ABC is trading currently at $100. Assume a one period Binomial Model, that the stock price will either go up or down by 10% over the next period and the risk-free rate over the period is 5% (Take the period to be a year).
a. Set up a synthetic riskless portfolio which consists of ABC stock and the call option on ABC stock written today with a strike price of 100. What is the value hedge ratio Δ?
b. From the results in a., how do you replicate a call option?
c. Calculate the risk-neutral probabilities and value the call using the risk-neutral probabilities. (Check that you get the same answer as in a. above).
d. Using the risk-neutral probabilities above also calculate the value of the find the value of a put option written today, lasting one period, and with an exercise price of 100.
e. Verify that the same price for the put results from put-call parity.