Suppose an investor has the opportunity to buy the followingcontract, a stock call option, on March 1. Thecontract allows him to buy 100 shares of ABC stock atthe end of March, April, or May at a guaranteed priceof $50 per share. He can exercise this option at mostonce. For example, if he purchases the stock at the endof March, he can’t purchase more in April or May atthe guaranteed price. The current price of the stock is$50. Each month, assume that the stock price eithergoes up by a dollar (with probability 0.55) or goesdown by a dollar (with probability 0.45). If the investorbuys the contract, he is hoping that the stock price willgo up. The reasoning is that if he buys the contract, theprice goes up to $51, and he buys the stock (that is, heexercises his option) for $50, he can then sell the stockfor $51 and make a profit of $1 per share. On the otherhand, if the stock price goes down, he doesn’t haveto exercise his option; he can just throw the contractaway.a. Use a decision tree to find the investor’s optimalstrategy—that is, when he should exercise theoption—assuming that he purchases the contract.b. How much should he be willing to pay for such acontract?
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 can’t purchase more in April or May at
the guaranteed price. The current price of the stock is
$50. Each month, assume that the stock price either
goes up by a dollar (with probability 0.55) or goes
down by a dollar (with probability 0.45). 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. On the other
hand, if the stock price goes down, he doesn’t have
to exercise his option; he can just throw the contract
away.
a. Use a decision tree to find the investor’s optimal
strategy—that is, when he should exercise the
option—
assuming that he purchases the contract.
b. How much should he be willing to pay for such a
contract?
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