Two-Step Tree and Butterfly Spread: Questions Essay

Published: 2020-02-25 06:10:07
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1. A company enters into a short futures contract to sell $5000. The current future price is 250 cents per pound. The initial margin is $3000 and the maintenance margin is $2000. What price change would lead to a margin call? Under what circumstances $1500 could be withdrawn from the margin account? 2. Stock is expected to pay a dividend of Tk 10 per share in 2 months and again in 5 months. The stock price is Tk 500 and risk free rate of interest is 8% p.a. with continuously compounded for all maturities. An investor has just taken a short position in a 6- month forward contract on the stock. a. What are the forward price and the initial value of the forward contract? b. Three months later, the price of the stock is 480 and the risk free rate is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

3. Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive three month LIBOR in return on a notational principle of TK 100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. The average of the bid and offer fixed rates currently being swapped for three month LIBOR is 12% per annum for all maturities. The three month LIBOR rate one month ago was 11.8% per annum. All rates are compounded quarterly, what is the value of the swap? 4. A four month European call option on a non-dividend paying stock is currently selling for $5. The stock price is $64, the strike price is $60 and a dividend of $0.80 is expected in one month. The risk free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur?

5. A Tk 100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the bid offer rate is being exchanged for six month LIBOR in swaps of all maturities is currently 10% per annum with continuous compounding. The six month LIBOR rate was 9.6% per annum too months ago. What is the current value of the swap to the party paying floating? What is the value of the swap to the party paying fixed? 6. A call with a strike price of Tk 60 costs Tk 6. A put with the same strike price and expiration date costs Tk 4. Construct a table that shows the profits from a straddle. For what range of stock prices would the straddle lead to a loss. 7. Company X and Y have been offered the following rates per annum on a $5 million 10-year loan:

Company| Fixed Rate| Floating Rate|
Company X| 5.0%| LIBOR+ .5%|
Company Y| 6.5%| LIBOR+ 1.0%|

Assume that the company X requires a floating rate loan; company Y requires a fixed rate loan. Design a swap that will net a bank, acting as intermediary, 20 basis point spread and which will benefit X and Y by 50 and 30 basis respectively. 8. Consider a European call options on a non-dividend paying stock where the stock price is Tk 40, strike price is Tk 40 and the risk free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is three months. c. Calculate u, d and p for a two step tree. d. Value the option using a two step tree.

9. A stock price is currently Tk 50. It is known that at the end of the 6 months it will be either Tk 60 or Tk 42. The risk free rate of interest with continuous compounding is 12% per annum. Calculate the value of 6 month European call option on the stock with exercise price Tk 48 using no arbitrage method. 10. Consider a European call options on a non-dividend paying stock where the stock price is Tk52, strike price is Tk 50 and the risk free rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months. e. Calculate u, d and p for a two step tree. f. Value the option using a two step tree.

11. Calculate the price of a 3 month American put option on a non-dividend stock, which the stock price is Tk 100, the exercise price Is Tk 100 and the risk free rate is 12% p.a. Use the following binominal tree within a time interval of 1 month to calculate the price of the put option. Also state the portfolio floor that will be maintained when portfolio combined with put.

12. Three put options on a stock have the same expiration date and strike prices of Tk 55, Tk60 and Tk65. The market prices are Tk3, Tk5 and Tk 8, respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss? 13. Consider a American call option when the stock price is TK 20, the exercise price is Tk. 24, the time to maturity is six months, the volatility is 20% per annum, the risk free interest rate is 5% per annum. Two equal dividends are expected during the life of the option with ex-dividend rates at the end of the two months and five months. Assume the dividends are Tk. 0.50. Use the Blacks approximation to value the option.

How high can the dividends be without the American option being worth more than the corresponding European option? 14. Consider a American call option when the stock price is TK 18, the exercise price is Tk. 20, the time to maturity is six months, the volatility is 30% per annum, the risk free interest rate is 10% per annum. Two equal dividends are expected during the life of the option with ex-dividend rates at the end of the two months and five months. Assume the dividends are Tk. 0.50. Use the Blacks approximation to value the option. How high can the dividends be without the American option being worth more than the corresponding European option? 15. Company A, a British manufacture, wises to borrow U.S dollars at a fixed rate of interest. Company B, a US multinational, wishes to borrow sterling at a fixed rate of interest. The amounts required by the two companies are roughly the same at the current exchange rate. The companies have been quoted the following interest rates:

Company| Sterling| Dollars|
Company A| 11.0%| 7.0%|
Company B| 10.6%| 6.2%|

Design a swap that will net a bank acting as intermediary, 10 basis points per annum. Make a swap appear equally attractive to the two companies and ensure that all foreign exchange risk is assumed by the company A. 16. A currency swap has a remaining life of 2 years. It involves exchanging interest at 14% on £20 million for interest at 10% on $30 million once a year. The term structure of interest rates in both the United Kingdom and the United States is currently flat and if the swap were negotiated today, the interest rates exchange would be 8% in dollars and 11% in sterling. All interest rate are quoted with continuous compounding.

The current exchange rate is $1.65 per £1. What is the value of the swap to the party paying sterling? What is the value of the swap to the party paying dollars? 17. Calculate the price of a 2 month American put option on a non-dividend stock, which the stock price is Tk 20, the exercise price Is Tk 21 and the risk free rate is 12% p.a. Use the following binominal tree within a time interval of 1 month to calculate the price of the put option. Also state the portfolio floor that will be maintained when portfolio combined with put.

18. In each cell of the following tree upper part represents the stock price and lower one the call price Call Option price if Strike Price is 21

It is supposed that each time step is 3 months long and the risk free interest rate is 12% per annum. Initial value of the portfolio is 20.934. You are asked to apply dynamic asset allocation strategy in order to insure portfolio by investing a part into active asset (such as shares) and the rest of the portfolio into reserved asset (bond). You are asked to fill up the empty box and show necessary computations to fill up the box. 19. On June 25, the call premium on a December 25 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 = $1.8470 and put-call parity holds, what is the put premium on a December 25 contract with an exercise price of $1.81?

Disclaimer: All the questions are picked from the previous year batch questions. There may exist mistakes in both questions and solutions. So please follow it in your own responsibility.

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