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MFIN703 – OPTIONS & FUTURES
创建日期：2024-04-07 16:27:57
所属分类：管理Management
标签： MFIN703
OPTIONS & FUTURES

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MFIN703 Assignment #2


MFIN703 – OPTIONS & FUTURES

Answer all of the following questions. For quantitative questions, show your work to earn the full marks
allocated. The final answer is only worth one mark. Questions requiring a qualitative response may be
written in point form.

Total Marks: 160


1. The current price of a non-dividend-paying high growth stock is $100 with a volatility of
50%. The risk-free rate is 3.5%. For a three-month time-step:

a. What is the percentage up movement?
b. What is the percentage down movement?
c. What is the probability of an up movement in a risk-neutral world?
d. What is the probability of a down movement in a risk-neutral world?
e. Use a two-step tree to value a six-month European call option and a six-month European
put option. In both cases the strike price is $125.
f. What would be the value of a six-month American call option and a six-month European
put option?
g. What is the value of the American call?

(Total marks: 40)


2. Consider an option on a non-dividend-paying stock when the stock price is $25, the exercise
price is $30, the risk-free interest rate is 3% per annum, the volatility is 30% per annum, and the
time to maturity is four months. (Total marks: 20)

a. What is the price of the option if it is a European call?
b. What is the price of the option if it is an American call?
c. What is the price of the option if it is a European put?
d. Verify that put–call parity holds.


3. For the same option above, ie. on a non-dividend-paying stock when the stock price is $25, the
exercise price is $30, the risk-free interest rate is 4% per annum, the volatility is 30% per annum,
and the time to maturity is four months, calculate and interpret the following greeks. (Total marks:
30)

a. Delta of the European call and put.
b. Theta of the European call.
c. Gamma of the European put.
d. Vega of the European put.
e. Rho of the European call.


4. Calculate the value of a five-month European futures put option when the futures price is $19, the
strike price is $20, the risk-free interest rate is 12% per annum, and the volatility of the futures
price is 20% per annum. (10 marks)

MFIN703 Assignment #2
Winter 2021
2
5. What does it mean if the:

a. delta of a call option is 0.7? How can a short position in 1,000 options be made delta
neutral when the delta of each option is 0.7? (5 marks)
b. theta of an option position is −0.1 when time is measured in years? If a trader feels that
neither a stock price nor its implied volatility will change, what type of option position is
appropriate? (5 marks)
c. gamma of an option position? What are the risks in the situation where the gamma of a
position is large and negative and the delta is zero? (5 marks)


6. A financial institution has just sold 1,000 seven-month European call options on the Japanese
yen. Suppose that the spot exchange rate is 0.80 cents per yen, the exercise price is 0.81 cent
per yen, the risk-free interest rate in the United States is 8% per annum, the risk-free interest rate
in Japan is 5% per annum, and the volatility of the yen is 15% per annum.

Calculate the delta, gamma, vega, theta, and rho of the financial institution’s position. Interpret
each number. (Total marks: 30)


7. A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap,
six-month LIBOR is exchanged for 4% per annum (compounded semiannually). Six-month LIBOR
forward rates for all maturities are 3% (with semiannual compounding). The six-month LIBOR rate
was 2.4% per annum two months ago. OIS rates for all maturities are 2.7% with continuous
compounding.

What is the current value of the swap to the party paying floating? What is its value to the party
paying fixed? (10 marks)


8. Give an example of how a swap might be used by a portfolio manager. Explain the nature of the
credit risks to a financial institution in a swap agreement. (5 marks)
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