Lecture 7 - Properties of stock options Flashcards
List six factors affecting stock option prices
Stock price - S0
Strike price - K
Time to maturity - T
Volatility - σ
Risk-free interest rate - r
Dividends - D
Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second
reason should apply even if interest rates are zero.
Delaying exercise delays the payment of the strike price. This means that the option holder is able to earn interest on the strike price for a longer period of time.
Delaying exercise also provides insurance against stock price falling below the strike price by the expiration date. Assume that the holder has an amount of cash K and that the interest rates are zero. When the option is exercised early it is worth S_T at expiration. Delaying exercise means that it will be worth max (K, S_T) at expiration.
However, deep in the money option (K is close to zero) with extremely negative interest rates could lead to a different answer.
The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put.” Explain this statement.
An American put when held in conjunction with the underlying stock provides insurance. It guarantees that the stock can be sold for the strike price, K.
If the put is exercised early, the insurance ceases. However, the option holder receives the strike price immediately and is able to earn interest on it between the time of the early exercise and the expiration date.
Why is an American call option on a dividend-paying stock always worth at least as much as its intrinsic value? Is the same true of a European call option? Explain your answer.
An American call option can be exercised at any time If it is exercised its holder gets the intrinsic value. It follows that an American call option must be worth at least its intrinsic value.
A European call option can be worth less than its intrinsic value. Consider, for example, the situation where the stock is expected to provide a very high dividend during the life of an option. The price of the stock will decline as a result of the dividend because the European option can be exercised only after the dividend has been paid, its value may be less than the intrinsic value today.
What is the impact (if any) of negative interest rates on the put-call parity result of European options?
The put-call parity still holds. The arguments are unchanged.
What is the impact (if any) of negative interest rates on the result that an American call option on non-dividend-paying stocks should never be exercised early?
Deep-in-the-money American calls might be exercised early because the option holder will prefer to pay the strike price earlier.
What is the impact (if any) of negative interest rates on the result that an American put option on non-dividend-paying stocks should sometimes be exercised early?
Deep-in-the-money American puts should not be exercised early because the option holder would rather delay receiving the strike price.
