Stock price and the stock volatility

Question:
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.

Required method:
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.

Sample Solution

ACED ESSAYS