Question

You long a European call option on Info Systems Technology (IST) stock with a strike price of $25. The option will expire in exactly three months’ time. a. Briefly explain the difference between American and European options. b. What are the key determinants of option price? Briefly explain two of the key determinants: why they have a relationship with the option price. c. If the stock is trading at $35 in three months, what will be the payoff of the call option? d. If the stock is trading at $16 in three months, what will be the payoff of the call option? (2 marks

Answer 1

a.

A European option cannot be exercised before maturity while an American option can be exercised before maturity. Due to this, generally, an American option is priced at least equal to the European option, since it provides the buyer the right to exercise it early.

b.

Key determinants of option prices are:

Value of the underlying - Option prices depends on the value of the underlying security. For a call option, as the value of the underlying increases, the call option value increases.Conversely, a put option value increases if the value of the underlying security decreases.

Volatility - Higher volatility increases the value of both call and put option. Since options have limited downside (equal to the premium paid), the upside can be potentially unlimited. Hence, higher the volatility, higher is the expected payoff for the option buyer.

c.

A call option will have a positive payoff since the stock price at maturity is higher than the strike price.

Payoff of the call option = Spot price at maturity - Strike price

Payoff of the call option = $35 - $25 = $10

d.

A call option will have a zero payoff since the stock price at maturity is lower than the strike price.

Hence, payoff of the call option = 0