How Market Option Prices Relate to Implied Volatility
Summary
The document explains the direction of the relationship between traded option prices and implied volatility. For listed options, the quoted market price is established through trading and supply and demand; implied volatility is then calculated by finding the volatility input that makes a pricing model, such as Black–Scholes, reproduce that market price. It is therefore a way to express or interpret a price, rather than the source from which the market price is generated.
For an option that does not trade, the response describes estimating a volatility input from a volatility surface built from market implied volatilities at other strikes and maturities. Interpolation across strike and expiry supplies an input for pricing the less liquid contract. The document emphasizes that a model explains or represents market observations, while the traded price is the observable amount. It offers a conceptual explanation, not a particular interpolation scheme or pricing procedure. Results depend on the model and surface construction, and a surface-based estimate may differ from an executable market quote, especially where the option is illiquid.
Key ideas
- A traded option’s market price is observed directly and reflects market supply and demand.
- Implied volatility is derived by inverting a pricing model to match the observed option price.
- For an untraded option, a volatility surface can provide an input through interpolation across strikes and maturities.
- A model-based value represents market information and depends on the model and surface construction.
Tags
Full text
# How are option values in real life calculated without volatility? # How are option values in real life calculated without volatility? Implied volatility is the volatility that when inputted in the Black-Scholes model, it returns the theoretical market price of a European option value. I understand that implied volatility is not observable. However, we have access to option value in real life. How is the option value calculated in real life? All the while I thought that we need all inputs for Black-Scholes model to calculate option value. But in real life, it seems that it is different. ## Answer by Oscar (score 3) https://quant.stackexchange.com/a/54880 I'm not sure if you're asking about listed market prices but if you are, then they are just that, . market prices, i.e. they're decided by the supply and demand of the market. The implied volatility is gotten from the market prices, not the other way around, hence the term "implied. If you're asking about how the volatility is found to price options not traded on the market then you would typically use a volatility surface of the underlying to find the volatility to use when pricing your option. Essentially it means you interpolate your volatility from existing implied volatilities of the market. The implied volatility is viewed to be a function of the strike price and time to maturity in this case which is what you're interpolating between on your surface. ## Answer by David Duarte (score 2) https://quant.stackexchange.com/a/54860 Everything in the market is a price. Stock price, bond prices, bond options, interest rates, caps, equity options, swaptions, etc. Models are used to try to explain reality. The market prices of options are absolute amounts and that is what counts. You can express the prices in volatilities (Black vol or others) but that is just a representation of a market price.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.