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) Delta of an option indicates the change in the price of the option for a unit change in the price of its underlying security.

Initial Price of stock = $72.63

Price changed to $71.15 -> there is a decrease in price = $71.15-$72.63 = - $1.48

Delta of option = N -> For $1 increase in stock price, the call option price increases by N and vice versa -> (Delta of an option*price change of the stock) gives the price change of the option

Value of put option on Oct 3rd = Initial Value + (Delta of put*change in the price of the stock)

= $5.00+(-0.65*(-1.48))

-> Value of put option on Oct 3rd = $5.962

Value of call option on Oct 3rd = Initial Value + (Delta of call*change in the price of the stock)

= $5.60+(0.7*(-1.48))

-> Value of call option on Oct 3rd = $4.564

B) Portfolio = 1,005 stock+20 call options + 37 put options

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

-> (Portflolio) = 1,005*1 + (20*0.7)+(37*(-0.65)) (Since the delta of a stock = change in price of stock for unit change in price of stock = 1. Delta of stock is always =1)

-> (Portflolio) = 994.95

C)

Porfolio Value before the change of price = 1,005 stock+20 call options + 37 put options

= (1005*72.63)+(20*5.6)+(37*5.00)

= 73,290.15

Porfolio Value before the change of price = $ 73,290.15

Price changed from 72.63 to 71.15 -> change in stock price = -1.48

Porfolio Value after the change of price = Porfolio Value before the change of price+ (Delta of portfolio*change in price)

Porfolio Value after the change of price = 73,290.15 + (994.95*(-1.48))

= 71,817.624

Porfolio Value after the change of price = $71,817.624