# Choose the correct answer from the following choices. Make your selection clear and distinct, otherwise you will not get credit.

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FI 4000: Exam 3

Spring 2021 Milind Shrikhande

Fundamentals of Valuation

Name:

Last First

Student ID #

Date: 04/12/2021Instructions

1. You have 120 minutes to answer all the questions.

2. You can use calculators and just the formula sheet provided in the exam.

3. Partial credit will be given for showing your work in detail, correct approach to the problem and writing legibly. You must write your final answer clearly.

4. State your assumptions, if any, clearly. For questions requiring numerical work, whether multiple choice or numerical problems, no credit will be given unless the working is shown as part of your answer.

5. Manage your time well during the test.

Answer all questions. The total score is 100 points.

• Exam is closed book and closed notes. You may not refer to any books, notes, or other materials during the exam.
• Good Luck!

Honor Codes

You are expected to follow the Honor Code. Please ask the professor if you need any clarification. Any violation of the code will be reported to the concerned authority.

Multiple Choice Questions: (20 points)

Choose the correct answer from the following choices. Make your selection clear and distinct, otherwise you will not get credit.

1. Options and futures are derivatives, however they differ because options are valuable _______ and futures are ­­­­­­­­­­­­­­­­­­­­­­­­_______, options have ­­­­­­­­­­­­­­­­­­­______ payoffs, futures ______ payoffs.

A) rights, obligations, nonlinear, linear

B) rights, linear, obligations, nonlinear

C) obligations, rights, linear, nonlinear

D) obligations, linear, rights, nonlinear

2. Rain-checks are like _______, car insurance is like _________.

A) currency forwards, currency futures

B) commodity-options, commodity-futures

C) index forwards, index futures

D) call-options, put-options

3. Spot futures parity is an equilibrium condition involving the following variables:

A) stock price, exercise price, time to maturity, interest rates

B) domestic interest rate, forward rate, foreign interest rate, spot rate

C) forward rates, spot rates, interest rates, time to maturity

D) domestic interest rate, stock price, foreign interest rate, exercise price

4. Cash and carry arbitrage and reverse cash and carry arbitrage apply

A) when dealing with dividend paying stocks

B) when dealing with derivative markets involving options

C) when dealing with non-dividend paying stocks

D) when dealing with an equilibrium condition

5. One of the following is not a determinant of option values

A) stock price

B) exercise price

C) rate of return on stock

D) time to maturity

Problem 1 (24 points)

An investor is considering buying a call option for stock ABC with the following parameters:

Exercise price of the call option is \$170, initial stock price \$165, call option price \$8.

A. Construct payoff and profit function and state the range of stock prices for which the call option will be in the money, and the range of stock prices for which the call option will be out of the money. (6 points)

B. Construct a payoff table for the covered call position. Show the payoff for the written call and the underlying stock for S(t) < X, and for S(t) > X, where X is the exercise price of the call-option. (12 points)

C. Discuss why the call option writer should undertake the covered call position as opposed to only writing the call option. (6 points)

Problem 2 (24 points)

You would like to be holding a protective put position on the stock XYZ. The stock XYZ is currently selling for \$120. Over the next year, the stock price will either increase by 10% or decrease by 10%. The exercise price of the put option is \$125. The riskfree interest rate is 3% per year.

1. What is the price of the put option? (Use a one-period binomial model)

(12 points)

Problem 2 (continued)

1. What is the cost of the protective put portfolio? What will be the payoff and profit of the protective put portfolio? [Hint: Use a tabular format to tabulate the payoff for S(t) < X, and for S(t) > X, where X is the exercise price of the put – option].

(12 points)

Problem 3 (24 points)

Consider a stock index fund that has a current value of \$1200. A dividend of \$10 will be paid on the index at the end of the year. A futures contract for \$1245 is also available on this stock index fund and the futures contract matures in one year.

1. Assume that the futures contract is fairly priced so it is the equilibrium price. Using the spot-futures parity condition, F = S (1 + r – d), where r is the risk-free interest rate, and d is the dividend yield, calculate the unknown risk-free interest rate.

(9 points)

1. Suppose the futures contract is mispriced and it is selling for \$ 1240. Construct an arbitrage strategy to exploit the mispricing and calculate the arbitrage profit.

(12 points)

Problem 3 (continued)

1. Show that the arbitrage profit you calculated above will equal the mispricing in the futures market.

(3 points)

Problem 4 (24 points)

Use the following data for answering all problem sub-parts:

A put option will mature in 6 months. The standard deviation of the underlying stock returns is 30% per year. The exercise price of the put option is \$40 and the stock price is also \$60. The risk-free interest rate is 3% per year.

1. Using the Black-Scholes option pricing formula, calculate the price of the put option. (15 points)

Problem 4 (continued)

1. Using put-call parity calculate the price of the corresponding call option that has the same exercise price and maturity date as that of the put option.

(9 points)

Conceptual Questions (8 points)

Question 1: (4 points)
There are two call options for the same underlying asset and same maturity. One call option C1 has exercise price of \$120 and the other call option C2 has exercise price of \$150. Also, one call sells for \$8 and the other sells for \$10. Select the prices of C1 and C2 from the given two values. Explain your argument for the price selection with the help of payoff and profit diagrams of the call options.

Question 2: (4 points)

If you construct a hedged portfolio that provides a payoff of \$100 thousand in one year irrespective of the economic conditions in the market, what is the discount rate that you are going to use to find the present value of the payoff? Give reasons for your selection of the discount rate.

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