Consider the non-dividend-paying stock in Homework 3, No.1. Its current price S(0) = S is still $40,
Question:
Consider the non-dividend-paying stock in Homework 3, No.1. Its current price S(0) = S is still $40, yet the economic situation has changed and after each period, there is a 35% chance that the stock price goes up by 20%, 40% chance that the stock price stays the same, and 25% chance that the stock price drops by 10%. A European call option and a European put option on this stock expire on the same day in 4 months at a $43 strike. The current risk-free interest rate is 6% per annum, compounded monthly. Count a month as one period.
(a) Construct a four-period binomial lattice tree to calculate the stock price after three months.
(b) Find risk-neutral probabilities q1, q2, and q3 that make the expectation of stock price after one period (1+rf )S(0) where rf is the risk-free rate per period, and the standard deviation 0.1. (In other words, find q1, q2, and q3 such that E[X] = (1 + rf )S(0) and Var(X) = 0.01 where X is the random variable that represents the stock price after one period).
(c) Use the above risk-neutral probabilities and a four-period binomial lattice tree to calculate the current (t = 0) call option price.
(d) Use the same method as above to calculate the current (t = 0) put option price.
(e) Use Put-Call Parity to verify your answers from (c) and (d). If there is any error (discrepancy), provide your opinion on what caused the discrepancy.
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler