See attached. Please include all calculations. Thanks

Homework 5 - corrected 10-27-2016 EBF 473 Fall 2016 Due in class, Thursday November 3 1) (25 pts) On April 22 2015, 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 8.0%. 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) (50 pts) Ceres Monopole Extraction (CME) stock sells for $42 a share. The annual interest rate is 5%, and the annual standard deviation on CME stock is 20%. The time to expiration of all options is 15 months. You are short 4000 put options on CME with a strike price of 45. To hedge you position, you can buy or sell CME stock, or put options on CME 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 CME jumps to X, X a number between 20 and 70. (So you'll want two curves on your graph, one with the return to delta hedging and one with the return to delta-gamma hedging.) 3) (25 pts) Use the Black-Sholes equation to price a call option on Ceres Monopole Extraction using the information in question 2 and a strike price of $55 and an exercise date 36 months in the future