Problem 2.6. (5 points) We are given the following European-call prices for opti

Question

Problem 2.6. (5 points) We are given the following European-call prices for options on the same underlying $50-strike $11 $55-strike $6 $60-strike $4 Assume that the continuously compounded interest rate is strictly positive. Which of the following portfolios asset: would exploit an arbitrage opportunity stemming from the above stock prices? (a) The call bull spread only (b) The call bear spread only. (c) Both the call bull and the call bear spread. (d) Neither the call bull or call bear spread, but there is an arbitrage opportunity (e) There is no apparent arbitrage opportunity

Explanation / Answer

An investor creating a spread buys and sells the same type of option with different strike prices having same maturity. A spread limits the profits and also limits the loss to the investor. So, their would be no arbitrage with respect the stock prices. However, arbitrage is possible with respect the option premiums.

A bull spread is created by buying an option at a lower price and selling option at a higher stike price. In this case, the investor will pay option premium on the option bought and receive premium on the option sold. In our case, the investor will have a loss in all the cases -

Therefore, no arbitrage in this a bull spread.

In a Bear spread, the investor does the exact opposite , i.e., buy option with higher stike price and sell option with a lower strike price. Lets see the combinations -

Therefore, arbitrage is possible in a Bear spread. Option (b) is correct.

Combination Net Premium Received / (Paid) Buy $50 option and sell $55 option $6 - $11 = ($5) Buy $55 option and sell $60 option $4 - $6 = ($2) Buy $50 option and sell $60 option $4 - $11 = ($7)

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