5 EBF 473 Due in class, Thursday December 10 1) (40 pts) On April 22 2011, at market close, the price of BP (symbol BP) was 40.50. The prices of various call options with expiration on July 22 2015 is set out below. Given this, derive the smile for BP. Assume the annual interest rate is 3.0%. Strike Price Price $27.50 $14.17 $30.00 $11.26 $32.00 $9.30 $35.00 $6.50 $38.00 $4.00 $40.00 $2.50 $42.00 $1.61 $45.00 $0.67 $48.00 $0.27 $50.00 $0.14 $52.50 $0.10 $55.00 $0.05 $57.50 $0.06 2) (40 pts) Vulcan Gravitational Fracking (VGF) stock sells for $77 a share. The annual interest rate is 8%, and the annual standard deviation on TASF stock is 20%. The time to expiration of all options is 9 months. You are short 1000 put options on TASF with a strike price of 75. To hedge you position, you can buy or sell TSAF stock, or put options on TSAF at the money. Given all this: A: Derive the position you will take if you want to delta hedge your position. B: Derive the position you will take if you want to delta-gamma hedge your position. C: Given your answers in A and B, graph (on the same graph) the net gain or loss in your positions if the price of TASF jumps to X, X a number between 1 and 100. (So you'll want two lines on your graph, one with the return to delta hedging and one with the return to delta-gamma hedging.) 3) (20 pts) A six month call option on Harkonnen BioSands stock with a strike of 50 currently sells for 3. A put option with the same strike and expiration date sells for 2. The interest rate is 2.5 percent. Harkonnen currently sells for 52 per share. Given all this, explain your arbitrage strategy and how much money you expect to make. - Hint, sounds like a review