Part A Consider a traded stock with an initial price of S0. The stock price can go up
by a factor 1 + c; c > 0 with probability pu or down by a factor 1 - c with probability
pd = 1 - pu every month for the next T months. The risk free interest rate is r per
annum and is compounded continuously.
There is a Barrier Put Option on this stock with payo:
X = 1{St》b; for any t: 1《t《T}(K - ST )+,
where St is the stock price after t months, K is the strike price and b is the barrier that
activates the option.
1. Estimate numerically, using Monte Carlo simulations of 1000 price paths, the ex-
pected discounted payo of the above option. For your simulations use the following
parameter values:
r T S0 pu K c b
0.6 5 100 50% 105 0.1 95
If you were an investor, would you pay this price to buy this option? Justify your answer.
2. Modify your simulation so that you obtain an estimate of the risk-neutral price
for the above option using the above parameter values.
3. For your risk neutral pricing model, investigate the role of the risk-free rate r, c and
strike price K numerically. Draw graphs of the risk-neutral option price with respect
to these parameters. Discuss your findings.
