28. Suppose an investor has the opportunity to buy thefollowing contract (a stock call option) on March 1.The contract allows him to buy 100 shares of ABCstock at the end of March, April, or May at a guaranteed price of $50 per share. He can exercise thisoption at most once. For example, if he purchases the stock at the end of March, he cannot purchasemore in April or May at the guaranteed price. If theinvestor buys the contract, he is hoping that the stockprice will go up. The reasoning is that if he buys thecontract, the price goes up to $51, and he buys thestock (that is, he exercises his option) for $50, he canthen sell the stock for $51 and make a profit of $1per share. Of course, if the stock price goes down, hedoesn’t have to exercise his option; he can just throwthe contract away.Assume that the stock price change each monthis normally distributed with mean 0 and standarddeviation 2. The investor uses the following strategy. At the end of March, he exercises the optiononly if the stock price is above $51.50. At theend of April, he exercises the option (assuming hehasn’t exercised it yet) only if the price is above$50.75. At the end of May, he exercises the option(assuming he hasn’t exercised it yet) only if theprice is above $50.00. (This isn’t necessarily hisbest strategy, but it is a reasonable one.) Simulate250 replications of this strategy and answer thefollowing:a. Estimate the probability that he will exercise hisoption.b. Estimate his net profit with this strategy. (Thisdoesn’t include the price of the contract.)c. Estimate the probability that he will net over$300.d. Estimate the worth of this contract to him
28. Suppose an investor has the opportunity to buy the
following contract (a stock call option) on March 1.
The contract allows him to buy 100 shares of ABC
stock at the end of March, April, or May at a guaranteed price of $50 per share. He can exercise this
option at most once. For example, if he purchases the stock at the end of March, he cannot purchase
more in April or May at the guaranteed price. If the
investor buys the contract, he is hoping that the stock
price will go up. The reasoning is that if he buys the
contract, the price goes up to $51, and he buys the
stock (that is, he exercises his option) for $50, he can
then sell the stock for $51 and make a profit of $1
per share. Of course, if the stock price goes down, he
doesn’t have to exercise his option; he can just throw
the contract away.
Assume that the stock price change each month
is
deviation 2. The investor uses the following strategy. At the end of March, he exercises the option
only if the stock price is above $51.50. At the
end of April, he exercises the option (assuming he
hasn’t exercised it yet) only if the price is above
$50.75. At the end of May, he exercises the option
(assuming he hasn’t exercised it yet) only if the
price is above $50.00. (This isn’t necessarily his
best strategy, but it is a reasonable one.) Simulate
250 replications of this strategy and answer the
following:
a. Estimate the probability that he will exercise his
option.
b. Estimate his net profit with this strategy. (This
doesn’t include the price of the contract.)
c. Estimate the probability that he will net over
$300.
d. Estimate the worth of this contract to him
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
