Question

2. Joel Franklin is a portfolio manager responsible for derivatives. Franklin observes an American-style option and a European-style option with the same strike price, expiration, and underlying stock. Franklin believes that the European-style option will have a higher premium than the American-style option.

a. Critique Franklin’s belief that the European-style option will have a higher premium. Franklin is asked to value a one-year European-style call option for Abaco Ltd. Common stock, which last traded at $43.00. He has collected the following information:

Closing stock price $43.00

Call and put option exercise price $45.00

One-year put option price $ 4.00

One-year Treasury bill rate 5.50%

Time to expiration One year

b. Calculate, using put-call parity and the information provided, the European-style call option value.

c. State the effect, if any, of each of the following three variables on the value of a call option: (1) an increase in short-term interest rate, (2) an increase in stock price volatility, and (3) a decrease in time to option expiration.

Answer 1

ANSWER

a.) If the stock is non-dividend paying stock, both American and European Call-Put options should carry the same value. The prime difference is that American option can be exercised any time whereas European option can be exercised only at expiry. In case, there is some differential existing in the price, then that must be due to early exercise of American options and time value of money explaining the variation.

b.) Using Put-Call parity relationship, Call option price will be given by,

C = S + P – K / (1+r)^T

   = 43 + 4.00 - 45 / (1.055)¹

   = 47.00 - 42.6540

   = 4.346

c.) Increase in Short term interest rate = Call options prices are positively impacted with increase in rate whereas the Put prices are negatively impacted with increase in interest rates.

Increase in price volatility = Direct impact i.e. increase in volatility will lead to increase in option prices.

Decrease in time to Option Expiration = Direct impact i.e. as options near to expiry, their price reduces and become more reflective of spot prices.

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