Suppose that you have offered two packages. Package A contains 1000 call options at a strike price of $182. Package B contains 100 call options at a strike price of $80. Suppose you are risk-neutral. Which package would you choose? Group of answer choices Package A Package B Both are equally good. Reject both because they have a negative value.
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A call option gives the holder the right, but not the obligation, to buy an asset at a specified strike price before a certain expiration date. The value of a call option increases as the price of the underlying asset rises above the strike price. Show more…
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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?
Akash M.
PROBLEM 4. You look up the prices of European calls today on a particular stock and discover the following prices for call options: Strike Price Price 195 47.80 200 C0^200 205 44.20 (a) Can the price C0^200 of the European call option with strike price K = 200 be C0^200 = 46.80? (b) Now suppose that the real price is C0^200 = 45.60. A friend has confidence that the stock price will rise in the future and offers to bet any amount of money Q (a constant that you two decide today) that the stock will be worth at least 200 in 1 year. The risk-free annual compounding interest rate r = 0.05. Can you make an arbitrage by betting with this friend and trading spread? If yes, give the value of Q and your corresponding strategies. (Hint: Look up the following contracts, Bull-spread, Bear-spread, and Butterfly-spread. Which spread will you choose?)
A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 - $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 - $1.00 = $2.50 per share. The point of purchasing a European option is to limit the risk of a decrease in the per-share price of the stock. Suppose you purchased 200 shares of the stock at $28 per share and 80 six-month European put options with an exercise price of $26. Each put option costs $1. (a) Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $20 and $29 per share in increments of $1.00. What is the benefit of the put options on the portfolio value for the different share prices? For subtractive or negative numbers, use a minus sign even if there is a + sign before the blank. (Example: -300. If your answer is zero, enter "0". Share Price Benefit of Options $20 $21 $22 $23 $24 $25 $26 $27 $28 $29 (b) Discuss the value of the portfolio with and without the European put options. The lower the stock price, the more beneficial the put options. The options are worth nothing at a stock price of $ or higher. There is a benefit from the put options to the overall portfolio for stock prices of $ or lower.
Madhur L.
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