Reference no: EM132443101
Problem 1: 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 July22 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
|
Problem 2: Ceres Monopole Extraction (CME) stock sells for $77 a share. The annual interest rate is 3%, and the annual standard deviation on TASF stock is 30%. The time to expiration of all options is 6 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 TASFjumps to X, X a number between 1 and 200. (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.)
Problem 3: 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 $75 and an exercise date 3 months in the future.