Why Option Prices Can Be Difficult to Fit Directly

# Numerical difficulties in fitting option prices


# Numerical difficulties in fitting option prices












In [1], the authors state that "Although some studies apply the curve-fitting method directly to option prices, the severely nonlinear relationship between option price and strike price often leads to numerical difficulties. [...], we apply the curve fitting method to implied volatilities instead of option prices".

I've seen this kind of statement made in many other places before, but I haven't yet seen an explanation of why this is the case. Precisely what kind of numerical difficulties can one encounter when fitting a curve to option prices? Isn't the relationship between implied volatilities and strike prices also severely nonlinear?

[1] Jiang, E J. and Tian, G S., The Model-Free Implied Volatility and Its Information Content ( 2005). The Review of Financial Studies, Vol. 18, Issue 4, pp. 1305-1342, 2005. www.u.arizona.edu/~gjiang/JiangTian-RFS05.pdf

## Answer by Matt Wolf (score 2)

https://quant.stackexchange.com/a/7124

- There is a market accepted standard to translate vanilla option prices to implied vols and backward which is the Black Scholes (BS) options pricing formula. There is no ambiguity here, everyone knows of the deficiencies of BS yet its what people use to translate between iVols <-> prices.

- The numerical difficulty I see is to make more realistic assumptions and to incorporate them into your model

- The real challenge in trading options is a) the relaxing of unrealistic but simplifying assumptions and b) to predict volatility which in turn enables you to determine whether you believe implied vols (or option prices) are trading too rich or too cheap. This in fact I believe is the true skill of a successful option trader.

Edit:

In case you refer to the commends in section 1.2, first of all there is really no model-free implied volatility. I find it ironic how they use this term throughout the paper and at the same time mention about B-S, SVJ Volatility model, and what have you. There is always an underlying "model" or translation engine at work to convert from implied vols to options prices and vice versa. Also when only considering vols and strike prices you must assume an underlying model. They go into detail in 1.2.4 but they make less and less sense: They concern themselves with curve fitting techniques but at the same time make the assumptions of "zero interest rates, zero dividends, model prices instead of market prices".

Now, I am a market practitioner, I have to make my living pricing and trading this stuff. I would claim I am able to follow most academic papers targeting quant finance space, but it does not mean I agree with them all. From the abstract I do not understand what they actually try to achieve, and even throughout the paper I am not sure which goal they actually try to reach. Everyone in the market interpolates and applies curve fitting techniques to vol surfaces and such. So what, and as I mentioned above "model free" does not exist in options world, imho. Otherwise options traders would be paid on about the same pay scale as a part-time convenience store employee. It takes a little more than model-free. Thats my take of this. I would concern myself with more interesting and challenging topics and not read too much into this particular paper.

Just my 2 cents