Mathematics of Finance

Mathematics of Finance

You are strongly encouraged to use a computing device for calculation, yet you should 311 write down all the steps.
1. (10 pt each) Trirnonial version 1 of Problem 14.3: consider a non-dividend-paying stock whose current price S(0) = S is $62 and the volatility a of In S is 0.20. Current risk-free interest rate is 10%(12) per annum.
(a) Derive the risk-neutral probabilities in Example 15.7, i.e. 91,92, qa fora = 1.1031277.
(b) Evaluate the option price using trinomial lattice trees.
2. (10 pt each) 711monial version 2 of Problem 14.3: Consider the call option above. After each period, there is a 40% chance for the stock price to go up, 25% chance to stay the same, and 35% chance to go down. Assurer p it the same as the risk-free rate.
(a) Find the up-factor u and down-factor d = (b) Find the corresponding risk-neutral probabilities gn,g2,g3 for the II and d above. (c) Evaluate the option price using the risk-neutral probabilities front (b).