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.

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

Explanation / Answer

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

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