Purpose of pricing models

[pierreyvessojic]

Hello,

I'm still quite new to the world of quant finance, and I have been having a question that I can't really get an answer to, I'm not actually sure this question even makes sense. This might just be a reasoning issue that I'm having, so someone could probably enlighten me with a simple answer. Why do companies spend millions in research to develop new models for the pricing of options (or any other financial instrument)? At the very end, isn't the market going to decide for the price of those instruments? Let's imagine the whole market uses the "basic" Black-Scholes model to price a specific call option (let's say the BS call price is $10). Now, a certain quant comes up with a new, state-of-the-art model, that gives a more "mathematically" accurate price for the same call option (let's say $15). In that case, how can this model be used in practice, when everyone else is selling the call for $10? Why would someone suddenly decide to pay a higher price for an option, only based on the fact that it is more "mathematically accurate"? In fact, if every company use different models to price a specific derivative, isn't the market simply going to choose the one that has the lowest price?

 

[benzenephi]

That's like saying the market is gonna choose the lowest price for any stock. Why waste time and money reading financial statements to figure out the true accurate value of a stock like Buffett does. We need to do this because the market can be wrong and will eventually catch up to the more accurate model. Of course, with the caveat that markets can be slow to adjust. if a new model suggests that a call option is worth $15 while the market is pricing it at $10, it doesn't automatically mean that someone will pay $15 right away. However, it indicates that the option might be undervalued. Traders using this model might start buying the option at $10, and if enough market participants recognize this value discrepancy and act similarly, the market price could indeed move towards $15.

 

[pierreyvessojic]

Thanks! That's the kind of answer I was waiting for and that makes sense!

 

[lourano.x]

Well, I’m not an expert in quant finance but I believe the enormity of the OTC market really puts things into perspective. It’s not just larger than public markets, it's on a whole different scale. I think this is a main reason why “High Finance” spends such a huge portion of resources for pricing models. From what I believe, these sophisticated models are key for firms to accurately price and manage the risks of the unique deals they handle in the OTC market. Every deal there is a unique itself, so investing in these models is a strategy I believe makes perfect sense. It's all about staying sharp in a market where the usual rules might not apply, and I think that's what keeps firms ahead in this complex environment.

 

[Ken Abbott]

That's like saying the market is gonna choose the lowest price for any stock. Why waste time and money reading financial statements to figure out the true accurate value of a stock like Buffett does. We need to do this because the market can be wrong and will eventually catch up to the more accurate model. Of course, with the caveat that markets can be slow to adjust. if a new model suggests that a call option is worth $15 while the market is pricing it at $10, it doesn't automatically mean that someone will pay $15 right away. However, it indicates that the option might be undervalued. Traders using this model might start buying the option at $10, and if enough market participants recognize this value discrepancy and act similarly, the market price could indeed move towards $15.

Well-said.

 

[Michael CQF]

What I think

what it matters is not the model that price vanillar option, you can invent thousands of model to price it, like use temperature or anything not relevant.

The key is calibration, if all the input, such as spot, interest rate are observable, you can compete in pricing, and try to profit by make a better price than competeor.

The reality is, paramters such as volatility, are not observable, so you can only assume the value from exchange, is fair. You calibrate those unobservable parameter, such as volatility, or jump coefficient(heston) from exchange traded option, then use those to price exotic option contract.

Also, use those parameter you "calibrated", to manage your risk. For example, if spot move, how vol surface going to change.

 

[achirikhin]

You are absolutely correct, market prices (quasi)-listed products, which are not true derivatives.

Rich models can then be calibrated to the prices of the (quasi)-listed, to price unobservable exotics under the assumption that the listed market is complete and arbitrage-free. Market will usually not price at the theoretical value though, not because of some intrinsic value vs market price mystery, but due to simple supply/demand and (il)liquidity premium. Your perfectly calibrated pricing model will then have to be fudged to account for this effect, which is a very common procedure.

In all cases, whether the model is used for price discovery or is merely calibrated to a family of observables in a no-arbitrage way to parametrize that family in lower dimension, the model's universal purpose is calculation of the hedge ratios and PNL explains (vs hedges). Even in the former case, when you calibrate your LV to a surface of options, the model will allow you to partition the observed movement of option prices into the part co-monotone with the movement of the underlying (delta + gamma), residual vega (what the option really trades) and theta, of course, as you are ultimately holding as stochastic bond.

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