Why Option Models Change Implied Volatility Surfaces but Not Market Prices
Summary
This question examines the claim that Black–Scholes–Merton often serves as an interpolation framework for quoting actively traded options. Traders can infer implied volatility from market prices, even though the model’s constant-volatility assumption does not fully describe observed smiles. The question asks how changing to another plausible pricing model could alter the volatility surface if market prices remain broadly stable.
The central distinction is that implied volatility is defined relative to a particular model: the same option prices can map to different volatility parameters under different models. Prices of actively traded options anchor the calibration, while model choice affects the parameter surface and the Greeks used for hedging. The document poses this conceptual issue but provides no answer or quantitative comparison, so it does not establish how large such differences would be in practice.
Key ideas
- Implied volatility is a model-dependent parameter inferred from observed option prices.
- Similar market prices can correspond to different volatility surfaces under different pricing models.
- Model choice affects calculated Greeks and therefore hedging decisions.
- Models have greater influence when comparable derivatives do not trade actively.
- The document poses the conceptual question but supplies no worked answer or evidence.
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Full text
# Black-Scholes-Merton and alternatives as interpolation tools # Black-Scholes-Merton and alternatives as interpolation tools This is a not very quantitative question, but is nevertheless related to quantitative methods in Finance. I was reading the following paragraph from Hull's Options, Futures, and other Derivatives: > It can be argued that the Black–Scholes–Merton model is no more than a sophisticated interpolation tool used by traders for ensuring that an option is priced consistently with the market prices of other actively traded options. If traders stopped using Black–Scholes–Merton and switched to another plausible model, then the volatility surface and the shape of the smile would change, but arguably the dollar prices quoted in the market would not change appreciably. Greek letters and therefore hedging strategies do depend on the model used. An unrealistic model is liable to lead to poor hedging. Models have most effect on the pricing of derivatives when similar derivatives do not trade actively in the market. If I understand correctly what Hull means, the point of his sentence is: - we have a model for pricing derivatives which is based on the no-arbitrage principle and on the assumption that the underlying asset follows a geometric Brownian motion with constant drift and volatility. - If we try to apply the model, we discover that we lack one crucial parameter, which we infer from actual market prices (the implied volatility). - The volatility smile tells us that the constant volatility assumption is not completely justified, but nevertheless we can still use the model and the market data to price new options. But then, why is Hull writing that if we used another plausible model, the volatility surface would change? If the prices of the options do not change, when we use this data to compute implied volatilities (using the Black-Scholes-Merton model), the volatilities would still be the same, right?
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