Derivatives Short Problems Problem 1 An investor purchases a call option with an exercise price of $55 for $2.60. The same investor sells a call on

Derivatives Short ProblemsProblem 1An investor purchases a call option with an exercise price of $55 for $2.60. The same investor sells a call on the same security with an exercise price of $60 for $1.40. At expiration, 3 months later, the stock price is $56.75. All other things being equal and given an annual interest rate of 4.0%, what is the net profit or loss to the investor?Problem 2Corn call options with a $1.70 strike price are trading for a $0.15 premium. Farmer Jayne decides to hedge her 20,000 bushels of corn by selling short call options. Six-month interest rates are 4.0% and she plans to close her position and sell her corn in 6 months. What is herprofit or loss if spot prices are $1.60 per bushel when she closes her position?Problem 3Consider an investment in five S&P 500 Index futures contracts at a price of $924.80. The initial margin requirement is 15.0% and the maintenance margin is 10.0%. If the continuously compounded interest rate is 5.0% what will the futures price need to be for a margin call to occur 10 days from now? Assume no settlement within the 10 days.Problem 4Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55.00 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. Draw a profit and loss graph illustrating the arbitrage.Problem 5Using a binomial tree, what is the price of a $40 strike 6-month call option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35Problem 6Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short put position if the option expires in 60 days and the price rises to $50.00 after 5 days?Problem 7 A commodity linked bond is issued with an embedded call option. The current commodity price is $110, as is the exercise price on the call option. The call option is priced at $3.41. If the promised payment on the bond is the same as the issue price of $100, what is the implied coupon if effective interest rates are 3.0% and the bond has a 1-year maturity?Problem 8A company issues an option grant with an outperformance feature, against the S&P 500. Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance option?