However if the market price of google goes to $110, i could, and probably would

Question

However if the market price of google goes to $110, i could, and probably would use my right to buy at 105, sell at 110 and pocket the difference. This type of instrument is called an 'option' as I, the owner, have the option to use or not use my right of ownership. Based on the price. Lets use the simple risk model we discussed in class. Ie, there is a 50/50 chance of one of two outcomes happening. Specifically, there is a 50% chance Google will go to $110, and a 50% chance it will go to $90. a) How much would you expect the call option to sell for?

Explanation / Answer

The option would sell at a price such that irrespective of the actual price outcome, there are zero arbitrage opportunities (opportunity to make a riskless profit) through a combination of using the expected stock price and the option's strike price ($ 105 in this case).

Price Scenario 1: Price = $ 110 and Probability = 50 %

Price Scenario 2: Price = $ 90 and Probability = 50 %

Expected Price = 0.5 x 110 + 0.5 x 90 = $ 100

Strike Price = $ 105

As the expected price of the option is lesser than the strike price, the option holder is not expected to make any profit by holding the option. Hence, the market value of the call option will be zero.

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