1. What are the alternative actions Gerald and Katie’s could take in 30 days’ time?

The alternative actions that Gerald and Katie could take in 30 days’ time could be the exercise of the option since it is the American option and therefore they could exercise it even before maturity within 6 months if the prices of shares raise high in the spot market. Also, they can adopt hedging methods to overcome their risks of losses from the exercise of call options (Song & Yang, 2014).

2. How would the alternative actions in question 1 change if the options were European options?

If the options with them were European Options rather than American options, then Gerald and Katie would not be able to exercise the option within 30 days’ time which is the time period before the maturity of an option of six months. In this case, they will be only left with the option of hedging. In this method, they can buy the equal number of put options so that if the prices fall after six months, they will not have to suffer high losses.

3. What is the total cost of buying the call options today?

The total cost of buying the call option today will be equal to the amount of option premium to be paid for the purchase of the option. Gerald and Katie intend to buy 200 call option contracts and each option contract includes 100 shares. Thus, the number of shares under 200 options contracts will be 200*100 = 20,000 shares. The option premium for each share is $0.10 per share. Therefore the total cost of buying the call option contracts today will be 20,000*$0.10 = $2,000.

4. What is the cost of exercising the call options in 30 days’ time?

There will be no cost of exercising the call options in 30 days’ time since the exercise of a call option will be at $20 which is lesser than the actual share price after 30 days and thus, they will earn gains on exercising the option. However, the option premium of $2,000 paid at the time of purchase of option will be the cost of the option to them.

5. What actual gain or loss will they make if they exercise their options in 30 days’ time and the share price is $30?

If they exercise their option in 30 days’ time at an exercise price of $20 per share when the price of the share is $30 per share, they will take again since they will be able to purchase the shares at a price lesser than the market price. The actual gain will be the difference in exercise price and actual price minus the option premium paid. The gain on exercising the option will be ($30 - $20)*20,000 = $200,000. The net gain will be $200,000 - $2,000 = $198,000.

6. What are the key risks associated with Gerald and Katie’s call option strategy?

The key risks associated with the call option strategy of Gerald and Katie is that the value of share price may fall over the time and they will have to suffer losses on exercising the option. Also, the value of the option may decline due to the influence of market factors such as interest rates, market volatility etc. (Aggarwal & Gupta, 2013).

References

Aggarwal, N. & Gupta, M. 2013, "Portfolio Hedging Through Options: Covered Call versus Protective Put", Journal of Management Research, vol. 13, no. 2, pp. 118-126.

Song, D. & Yang, Z. 2014, "Utility-Based Pricing, Timing and Hedging of an American Call Option Under an Incomplete Market with Partial Information", Computational Economics, vol. 44, no. 1, pp. 1-26.