On Sept 30th, 2011, Exxon Mobil (XOM) stock was traded at $72.63 while the Decem

Question

On Sept 30th, 2011, Exxon Mobil (XOM) stock was traded at $72.63 while the December XOM put option with $75 exercise price is traded at $5.00 and the December XOM call option with $70 exercise price is traded at $5.60. The put option's delta is -0.65 and the call option's delta is 0.7.

A) On October 3rd, XOM stock price changed to $71.15 on Oct 3rd, what will be the values of the put and call options?

B) Consider a portfolio composed of:

1,005 XOM stocks

20 Dec XOM Call options

37 Dec XOM Put options

     What is the portfolio position delta?

C) Using the portfolio position delta, calculate the portfolio value before AND after the stock price change.

Explanation / Answer

change in stock price = 71.15 - 72.63 = -1.48

A) change in put option value = -1.48 * -0.65 = 0.962

new put option value = 5 + 0.962 = 5.962

change in call option value = -1.48 * 0.7= -1.036

new call option value = 5.6 - 1.036 = 4.564

B) portfolio delta =1*1005 + 0.7 * 20 - 0.65*37 = 994.95

C)portfolio value before change = 1005*72.63 + 20*5.6 + 37*5 = 72993.15+112+185= 73290.15

change in portfolio value after change = change in stock value * delta = -1.48 * 994.95 = -1472.526

new portfolio value = 73290.1 -1472.526 = 71817.624

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