Set out the factors that drive an option's value
The idea
Six inputs determine an option's value: the underlying price, the exercise price, time to expiry, the risk-free rate, volatility of the underlying, and any cash flows on the underlying such as dividends. A call gains value as the underlying rises, as volatility rises, and generally as time to expiry lengthens; a higher risk-free rate helps a call and hurts a put because the exercise price is discounted more heavily. Dividends work the other way, reducing call values and raising put values, since the holder of the option does not receive them.
A practice question
How does an increase in the volatility of the underlying affect the value of both a call and a put?
- It raises both — correct
- It lowers bothWhy not: Reverses the effect. More dispersion means more chance of a large favourable move, with the downside still floored at zero.
- It raises the call and lowers the putWhy not: Volatility is directionless. Both options gain from a wider range of outcomes.
Options have asymmetric payoffs: the upside from a large move is kept while the downside is truncated at zero. Wider dispersion is therefore valuable to both holders.
A harder one
Why does a higher risk-free rate raise the value of a call option?
- Because the underlying is expected to grow fasterWhy not: An expected growth rate does not enter a no-arbitrage option value; the effect runs through discounting.
- Because the present value of the exercise price the holder will pay is lower — correct
- Because volatility rises with interest ratesWhy not: No such general relationship holds, and volatility is a separate input.
The call holder pays the strike only at exercise, in the future. Discounting that obligation at a higher rate makes it cheaper in present value terms.
The hardest tier
Why can a longer time to expiry occasionally reduce the value of a European put?
- Because volatility always falls over longer horizonsWhy not: Volatility over a longer period is generally larger in total, which raises value rather than lowering it.
- Because European puts cannot be exercised earlyWhy not: True, and it is the condition that allows the effect rather than the mechanism behind it, which is the discounting of the strike.
- Because the exercise price the holder will receive is discounted over a longer period — correct
The deep-in-the-money European put's value is close to the discounted strike. Pushing the receipt further out lowers its present value, and that effect can outweigh the added time value.
In the app: 12 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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