Suppose that call options on ExxonMobil stock with time to expiration 3 months and strike price $104 are selling at an implied volatility of 28%. ExxonMobil stock currently is $104 per share, and the risk-free rate is 6%. If you believe the true volatility of the stock is 30%. a. If you believe the true volatility of the stock is 30%, would you want to buy or sell call options? Buy call options Sell call options b. Now you need to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold? (Round your answer to 4 decimal places.)

Explanation:

a). The price of options is directly related to implied volatility. An increase in implied volatility will result in a rise in the price of options, and a decrease in implied volatility will result in a fall in the price of options.

If the true volatility is higher than the implied volatility, the implied volatility can be expected to rise to match the true volatility. This will result in a rise in the price of the call option (other factors being unchanged).

Therefore, you would want to buy call options as the price of call options can be expected to rise.

b)

d1 = (ln(S0 / K) + (r + σ2/2)*T) / σ√T,

Given

Stock price = $104

Interest rate = 6%

Exercise price = $104

True volatility = 30%

Implied volatility = 28%

Time to expiration = 0.25

The solution is shown in the picture attached

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