# Puts and Calls

Task 3a: Problem Set

Directions: Type your answer to each question where indicated. Use more space if needed.

1. On Monday morning, an investor takes a long position in pound futures contract that matures on Wednesday afternoon. The agreed-upon price is $1.78 for 62,500 pound sterling. At the close of trading on Monday, the futures price has risen to $1.79. At Tuesday close the price rises further to $1.80. At Wednesday close, the price falls to $1.785, and the contract matures. The investor takes delivery of the pounds at the prevailing price of $1.785. Detail the daily settlement process (refer to exhibit 8.3). What will be the investor's profit (loss)?

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2. The DEC buys a Swiss franc futures contract (contract size is SFr 125,000) at a price of $0.83. If the spot rate for the Swiss franc at the date of settlement is SFr1 = $0.8250, what is DEC's gain or loss on this contract?

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3. Assume that the spot price of the British pound is $1.55, the annualized 30-day sterling interest rate is 10%, the annualized 30-day U.S. interest rate is 8.5%, and the annualized standard deviation of the dollar:pound exchange rate is 17%. Calculate the value of a 30-day PHLX call option on the pound at a strike price of $1.57.

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4. On August 6, you go long one IMM yen futures contract at an opening price of $0.00812 with a performance bond of $4,590 and a maintenance performance bond of $3,400. The settlement prices for August 6, 7, and 8 are $0.00791, and $0.00845, and $0.00894, respectively. On August 9, you close out the contract at a price of $0.00857. Your round-trip commission is $31.48.

a. Calculate the daily cash flows on your account. Be sure to take into account your required performance bond and any performance bond calls.

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b. What is your cash balance with your broker on the morning of August 10?

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5. On June 25, the call premium on a December 25 PHLX contract is 6.65 cents per pound at a strike price of $1.81. The 180-day interest rate is 7.5% in London and 4.75% in New York. If the current spot rate is 1 pound sterling = $1.8470 and the put=call parity holds, what is the put premium on a December 25 PHLX pound contract with an exercise price of $1.81?

Type your answer here.

Currency Derivatives Framework

Forward and Futures Contracts

A forward contract is a contract between a multinational corporation and a financial institution to exchange a specified amount of currency on a specific date at a specific exchange rate. By doing so, multinational corporations lock in the exchange rate for delivery of currency in future.

A futures contract is a standardized contract between a multinational corporation and a futures exchange to exchange a specified amount of currency on a specific date at a specific exchange rate. A futures contract is a promise, although less than 1 percent of futures contracts are delivered.

Multinational corporations use futures and forward contracts for hedging purposes. Speculators use futures contracts to make money on exchange rate movements (arbitrage).

The currency premium or discount is related to forward rates (Unit 1).

Currency Options

A call option is a right to buy a specific currency at a specified price (rate) within a specific time period. A put option is a right to sell a specific currency at a specified price (rate) within a specific time period. The specific price is known as "exercise price" or "strike price." Buying an option is known as the "long position," and selling an option is known as the "short position"; the seller is called the "writer."

Keep the following points in mind for call options and put options:

A call option is

? in-the-money if the spot exchange rate exceeds the strike rate

? out-of-the-money if the spot exchange rate is less than the strike rate

? at-the-money if the spot rate is equal to the strike rate

A put option is

? in-the-money if the spot exchange rate is less than the strike rate

? out-of-the-money if the spot exchange rate is more than the strike rate

? at-the-money if the spot rate is equal to the strike rate

The price of an option is known as the "premium."

There are four basic strategies in the options market:

1. Long call

2. Short call

3. Long put

4. Short put

https://brainmass.com/economics/contracts/puts-and-calls-120568

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Time Action Cash Flows

Monday Morning Buys pound futures contract that matures in two days at ...

#### Solution Summary

Forward and Futures Contracts are embedded.

Textbook: Essentials of Investments. Chapter 16 (1, 2, 5, 6, 7 & 12). Problems on call and put options.

We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? In each of the following questions, you are asked to compare two options with parameters as given. What is the hedge ratio of the put? Verify that the put-call parity relationship is satisfied by your answers. Use the Black-Scholes formula to find the value of a call option on the following stock. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

1.We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer.

2.In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be 6%. Assume the stocks on which these options are written pay no dividends.

I.

Put T X s Price of Option

0.5 50 0.20 10

B 0.5 50 0.25 10

Which put option is written on the stock with the lower price?

(1) A

(2) B

(3) Not enough information

II.

Put T X s Price of Option

A 0.5 50 0.2 10

B 0.5 50 0.2 12

Which put option must be written on the stock with the lower price?

a. A

b.B

c. Not enough information

III.

Call S X s Price of Option

A 50 50 0.20 12

B 55 50 0.20 10

Which call option must have the lower time to expiration?

a. A

b. B

c. Not enough information

IV.

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 50 55 12

Which call option is written on the stock with higher volatility?

a. A

b. B

c. Not enough information

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 55 55 7

Which call option is written on the stock with higher volatility?

a. A

b. B

c.Not enough information

5. We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.

1. Show that the range of S is 50 while that of P is 30 across the two states. What is the hedge ratio of the put?

2. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio?

3. Given that the stock currently is selling at 100, show that the value of the put must be 10.91.

6. Calculate the value of a call option on the stock in Problem 5 with an exercise price of 110. Verify that the put-call parity relationship is satisfied by your answers to Problems 5 and 6. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective annual yield.)

7. Use the Black-Scholes formula to find the value of a call option on the following stock:

Time to expiration = 6 months

Standard deviation = 50% per year

Exercise price = $50

Stock price = $50

Interest rate = 10%

12. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

Please see attached for problem. Thanks.

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