Why ANN Option Pricing Comparisons Need Market-Based Validation
Summary
The document examines claims that artificial neural networks outperform Black–Scholes in option pricing. The cited study generates Black–Scholes estimates using simplified inputs, including a closing spot price, fixed volatility and interest rate, no dividends, and discrete time to expiry, then compares those estimates with market quotes. An ANN is trained on weighted inputs, and its reported mean squared error is compared with the model’s error against those same quotes.
The answer argues that an apparent ANN advantage may result from correcting flawed Black–Scholes inputs rather than demonstrating that neural networks outperform a properly specified model. It identifies missing quote-time spot prices, dividends, term-dependent interest rates, implied volatility, and exact expiry timing as relevant sources of mispricing. The discussion questions the study’s setup but offers no independent reanalysis or numerical evidence; a fair comparison requires market observations and appropriate inputs for both approaches.
Key ideas
- An ANN comparison requires a clear target, such as observed option market quotes.
- A Black–Scholes benchmark built from simplified inputs may be mispriced before comparison.
- The cited study uses fixed volatility and rates, omits dividends, and does not use exact expiry timing.
- An ANN may improve results by correcting input assumptions rather than by capturing relationships beyond analytical models.
- A credible comparison should use appropriately specified inputs and identical evaluation data.
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Full text
# The metric to evaluate the efficiency of ANN based option pricing over mathematical option pricing models # The metric to evaluate the efficiency of ANN based option pricing over mathematical option pricing models The stock exchanges provide the data of option prices using theoretical formulations such as Black-Scholes formula. The dataset necessary for training an artificial neural network (ANN) to address option pricing models, specifically the Black-Scholes model, has already been produced using the same formulas. However, the literature claims that ANNs can capture more realistic and broadly applicable market assumptions, including non-linearity and stochastic volatility. I wonder how can we substantiate, through mathematical reasoning, the claim that ANNs are more effective than exact and numerical solutions? OR On what basis should I justify ANNs can potentially capture and generalize complex relationships between the variables in a way that analytical or numerical methods may not? In a paper entitled "A neural network model for estimating option prices", the author claims 'Approximately for half of the cases that they examined, mean squared error for the neural network is smaller than that of Black-Scholes, which implies the good performance of ANN relative to Black and Scholes'. I know how to calculate the MSE error of ANN predictions from Black-Scholes formula. What does the phrase 'smaller than that of Black-Scholes mean'? How is the MSE error of the BS formula calculated? Relative to what it is calculating? From where that true data we get? How does that true data generate? Can I say the error comes due to continuous evolution of the Black–Scholes models over time, such as regime switching, Jump diffusion, variable volatility, stochastic volatility, fractal dynamics, etc.? Thanks for your valuable response in advance. ## Answer by AKdemy (score 2, accepted) https://quant.stackexchange.com/a/77713 The paper that you last linked in a comment can be accessed free of charge and if the original paper is using something similar it's a tautology that the ANN model is better. The author describes that he uses (section 4.1) - the closing spot price but - for option prices he uses all exercise prices available on a given day (no matter the time) - a fixed risk free interest rate (obtained from discount rates of Treasury bills), - a fixed volatility, obtained as the 60 day standard deviation of historical returns - no dividends - only discrete days (not exact time to expiry) After that, the author computes the value of nifty call options from these inputs with Black Scholes and compares the results with market quoted prices. Subsequently, the author assigns weights to all inputs (section 4.3) and runs the model. The claim is that this is better than Black Scholes, which is in my humble opinion complete bogus for at least the following reasons: - you would need the spot price at the time of the option quote - nifty pays dividends (I think, didn't check in detail) but they are completely neglected - using a fixed historical IV is completely mispricing options as shown for example in this answer - risk free interest rates are not constant across all expiries - exact time to expiry is important, especially for options with shorter maturity (the link showing how using historical vol misprices options also uses exact time to expiry, visible on the code where T+m is computed) To sum up, by assigning weights to each input the author simple corrects the inputs into Black Scholes for all mis-specifications the author has. The procedure is completely ignoring how Black Scholes is used in the market and I am honestly surprised you can actually write papers like that.
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