Question 1: Consider an option on dividend-paying stock when stock price $30, the exercise price is $29, the risk-free interest rate is 5% p.a., the volatility is 25%p.a. and time to maturity is 4 months. Assume that the stock is due to go ex-dividend in 1.5 months. The expected dividend is 50cents. a. b. c.

what is the price of the option if it is a European call? What is the price of the option if it is a European put? Use the results in the Appendix to this chapter to determine whether there are any circumstances under which the option is exercised early. (a) The present value of the dividend must be subtracted from the stock price. This gives a new stock price of: and

30−0.5e−0.125x0.05= 29.5031 1n(29.5031/29)+(0.05+0.252 /2)x0.3333 d1=0.250.3333= 0.3068 d2 =1n(29.5031/29)+(0.05−0.252 /2)x0.3333=0.1625 N(d1) = 0.6205;N(d2 ) = 0.5645 The price of the option is therefore 29.5031x0.6205 − 29e−0.05×4 /12 x0.5645 = 2.21

or $2.21. (b) Because
N (−d1 ) = 0.3795,N (−d2 ) = 0.4355 the value of the option when it is a European put is 0.25 0.3333
29e−0.05×(4 /12) x0.4355 − 29.5031x0.3795 = 1.22 (c) If t1 denotes the time when the dividend is paid: X (1 − e− r (T −t1 ) ) = 29(1 − e−0.05 x 0.2083 ) = 0.3005 This is less than the dividend. Hence the option should be exercised immediately before the ex-dividend date for a sufficiently high value of the stock price. or $1.22.

Question 2: A foreign currency is currently worth $1.50. The domestic and foreign risk-free interest rates are 5% and 9% respectively. Calculate a lower bound for the value of a six-month call option on the currency with a strike price of $1.40 if it is (a) European and (b) American. Lower bound for European option is

S0e−rf T − Xe−rT =1.5e−0.09x0.05 −1.4e−0.05x0.5 = 0.069 Lower bound for American option is S0 − X = 0.10
Question 3: Show that if C is the price of an American call with exercise price X and maturity T on a stock paying a dividend yield of q, and P is the price of an...

...B. $200 C. $5,000 D. $5,200 E. None of these is correct The following price quotations on IBM were taken from the Wall Street
2.
Journal. The premium on one IBM February 90 call contract is A. $4.1250 B. $418.00 C. $412.50 D. $158.00 E. None of these is correct 3. A put on Sanders stock with a strike price of $35 is priced at $2 per share, while a call with a strike price of $35 is priced at $3.50. The maximum per-share loss to the writer of an uncovered put is __________, and the maximum per-share gain to the writer of an uncovered call is _________. A. $33; $3.50 B. $33; $31.50 C. $35; $3.50 D. $35; $35 You are cautiously bullish on the common stock of the Wildwood Corporation over the next several months. The current price of the stock is $50 per share. You want to establish a bullish money spread to help limit the cost of your option position. You find the following option quotes:
4.
To establish a bull money spread with calls, you would _______________. A. buy the 55 call and sell the 45 call B. buy the 45 call and buy the 55 call C. buy the 45 call and sell the 55 call D. sell the 45 call and sell the 55 call
5.
You are cautiously bullish on the common stock of the Wildwood Corporation over the next...

...8.3.)An investor sells a European calloption with strike price of K and maturity T and
buys a put with the same strike price and maturity. Describe the investor's position.
The payoff to the investor is
- max (ST - K , 0) + max(K - ST, 0)
This is K- ST in all circumstances. The investor's position is the same as a short position in a forward contract with delivery price K.
8 .4.)Explain why brokers require margins when clients write options but not when they buy options?
When an investor buys an option, cash must be paid up front. There is no possibility of future liabilities and therefore no need for a margin account.. When an investor sells an option, there are potential future liabilities. To protect against the risk of a default, margins are required.
8.5.)A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b)May 30?
On April 1 options trade with expiration months of April, May, August, and November. On May 30 options trade with expiration months of June, July, August, and November.
8.6.)A company declares a 2-for-l stock split. Explain how the terms change for a calloption with a strike price of $60.
The strike price is reduced to $30, and the option...

...46 minutes. 2. Each question carries 2.5 points. 3. Answer All questions 4. Students who attempts the test twice will be given zero credit.
1
The price of a stock is $50. The stock pays a dividend of $5 in 3 months. A 6-month European put option on the stock has a strike price of $48 and a premium of $4.38. The continuously compounded interest rate is 8%. Calculate the premium for a 6-month European calloption on the stock with a strike price of $48.
* A 1.02
* B 3.36
* C 3.46
* D 4.38
* E 5.40
2
1. An "exchange calloption" gives the owner of the option the right to give up one share of Stock A in exchange for receiving one share of Stock B. Stock A currently has a price of $56 and Stock B has a current price of $52. The continuously compounded risk-free rate of interest is 5% and the price of a one-year European exchange calloption is $7. Suppose that neither Stock A nor Stock B pays any dividends. Find the price of a European exchange put option expiring in one year which gives the owner the right to give up one share of Stock B in exchange for receiving one share of Stock A.
* A) $3
* B) $5
* C) $7
* D) $9
* E) $11
3.
The price of a 6-month dollar-denominated...

