Factors affecting value of an option
Factors |
Value of European call option |
Value of European put option |
Value of underlying |
Directly proportional |
Inversely proportional |
Exercise price |
Inversely proportional |
Directly proportional |
Time to expiration |
Directly proportional |
Directly proportional with the exception of long-dated options, deep-in-the-money options, higher-risk free rate |
Risk-free rate |
Directly proportional |
Inversely proportional |
Volatility |
Directly proportional |
Directly proportional |
Benefits |
Inversely proportional |
Directly proportional |
Costs |
Directly proportional |
Inversely proportional |
Check your concepts:
(58.18) Which of the following factors is least likely to impact the call and put options differently?
(a) Time to expiration
(b) Risk-free rate
(c) Costs associated with holding the asset
(58.19) What will be the most likely impact on the value of a European call option with a decrease in the risk-free rate?
(a) Increase
(b) Decrease
(c) No impact
(58.20) Which of the following options is likely to be most valuable on the same underlying trading at $100?
(a) European put option with exercise price of $80 and two months to expiry
(b) European put option with exercise price of $80 and three months to expiry
(c) European put option with exercise price of $75 and two months to expiry
(58.21) Which of the following factors is least likely to be favorable for the value of a European call option?
(a) Increase in exercise price
(b) Increase in underlying price
(c) Increase in risk-free rate
Solutions:
(58.18) Correct Answer is A: The risk-free rate impacts the call and put options in opposite way. The costs of holding the asset also impact the options in opposite way. Both call and put options increase in value with increase in the time to expiration with the exception of European deep-in-the-money put option with a higher risk-free rate, low volatility and longer time to expiration.
(58.19) Correct Answer is B: The European call option will decrease in value with a decrease in the risk-free rate as the call option value is directly proportional to the risk-free rate.
(58.20) Correct Answer is B: The European put options increase in value with increase in time to expiration with exception of deep-in-the-money put options or when the time period is too long. The lower is the exercise price of the European put option, the lower is its value. Therefore, the European put option with an exercise price of $80 and three months to expiration will have the maximum value.
(58.21) Correct Answer is A: An increase in risk-free rate and the underlying price will lead to an increase in the value of a European call option. An increase in the exercise price will decrease the value of a European call option.
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