1. The mean rate of return on a stock is estimated at 20% while the volatility is 40%: The risk free interest rate is 5%:
(a) What is the mean for the log price relative?
(b) Construct the final stock prices for a 10 period one year tree.
(c) Construct the statistical probabilities for these stock prices
(d) Construct the associated risk neutral probabilities.
(e) Graph the statistical and risk neutral probabilities against the stock prices on the same graph.
(f) For the two strikes of 80; 120 construct the final cash flows to calland put options at these strikes.
(g) Price the puts and calls using the statistical probabilities.
(h) Price the puts and calls using the risk neutral probabilities.
(i) Identify an arbitrage you would use against a counterparty quoting on statistical probabilities.
(j) Show that this arbitrage fails against the counterparty quoting on the risk neutral probabilities.