A European call option is a contract with the following conditions: At a prescribed time in the future, known as the expiration date, the holder of the option has the right, but not the obligation to purchase a prescribed asset, known as the underlying asset/security, for a prescribed amount, known as the strike price or exercise price. For example, suppose an investor purchases a call option on stock XYZ with a $50 strike price. At expiration, say a month from the time of purchase, the spot price of stock XYZ is $75. In this case, the owner of the call option has the right to purchase the stock at $50 and exercises the option, making $25, or ($75 - $50), per share. However, in this scenario, if the spot price of stock XYZ is $30 at expiration, it does not make sense to exercise the option to purchase the stock at $50 when the same stock could be purchased in the spot market for $30. In this case, the payo is $0. 

Note the payo and prot are dierent. To calculate the prot from the option, the cost of the contract must be subtracted from the payo. In this sense, the most an investor in the option can lose is the premium price paid for the option. In general, if S is the spot price of stock XYZ on the expiration date and K is the strike price of the European call option, then the call option payo = max {0, (S − K)} and the prot = payo-option price. Consider the following problem: You have $20,000 to invest. Stock XYZ sells at $20 per share today. A European call option to buy 100 shares of stock XYZ at $15 exactly six months from today sells for $1000. You can also raise additional funds which can be immediately invested, if desired, by selling call options with the above characteristics. In addition, a 6-month riskless zero-coupon bond with $100 face value (the amount you will make at the end of 6 months) sells for $90. You have decided to limit the number of call options that you buy or sell to at most 50. You consider three scenarios for the price of stock XYZ six months from today: the price will be the same as today, the price will go up to $40, or drop to $12. Your best estimate is that each of these scenarios is equally likely. Formulate and solve (in Solver) a linear program to determine the portfolio of stocks, bonds, and options that maximizes expected prot.

What happens to protability if the price of XYZ goes to $40 per stock? 

Suppose you want a prot of at least $2000 in any of the three scenarios. Write and solve (in Solver) a linear program that will maximize your expected prot under this additional constraint. How does the solution compare to the earlier case described. 

Riskless prot is dened as the largest possible prot that a portfolio is guaranteed to earn, no matter which scenario occurs. Formulate and solve (in Solver) the model to determine the portfolio that maximizes riskless prot for the above three scenarios?

Answer rating: 100% (QA)

Answer If the price of XYZ goes to 40 per stock the payo of the call option will increase to max 0 4... View the full answer