method. Motivated groups may consider using both and comparing outcomes. I also leave it up to you how many stock price- and time-steps you use in your grid (but go for more than used in the lecture). I would, however, advise you to simulate the stock price, not the log of the stock price – that’s more intuitive and thus a lot easier.
Show the calculation process in the essay and describe what you do, report your results and comment your results. Numbers should be rounded to two or three digits.