Let’s look at the impact of exercise price and time to expiration on option prices.

Exercise Price

• The price of a put option increases with the increase in exercise price. This is because the put option holder can sell the stock at a higher price.
• The price of a call option increases with the decrease in exercise price. This is because the call option holder can sell the underlying at a lower price.

To remember it easily, we can say that put option prices are directly related to exercise price and call option prices are inversely related to exercise price.

Time to Expiry

For all options (except European Puts), the longer time to expiry will increase the option’s value. This is because of increased volatility.

In case of European options, this condition doesn’t always hold true.

Remember that for European puts: pt>= Max(0, X/(1+rf)^T-t - S)

So, on one side the longer time to expiry increases volatility, which increases the option’s value, on the other side it decreases the present value of the payoff, which decreases the option’s value.

We cannot be certain whether the value will increase or decrease. To be certain about the impact on the option value, we will need to look at both volatility and discount rate. If volatility is high and discount rate is low, then the option value will increase. If volatility is low and discount rate is high, then the option value will decrease.