Why Complex Option Models Matter and How Implied Volatility Helps
Summary
The discussion asks whether detailed option pricing research is useful when traders often apply Black–Scholes and absorb real-world frictions, such as changing borrow costs and wider spreads, into its inputs. The answer points out that options span several markets, including rates, futures, and foreign exchange, where assumptions can sometimes be modeled with greater precision than in equities.
For equity options, event risk and other hard-to-model features limit the value of increasingly elaborate assumptions. Black–Scholes can still serve a practical role as a nonlinear conversion from option prices to implied volatility. That common measure makes contracts easier to compare across strikes, whose prices can vary widely. The discussion offers a conceptual rationale rather than empirical evidence or a quantitative comparison of models. It does not claim that implied volatility captures all frictions, or that complex models are useless; model choice depends on the market and the intended use.
Key ideas
- Option model complexity can be more useful in markets whose behavior is easier to characterize than single-name equities.
- Equity options face event and trading frictions that can be difficult to represent precisely.
- Black–Scholes is often used to convert option prices into implied volatility rather than as a literal market model.
- Implied volatility provides a common basis for comparing option contracts across strikes.
- The discussion gives conceptual reasoning, not empirical tests of model performance.
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Full text
# What's the point of complex option formula adjustments? # What's the point of complex option formula adjustments? I had a discussion with a colleague of mine about the implications of risk modelling for the Gamestock/Wirecard cases in the recent weeks and that stock borrow rates could be an important risk factor at times, joint with the situation of different lending/borrowing fees. This makes option pricing models potentially quite complex, having to solve optimal control problems in some cases. But what's the point if your average trader simply uses Black-Scholes (BS) and fudges all those real-wold problems like widening spreads, suddenly significant borrow rates, etc. etc. into the "risk-free rate" (with which we all can borrow and lend any amount, sure cough), the "volatility of the stock" (yeah, we all know about that one.) and so on? Doesn't that render most of the body of mathematical research there useless, even if it starts taking more and more realistic assumptions? ## Answer by Brian B (score 4, accepted) https://quant.stackexchange.com/a/61092 > what's the point if your average trader simply uses Black-Scholes (BS) and fudges all those real-wold problems like widening spreads, suddenly significant borrow rates, etc. etc. into the "risk-free rate" (with which we all can borrow and lend any amount, sure cough), the "volatility of the stock" (yeah, we all know about that one.) and so on? Keep in mind that not all options are equity options. We also have interest rate swaptions, futures options, FX options, et cetera. Equity options really have about the most "hair" because they come with so many difficult- or impossible-to-model events, as you note. So, one point of the complicated option models is to deal with these cases that have more attainable precision. In fact, it is a general principle that, the simpler a phenomenon is, the more complex one can make the mathematics successfully applied to it (think of quantum mechanical models of the helium atom versus, say, demographic research). With all the "hair" on equity options, we need simple mathematics. Here, Black Scholes is used but not really as a model per se. Instead it is employed as a highly nonlinear transformation between option prices and an unobservable parameter that we happen to call implied volatility. This helps create numbers that are more directly comparable between option contracts, since the option prices themselves exhibit extremely high dynamic ranges over various strikes.
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