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

A) The value of an option is the amount the option is in the money.

The value of Put Option = Max (0, X - S )

Where X = Strike price , S = stock price

Value of Put option = Max ( 0, 75 - 71.15)

= $3.85

Value of Call option = Max ( 0, S - X )

= Max ( 0, 71.15 - 70)

= $ 1.15

B. To calculate the portfolio position delta we need to calculate the delta of both put and call option and add the up.

Position Delta = Option Delta * No of contracts traded * 100

It is given that delta of call option is 0.7 that means if the share price increases by $1 the call will go up by $ 0.70

Total Call delta = 0.7 * 20 * 100 = $1400

ie if the stock price changes by $1 the total call value will increase by $1400.

It is also given that delta of put option is - 0. 65 which means if the price of the share falls by $ 1 the put will increase by $ 0.65.

Total Put delta = -0.65 * 37 * 100= -$2405

ie if the price of the share rises by $1 then the put will lose by -$ 2405 for 37 put options

The portfolio position delta = Total call delta + total put delta + stock delta
= 1400 - 2405 + 1005

= $ 0

C) The portfolio value before stock price change = 1005 * 72.63

=$ 72993.15

The portfolio value after the stock price change = $ 72993.15 as the portfolio position delta is 0.