Option and Dividend Yield
Chapter 15
Quiz
15.1) A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800. Explain how a put option with a strike price of 700 can be used to provide portfolio insurance.
Index goes down to 700
10*(800/700)= 8.75 million
Buying put options= 10,000,000/800= 12,500
If you buy the options at 800, the value will be 12,500 times the index with a strike price of 700 therefore providing protection against a drop in the value of the portfolio below $8.75 million. Each contract is on 100 times the index, a total of 125 contracts would be required.
15.2) "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.
A stock index is similar to a stock paying a dividend yield, only if the dividend yield is the dividend yield of the index. Currencies are similar to a stock paying a dividend yield, the dividend yield being the foreign risk-free interest rate.
15.3) A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a six month European call option on the index when the strike price is 290?
(300e^-0.03*.5)- 290e^-.08*.5 = $16.90
15.4) A currency is currently worth $.80. Over each of the next two months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%, respectively. What is the value of a two-month European call option with a strike price of $.80?
.8160
.0147
.8323
.0323 p= (e^.06-.08)*.08333 - .98 / 1.02-.98 = 0.4584
.7997
.0000
..8000
.0067
.7840
.0000
.7683
.0000
The purchase price of one unit of currency is $.0067
15.5) Explain how corporations can use range-forward contracts to hedge their foreign exchange risk when they are due to receive certain amount of a foreign currency in the future.
Corporations can
Quiz
15.1) A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800. Explain how a put option with a strike price of 700 can be used to provide portfolio insurance.
Index goes down to 700
10*(800/700)= 8.75 million
Buying put options= 10,000,000/800= 12,500
If you buy the options at 800, the value will be 12,500 times the index with a strike price of 700 therefore providing protection against a drop in the value of the portfolio below $8.75 million. Each contract is on 100 times the index, a total of 125 contracts would be required.
15.2) "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.
A stock index is similar to a stock paying a dividend yield, only if the dividend yield is the dividend yield of the index. Currencies are similar to a stock paying a dividend yield, the dividend yield being the foreign risk-free interest rate.
15.3) A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a six month European call option on the index when the strike price is 290?
(300e^-0.03*.5)- 290e^-.08*.5 = $16.90
15.4) A currency is currently worth $.80. Over each of the next two months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%, respectively. What is the value of a two-month European call option with a strike price of $.80?
.8160
.0147
.8323
.0323 p= (e^.06-.08)*.08333 - .98 / 1.02-.98 = 0.4584
.7997
.0000
..8000
.0067
.7840
.0000
.7683
.0000
The purchase price of one unit of currency is $.0067
15.5) Explain how corporations can use range-forward contracts to hedge their foreign exchange risk when they are due to receive certain amount of a foreign currency in the future.
Corporations can