How Volatility Changes an Option’s Value Before Expiration
Summary
This beginner discussion distinguishes an option’s payoff at expiration from its value before expiration. Changing volatility does not alter the European option’s terminal payoff diagram; it changes the premium beforehand by changing the range of possible underlying prices and the chance that the option finishes in the money. Because an option’s downside is limited to its premium while a call can benefit from a price rise, greater uncertainty can increase its value.
The answer also points to time remaining and volatility as influences on the option’s time value, with that value disappearing at expiration. It gives an intuitive explanation rather than a worked formula or numerical example. One reply’s statement that an at-the-money option has zero value five days before expiry confuses intrinsic value with total option value: it may have little or no intrinsic value while still carrying time value. The discussion is therefore useful as an introduction, but is not a full pricing treatment and does not address assumptions such as interest rates, dividends, or volatility dynamics.
Key ideas
- Volatility affects an option’s value before expiration by changing the distribution of possible underlying prices.
- A European option’s payoff at expiration is determined by spot price and strike, not by volatility.
- An option’s limited downside and potential upside make greater volatility valuable to its holder.
- Time value generally diminishes as expiration approaches and is gone at expiration.
- An at-the-money option can retain time value before expiration even when its intrinsic value is zero.
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Full text
# How does volatility affect an option payoff diagram?
# How does volatility affect an option payoff diagram?
I am a beginner to financial mathematics, and my lecturer asked me to ponder about how volatility may affect the value of an option (as a function of spot price). For example, if an option had a (daily) volatility of 1%, how would the option value look like say 5 days before expiry? So far, the only quantity I know which can affect the value time-wise is interest rate - an extra factor of $\text{e}^{-rt}$ needs to be applied, and the step-function becomes slightly curved. I haven't seen any resources which describe how volatility comes into play. Will greatly appreciate some explanation about this! (I have seen an upvoted question about volatility and binary options, but it’s quite out of my depth!)
## Answer by Preston Lui (score 3)
https://quant.stackexchange.com/a/59201
The option payoff diagram for European Option will be exactly the same.
The intuitive reason that option value changes with volatility is that it changes the probability of winning the jackpot.
Think about it, options provide you downside protection. So, for example, when the stock is volatile, it has a higher probability of getting to a high price. If you held a call option, you got the jackpot. If the stock dropped, you don't care how much it drop below the strike price. It kind of creates an asymmetry of risk and benefit.
Of course, there is no free lunch in derivative markets, it makes option with high underlying volatility worth more and priced higher.
## Answer by tatvamiam (score 1)
https://quant.stackexchange.com/a/59200
Have you reviewed the Black Scholes formulae? For a given spot price, volatility is back-calculated based on options premium that investors are willing to pay.
Given constant volatility as you suggest, the option value will decay as it gets close to the expiration. In other words, an option at a strike price equal to spot price, will have an intrinsic value 5 days from expiration (this is the option premium that an investor is willing to bet on the price of the underlying asset at expiration). Simply put, this premium is dependent on 1)volatility and 2)the time left to expiration. At expiration, the time remaining goes to zero, so the intrinsic value also becomes zero ie an option at strike price =spot price will have zero value. HTHShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.