Black-Scholes Limits and Alternative Models for Option Pricing

Summary

The document presents Black-Scholes as a foundational model and starting point, while explaining that its simplifying assumptions do not capture several observed features of market returns. It names fat tails and skew, changing volatility over time, and return autocorrelation as examples of stylized facts that challenge assumptions such as normality, constant variance, and the Markov property.

It suggests studying models that relax one or more of those assumptions and gives GARCH option pricing as an example, since GARCH models allow volatility to vary over time. The discussion is an introductory research direction rather than a comparison of models or a pricing derivation. It offers no empirical results or reading list, so it does not establish which model performs best in practice or address the tradeoffs involved in calibration and implementation.

Key ideas

• Black-Scholes is described as a basic model and a starting point for more complex approaches.
• Market returns can exhibit fat tails, skew, changing volatility, and autocorrelation.
• These observed features conflict with assumptions used in the basic Black-Scholes framework.
• GARCH option pricing is offered as an example of a model that allows volatility to change over time.
• The document does not compare model performance or provide empirical pricing evidence.

Tags

# how to price options in reality


# how to price options in reality












I'm getting to know the Black Scholes model, which apparently is no longer suitable for pricing options on the market. I would like to write a Master's thesis on option pricing but I do not know what specific topic related to option pricing may be interesting, what model are you using now. Someone will tell me what to write about? I would also like to ask for some nice articles / books that focus on option pricing and which I could use.

## Answer by SlavicDoomer (score 1, accepted)

https://quant.stackexchange.com/a/53320

Black-Scholes model is the most basic model and is used mainly for teaching purposes or as a starting point to more complex models.

I advise you to read about "stylized facts" which are empirical observations from markets and are not captured by Black Scholes model due to simplistic assumption. For example:

- fat-tailed and skewed distribution of returns (which violates normality assumption),

- volatility clustering (which violates homoscedasticity assumption)

- autocorrelation of returns (which violates Markov property).

There are many models which relax one or more of Black-Scholes model assumptions. For instance I am currently writing my master thesis on option pricing in GARCH models which captures volatility changing over time.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.