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.

A)	new Call option premium?
	new Put option premium?
B)	Position delta?
C)	Portfolio value before the change?
	Portfolio value after the change?

Answer 1

Hi,

Delta of a product is how much the value of the option would change with $1 change in the spot price.

We have the following information available with us:

A	Current Spot		72.63
	Put Strike		75		Call Strike		70
	Put Premium		5		Call Premium		5.6
	Delta		-0.65		Delta		0.7
	As the spot prices have moved
	New Spot=		71.15
	Difference between the spots			-1.48
	Put Premium canges by delta times change in spot
	0.962
	Call Premium canges by delta times change in spot
	-1.036
	New Put Premium		5.962
	New Call Premium		4.564
B	New portfolio
	Portfolio delta is the weighted average of the delta of the constituents
				Delta	Weighetd Delta
	Stocks		1005	0	0
	Call		20	0.7	14
	Put		37	-0.65	-24.05
				Weighted average		-0.00946
C	Portfolio value before change
				Price
	Stocks		1005	72.63
	Call		20	5.6
	Put		37	5
				73290.15
	Portfolio value after change
				Price
	Stocks		1005	71.15
	Call		20	4.564
	Put		37	5.962
				71817.62