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.

Answer 1

Answer ;

A)

* Firmly we need to find out the change in stock price to get the values of the put and call options.
* Delta indicates the change in the price of the option
*Initial Price of stock = $72.63, then it changed( decreased)to $71.15
*change in stock price (Initial Value + (Delta of call*change in the price of the stock)) = 71.15 - 72.63 = -1.48
*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
Value of call option on Oct 3rd =  5.6 - 1.036 = 4.564

B)
(Portflolio) = 1,005* (stock) + 20* (call) + 37* (put)

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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