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...

...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...

...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...

...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...

...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...

...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...

...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/strike price)
- An American...

...1. _____ is the rate of change of delta with 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...

...opportunity to purchase stock options. As of 2001, ten million employees have chosen to purchase stock options. Another survey established that 97 of the top 100 e-commerce companies gave the choice of options this year. For these reasons, it is important to understand what stock options are, the different types of options, and their advantages and disadvantages.
A stock option gives any employee the...

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