Questions on option pricing

[DiogoPF]

I'm currently reading academic papers in preparation for my Master's thesis and I have a few questions:
* At the end of the day, what is the ultimate goal of option pricing? Why is there still so much research on it? I've read about models that incorporate a lot of the "stylized facts" known about asset returns (in contrast with the BSM model). What is missing?
* As far as I understand we evaluate how good an option pricing model is by how well it fits the market data. But this raises a question: if everyone is using models, aren't we creating feedback loops?
* Is the BSM model really used in the market? Do we have any data (surveys for example) on what models practitioners use (if any)?
* Why the obsession with analytical closed-form solutions? Why not just program whatever form the solution takes (according to the model used) and use that? I understand pricing needs to be somewhat fast, but I don't understand the need for closed formulas.

Thx

 

[quanttrader]

The Black Scholes model isn't actually 'right' and everyone knows that - firms that trade solely based on the BSM have been extinct for at least a decade. The assumptions are simply unrealistic. Stocks don't truly follow Geometric Brownian Motion, options across a vol surface aren't priced on the same IV, vol isn't consistent through time. But it provides a way to easily compare options with different maturities and is a useful proxy in terms of evaluating options positions, i.e. if an option expiring in a week is trading on a 15% vol (annualized) and an option expiring in 2 weeks is trading on a 20% vol, you know an approximate range for the IV of an option expiring in between those two and can use the BSM to price it.

Feel free to PM me if you have any questions, I'm not a super expert on the academic side but I worked at an OMM for a few years.

 

[quanttrader]

Also, it doesn't create a feedback loop because the big unknown is the 'implied vol' - if one firm thinks that fair value is lower than the market and another thinks that it is higher, there will be some trades.

 

[DiogoPF]

@quanttrader

What I mean by feedback loops is the following: what we are trying to figure is not some static natural variable. It's a price that fluctuates with supply and demand. So if the market is using models to price these things, then I would expect the prices to converge to those models. It then follows that new fish will be trying to figure out a model to a system "rigged" by previous models.

It seems to me (a student with no market experience) that its a never ending pursuit.

P.S. What does OMM mean?

Thx

 

[IntoDarkness]

everything is traded on price so its a price -> vol conversion, which means models need to converge to observable prices not the other way around

 

[quanttrader]

@quanttrader

What I mean by feedback loops is the following: what we are trying to figure is not some static natural variable. It's a price that fluctuates with supply and demand. So if the market is using models to price these things, then I would expect the prices to converge to those models. It then follows that new fish will be trying to figure out a model to a system "rigged" by previous models.

It seems to me (a student with no market experience) that its a never ending pursuit.

P.S. What does OMM mean?

Thx

Basically, the BSM has four known inputs (spot, strike, time to exp, int rate) and one unknown input, which is implied volatility. So say you assume a 0% interest rate, and are trying to price a 100 strike call option that expires in 3 months on a non-dividend paying stock that's trading at 100. If you notice the option is trading at $6 in the market, you can backsolve the BSE and find an implied vol of approximately 30%. All of a sudden, there is a big management shake up and the stock price doesn't move but the market prices in more uncertainty - the price of the option goes up to $8, and now the implied vol is 40%. Maybe some large firm thinks that the market is overestimating the volatility over the next 3 months, and so sells it back down to $6. Basically, it's still a free market, and no one knows what the TRUE volatility is/will be.

There are some new models out there but from what I've seen it's mostly just different ways of modeling the stochastic process of the price of the underlying stock. Some firms try and predict what the future vol will be, but it's (obviously) incredibly difficult.

An OMM is an options market making firm.

Let me know if you have any more questions!

 

[DiogoPF]

@quanttrader I do have more questions =). I write them here so that other people can also contribute and learn.

1. If we know that models such as BSM or Heston are flawed, why is there still SO MUCH research on them? I'm sure there is a good reason, but it seems everyone is so focused on solving micro-problems that no one explains the overarching goal.
2. Do the models used in practice cover many or all of the market "stylized facts" (volatility smile/skew, non-normality of asset returns, price jumps, volatility clustering, etc)? Or do practitioners prefer to use simpler models that do it "good enough"? If the latter, why?
3. Finally a question I wrote in my initial post but no one answered: why is there a pursuit of analytical pricing formulas when we can just automate everything? Shouldn't the goals be accuracy and speed? Maybe with analyitic formulas it's easier to calculate the greeks?

Thanks

 

[Daniel Duffy]

3. Most problems don't have an analytical solution, so numerical methods needed.
Here is a detailed treatment of 6 methods to compute greeks for use in finance and Machine Learning.

https://www.datasim.nl/application/files/5915/7045/5027/Matt_Robinson_Thesis_.pdf

ML ->

https://www.datasim.nl/application/files/8115/7045/4929/1423101.pdf

Accuracy and efficiency are imporant. And robustness (method works for a range of parameter values).

 

[Daniel Duffy]

Why the obsession with analytical closed-form solutions?

No errors or approximation assumptions I suppose. But it can be an unhealthy obsession indeed (what if NO closed solution can be found???) Better to be approximately right than exactly wrong.

Pure mathematicians tend to search for closed solutions. You might get lucky once in a blue moon.
Plan B (less common in articles) is to use 'pure maths' to study qualitative properties of a problem and/or convert it to a an easier-to-solve computational problem.

 

[quanttrader]

@quanttrader I do have more questions =). I write them here so that other people can also contribute and learn.

1. If we know that models such as BSM or Heston are flawed, why is there still SO MUCH research on them? I'm sure there is a good reason, but it seems everyone is so focused on solving micro-problems that no one explains the overarching goal.
2. Do the models used in practice cover many or all of the market "stylized facts" (volatility smile/skew, non-normality of asset returns, price jumps, volatility clustering, etc)? Or do practitioners prefer to use simpler models that do it "good enough"? If the latter, why?
3. Finally a question I wrote in my initial post but no one answered: why is there a pursuit of analytical pricing formulas when we can just automate everything? Shouldn't the goals be accuracy and speed? Maybe with analyitic formulas it's easier to calculate the greeks?

Thanks

I'll do my best to answer these, but keep in mind this is just my perspective.

1. There is quite a bit of research on the academic side, less so in industry, though there still is some. One useful idea that can come out of using BSM is understanding which options are relatively expensive relative to others--for example, comparing implied vols makes comparing options through time on similar parts of the delta surface much easier. That being said, of course it still isn't perfect--there may be large vol events in between expirations, and different firms have different ways to address that (for example, by modeling how much variance should be priced into that event and subtracting it from the farther expiration, etc.).

2. One way to think of modeling a vol surface/smile is a "chopped up" version of Black-Scholes--i.e., modeling the implied vols at each strike, but not using the same vol to price each option. That allows you to model the skew, kurtosis on both sides, etc.

3. Accuracy and speed is huge, of course. Analytic formulas allow firms to have a better idea of the risk they have on, i.e., gamma vs. theta, vega exposure, as well as risk measures that don't draw directly from BSM, such as the exposure a firm has to skew changing (getting steeper, or even flipping) in a certain expiration.

Let me know if any of that isn't clear.