1) An interest rate swap has 3 years of remaining life. Payments are exchanged annually. Interest at 3% is paid and 12-month LIBOR is received. A exchange of payments has just taken place. The 1 year, 2 years and three years LIBOR/swap zero rates are 2%, 3% and 4%. All rates an annually compounded. What is the value of the swap as a percentage of the principal when LIBOR discounting is used?
2) You observe the following in relation to a 4-month European put option on the S&P200 index.
Strike price of 3400
The S&P200 Index is currently at a level of 3600
The dividend yield is on the S&P200 Index is 4% p.a compounded quarterly
The risk free interests rate is 5% p.a compounded semi-annually
The volatility of the S&P200 Index is 25% p.a.
REQUIRED:
Use Black-Scholes option pricing model to value the put option. State any assumptions you make.
3) A futures is currently at $75. The risk free interest rate is 6.5% p.a. compounded monthly. The volatility of the futures price is 30% p.a. continuously compounded. Using binomial option pricing model, what is the value of 6-month American call option on the futures contracts with strike price of $50? You may assume there are 2 time steps of 3 months each. In providing your answer be sure to include a diagram of the binomial tree with all nodes carefully labeled.
4) a) Use put-call parity to show that the cost of butterfly spread created from European outs is identical to the cost of butterfly spread created from European calls.
b) A trader creates a long butterfly spread from options with strike price $60, $65 and $70 by trading a total of 400 options. The options are worth $11, $14 and $18. What is the maximum net gain( after the cost of the option is taken into account)?
c) Six-month call option with strike price of $35 and $40, cost $6 and $4, respectively. What is the maximum gain when the bull spread is created by trading a total of 200 options?