Note: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock went up for the first three periods and thendown for the next two. Determine the price of the stock at that position, the priceof each of the put and call and determine how many shares of stock you should beholding in the hedging portfolio for each of the call and the put.(d) Repeat questions (a)-(c) in the case where r = 0. Comment on the results.Hint: take advantage of the fact that the model is recombining: moving up, then downtakes you to the same value as moving first down, and then up. It reduces the amount ofcalculations necessary and will speed up your code.
Note: The purpose of this problem below is to use computational techniques (Excel
spreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen in
class. Please provide the numerical answer to the questions as well as a sample of your
work (spreadsheet, code file, etc.).
We consider an N-period binomial model with the following properties: N = 60, the
current stock price is S0 = 1000; on each period, the stock price increases by 0.5% when
it moves up and decreases by 0.3% when it moves down. The annual interest rate on the
money market is 5%. (Notice that this model is a CRR model, which means that the
binomial tree is recombining.)
(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040
and maturity T = 1 year.
(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040
and maturity T = 1 year.
(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1
month later). Assume that the stock went up for the first three periods and then
down for the next two. Determine the price of the stock at that position, the price
of each of the put and call and determine how many shares of stock you should be
holding in the hedging portfolio for each of the call and the put.
(d) Repeat questions (a)-(c) in the case where r = 0. Comment on the results.
Hint: take advantage of the fact that the model is recombining: moving up, then down
takes you to the same value as moving first down, and then up. It reduces the amount of
calculations necessary and will speed up your code.
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