...
1. A portfolio is currently worth $10 million and has a beta of 1.0. The S&P 100 is currently standing at 800. Explain how a put option on the S&P 100 with a strike price of 700 can be used to provide portfolio insurance.
2. “Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices and currencies.” Explain this statement.
3. Explain how corporations can use range-forward contracts to hedge their foreign exchange risk.
4. Calculate the value of a three-month at-the-money European calloption on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is 18% per annum, and the dividend yield on the index is 3% per annum.
5. Calculate the value of an eight-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic risk-free interest rate is 4% per annum, and the foreign risk-free interest rate is 8% per annum.
6. Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European calloption on the index with a strike price of 245 is currently worth $10. What is the value of a three-month put...

...Keller Case
1. To analyze the profit and loss possibilities inherent in the option investment strategies, please perform the following analyses for call and put options on Lotus’s common stock that mature in February 1994 and that have an exercise price of $55 per share.
a. Compute net profits and losses per share (actual dollar profit and losses, not rates of return) at expiration (February 19, 1994) for the following investment strategies:
Buying a calloption on Lotus’s stock;
Writing a calloption on Lotus’s common stock;
Buying a put option on Lotus’s common stock;
Writing a put option on Lotus’s common stock.
Hint: Start by calculating the profit or loss per share assuming that, by February 19, 1994, Lotus’s common stock is selling at, say, $60 per share. Repeat this calculation for several other possible stock prices at the time of expiration that span a wide range above, below and at the exercise price of $55 per share (e.g., $45, $50, $55, $65, and so on.)
b. For each of the option investment strategies listed above, draw a graph relating possible profits and losses per share to Lotus’s stock price at the time of expiration. Put profit and losses per share on the vertical axis of your graph and stock prices on the horizontal axis.
c....

...ASSIGNMENT
(a) Comparing Optionprice, time to maturity, and strike price:
1. Optionprice against Time to Maturity, For a given strike price:
i) APOL calls (K=40) and puts (K=40)
(ii) SBUX calls (K=40) and puts (K=40)
(iii) ABAT calls (K=5.00) and puts (K=5.00)
2. Optionprice against StrikePrice, for a given maturity:
i) APOL calls and puts
ii) SBUX July 2011 calls and puts
iii) ABAT 2011 calls and puts:
(b) Observing the effect on optionprice due to changing strike price and time to maturity:
* Optionprice vs. time to maturity:
We observe that as time to maturity increases, so too does the respective price for both call and put options. This can be explained by the increasing time value characteristic of options. This asymmetry of option payoffs offers a higher probability of finishing in the money for options with longer maturities, whilst capping the losses on the premium paid.
There were some abnormalities, most prevalent in the ABAT put option, which may be due to illiquidity considering their small firm size.
*...

...Markets
FI 4200/AFM
Characteristics of Options
r Definitions and Positions:
- A CallOption gives its owner for a specified time the right to purchase an underlying good at a specified price (= exercise price or
strike price)
- A Put Option gives its owner for a specified time the right to sell an
underlying good at a specified price (= exercise/strikeprice)
- An American Option permits the owner to exercise (=buy/sell the
underlying) at any time before or at expiration.
A European Option can be exercised only at expiration
- There are always two positions in an option contract:
BUYER and SELLER.
The buyer of an option has to pay a “price”, the so-called option premium. The seller of an option receives the option premium.
The option premium is an immediate expense for the buyer and an immediate return for the seller, whether or not the owner (=buyer) ever
exercises the option
- Four basic positions in options:
(1) Buying a Call à Long Call
(2) Selling a Call à Short Call
(3) Buying a Put à Long Put
(4) Selling a Put à Short Put
Buyer (Long)
Seller (Short)
Put
- Obligation to deliver the...

...respect to the price of the underlying asset.
a. Gamma
b. Theta
c. Rho
2. The short term risk-free rate usually used by derivatives traders is
b. The LIBOR rate
3. Duration of a ten-year 6% coupon bond with a face value of $100 is
a. Less than 10 years.
4. Which of the following are always positively related to the price of a European calloption on a stock?
c. The volatility
5. When we talked about Vega hedging, if a portfolio has 1000 shares of SPY and 10 contracts of at-the-money December 2013 put option on SPY (and nothing else in the portfolio), is the portfolio vega neutral?
c. No, the portfolio can never be vega neutral.
6. Which of the following is not true?
a. When a CBOE option on IBM is exercised, IBM issues more stock
7. Which of the following is not true?
a. Futures contracts nearly always last longer than forward contracts
8. In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true?
b. This flexibility tends decrease the futures price.
9. Which of the following is true?
b. The principal amounts usually flow in the opposite direction to interest payments at the beginning of a currency swap and in the same direction as interest payments at the end of...

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