Market-Calibrated and Prescriptive Models of Option Value
Summary
The document contrasts two meanings of an option’s “true” value. A prescriptive model aims to estimate what the option should be worth independently of its observed market price. A descriptive model instead takes market prices as inputs and calibrates parameters, often implied volatility, to make prices comparable and maintain consistency across instruments. Hedging arguments and risk-neutral assumptions are described as common ways to impose that consistency.
The distinction is connected to trading roles: a buyer seeking mispricing may rely on an independent valuation view, while a seller may use a calibrated model to manage a book and earn spreads. The answer cautions that apparent pricing inconsistencies may not be monetizable once trading frictions are considered. It offers a conceptual framework rather than a procedure for calculating a benchmark price, and it does not claim that either model type reveals an objectively correct value. The usefulness of a model depends on its purpose and business context.
Key ideas
- A prescriptive model estimates option value independently of market prices.
- A descriptive model calibrates its parameters to observed prices, often using implied volatility.
- Hedging arguments and risk-neutral assumptions can support consistency across option prices.
- Buy-side searches for mispricing and sell-side spread management can call for different model uses.
- Transaction frictions can prevent traders from exploiting apparent pricing inconsistencies.
Tags
Full text
# Finding the True Option Value # Finding the True Option Value Many research papers use differing solution methods to attempt to find the 'true' value of an option whether it be Euro, American, etc. They never mention how they do find the true option value to test against however. Which becomes my question: how does one find the true value of an option for given input variables to test against? Appreciate any help. ## Answer by vonjd (score 3) https://quant.stackexchange.com/a/31668 Basically it boils down to this: You either use a descriptive or a prescriptive (normative) model, i.e. you either think that the market is always right or you think that you alone know how to determine the "true" price of an option. The original idea of BS was to build a prescriptive model but most modern models try to take the market prices as given and calibrate their models accordingly, thereby gaining one common variable to make all prices comparable: volatility. One prerequisite is to seek consistency for all prices which is normally done via hedging arguments (which often leads to risk-neutrality assumptions). Yet in practice even in the case of minor inconsistencies they often cannot be used to make money due to friction. At the end it all boils down to your business model (this is what I meant with my question about the true value of a stock). When you are on the buy side you try to find mispriced options with a prescriptive model (so you are saying that you know which is the true price - and all other market participants are wrong). When you are on the sell side you use a calibrated descriptive model which mainly seeks consistency so that you can live on the spread. (This is why I gave this link in the comments: How do we use option price models (like Black-Scholes Model) to make money in practice?) So in a way truth is relative: It either means overall consistent with the market or it means smarter than the market.
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