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Short version

Why do we take market prices as the prices to be estimated and predicted? The common answer is efficient markets hypothesis as in "Market agents do their best effort given their information set, therefore market prices are optimal." Is there another way?

Edit: I should add that it is the academic way of doing this. If you are to publish a paper you show how well your model represents the market compared to other models. See an example

http://www.researchgate.net/publication/222404856_GARCH_vs._stochastic_volatility_Option_pricing_and_risk_management

Long Version

Suppose I have a nice option pricing model (say Model A) to estimate some option contracts' fair prices. I use this model to estimate some of the contracts existing in the market. Let's denote the set of the price estimates as "Estimate Set A".

And let's say there is another option pricing model (say Model A) doing the same thing and get some estimates as "Estimate Set B".

And then we have the market prices since those are exchange traded options. And let's call them, well, "Market Prices".

I would like to know whether model A or model B is a 'better' option pricing model.

From what I have seen on numerous academic studies, the convention is to use an error function like root mean squared error (RMSE) and sometimes relative pricing error or some other derivation and take the Market Prices set to measure the error from. To illustrate let's say there are 4 contracts Estimate set A consists of (1, 2, 3, 4) and estimate set B consist of (4, 1, 3, 2) and market prices are (2, 3, 2, 3).

RMSE of A is sqrt((1-2)^2+(2-3)^2+(3-2)^2+(4-3)^2) = 2 RMSE of B is sqrt((4-2)^2+(1-3)^2+(3-2)^2+(2-3)^2) = sqrt(10) ~ 3.16

Conclusion: A is better than B (of course it is slightly more complicated)

The only rationale I can find from the literature behind this logic is the assumption that comes from efficient markets hypothesis.

All that is required by the EMH is that investors' reactions be random and follow a normal distribution pattern so that the net effect on market prices cannot be reliably exploited to make an abnormal profit, especially when considering transaction costs (including commissions and spreads). Thus, any one person can be wrong about the market—indeed, everyone can be—but the market as a whole is always right.

Option pricing performance convention is built right atop of this hypothesis. The problem is the implicit assumption of the market price optimality. If the market prices are optimal then there is no way a model can be used as a trading strategy.

Suppose your model estimate the price of the contract as 1.5 (say dollars) and the market price of the contract is 1.2. If you gauged your model with the market prices you should accept you are off 0.3$. So why bother with a model, even more why bother with trading?

Is there any other way?

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Your reflection of the common answer of "Why do we take market prices as the prices to be estimated and predicted?" is incorrect: We care about market prices because that is what we trade against. If you believe in emh then you should not ever engage in risk taking. But if you think market prices are NOT correctly valued then you still care about market prices because that is how the profit and loss is calculated against. –  Matt Wolf May 27 at 14:43
    
My arguement is neither about EMH nor from the trading perspective. The common academic approach to test a model is to measure its proximity to market and their main reason to do so is EMH. This is the criticism part, but I am looking for a solution also. –  berkorbay May 27 at 18:08
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I do not share the same summary of the "academic approach". I do not think that academicians consider market prices as benchmark because they believe in the EMH theory. I can again only repeat that most everyone considers market prices because they function as yardstick against which everything is measures. Even my own models, if market prices do not converge to my model then my model was obviously flawed and not the market. You look to either (a) derive a model as close to market prices as possible in order to price similar assets that may not be traded using inputs that were calibrated to.. –  Matt Wolf May 28 at 7:01
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..the market, or (b) you derive a model that makes its own asset price level/return prediction in the hope that market prices are dislocated short-term and converge to levels a model predicts. –  Matt Wolf May 28 at 7:05
    
I honestly don't know what is the real rationale behind it, but it is the only one I found so far. Actually it might occur from the dichotomy of the markets (options and underlying). Options market is actually and estimate on the future of the underlying's market but has its own exchange, therefore prices might diverge from the underlying's. The problem is people usually calibrate their models using underlying market and measure their model's performance using the options market. But acceptance of such arrangement is that you make an estimate over an estimate which I believe increases error. –  berkorbay May 28 at 10:49

3 Answers 3

You could go for a backtesting strategy and measure the p&l that trading according to your model would generate over different time intervals. Your model might be off the market prices today, but if your model is better, there will be a time-frame where it aligns again. This would be an opportunity to make money. One could say you would have found a model arbitrage opportunity.

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Although my objective is more about model validation, that is what I do now. The only difference is I try take the market error (option price vs. realized payoffs) into account for model validation and choose the best model for a specific contract to make the short-long decision, and then calculate the p&l. –  berkorbay May 28 at 10:54

This may well off-topic, but I'd like to clarify on the concept of risk-neutral pricing, which is the framework where most of the option pricing models operate. This should maybe add a perspective over the topic and this should give a partial answer to your very open-ended question.

When we are talking about option pricing, we are generally talking about "risk-neutral" pricing.

The goal is to price a product in a risk-neutral framework is to take some liquid products and put them together to replicate the payoff of some other product (look up the derivation of the B-S formula). In the business, once your pay-off has been replicated, you can hedge risk exposures through liquid products. This is particularly cornerstone in the case of a dealer of OTC products.

Perfect replication of a pay-off is not always possible. Therefore, you may want to extract "information" from liquid products to price your OTC. This is the context where I have seen the use of RMSE as a mean to gauge the quality of the calibration of your model - first you fit the model to your liquid products, then you use the model to price your OTC.

One other goal of model calibration might be extract information from a term structure, an array of securities. In this case, I have in mind, for example, local and stochastic vol models. The benefit of such models is to manage an entire portfolio of options in the present of a volatility smile/smirk.

In conclusion, risk-neutral pricing does not lead to any conclusion over market expectations. The goal is to price something and hedge away the risk with the liquid assets, available on the market right now.

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All you wrote above is right but it misses the point (good catch on the OTC but there are less painful ways to do that if we are assuming market is optimal, but let's restrict ourselves with exchange traded markets). I think I should clarify that it is an academic way of model validation. They simply say "My model represents the market option prices better (than the benchmark models) so it is a better option pricing model." I say "if you assume market is optimal, then your model will never be useful since there will always be a market price when you trade on the market." –  berkorbay May 27 at 19:04

Speaking from a practitioner's point of view, some of the these would be:

  1. Model sensitivity: what happens when the price shifts by a small amount..are we still able to price correctly or do we have to adjust the model?
  2. Greeks: Is the model able to calculate the greeks accurately/quickly?
  3. Model "speed": How long does it take to calculate the price & greeks..one of the most important factors for practioners usually. the model should also be able to price non- vanilla instruments quickly (e.g. asian options, barrier options etc.)
  4. Calibration: how many instruments are necessary to ensure a stable model environment? can we use this model for non-liquid markets?

If you are really only interested in the academic way, then I would assume that some of these points would still be quite important. Your model should still be able to calculate greeks, converge quickly and maybe most importantly, not be overparameterized.

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What is the correct price for you? In terms of options, is it the market option price or some p&l function? Or in other words how do you determine the correct (I assume fair) price? –  berkorbay May 31 at 13:34

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