Model-Free Finance and Option Prices Without a Specified Pricing Model
Summary
The document asks what model-free finance means and presents two possible interpretations. One strand studies which derivative prices are consistent with the absence of arbitrage, using current prices of traded options on the same underlying rather than committing to a conventional pricing model. The cited survey situates this work alongside Black–Scholes results, volatility surfaces, and the Breeden–Litzenberger and Dupire formulas.
A second answer connects the idea to game-theoretic probability, where pricing arguments may be developed through strategies rather than probability measures. The discussion uses a simple binomial option as intuition for avoiding an explicit risk-neutral measure. These are pointers and sketches, not a full definition or a technical treatment; the document does not establish that every use of “model-free” has the same meaning. The practical takeaway is that the term can refer to deriving valuation or hedging constraints from market prices and arbitrage arguments with fewer probabilistic assumptions.
Key ideas
- Model-free derivative research can identify prices consistent with no arbitrage from observed option prices.
- The cited survey relates this approach to volatility surfaces and standard option-pricing formulas.
- Game-theoretic probability offers a related view that uses strategies instead of probability measures.
- The term is presented through references and intuitions rather than a single definitive definition.
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Full text
# What is model-free finance? # What is model-free finance? I have run across the term "model-free finance" (e.g. there was a Thalesian talk in London recently), yet haven't found any real definition of it nor anything really substantial. Could you point me to resources or material which could provide some ideas what this new approach is all about? ## Answer by Richi Wa (score 3, accepted) https://quant.stackexchange.com/a/36614 Carefully searching Mark Davis' webpage I found this article Model-Free Methods in Valuation and Hedging of Derivative Securities which seems to be a survey on this topic. I quote from the abstract: > In contrast to conventional model-based derivative pricing, a recent stream of research aims to investigate what prices are consistent with absence of arbitrage, given only the current prices of traded options on the same underlying. This paper gives a succinct survey of work in this area. After summarising results on the Black-Scholes model, the volatility surface and the Breedon-Litzenberger (BL) and Dupire formulas, the two main streams of work are described. ## Answer by Bjørn Kjos-Hanssen (score 1) https://quant.stackexchange.com/a/36612 It sounds a bit like the game-theoretic probability (GTP) of Shafer and Vovk. See http://www.probabilityandfinance.com As you know when pricing a simple binomial option, instead of talking about risk-neutral measure you can argue directly that a certain price is correct (by linearity essentially). In GTP they keep going in that direction and try to eliminate probability measures in favor of game strategies. So if this is right then model-free really means probability-measure-free.
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