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Stock Option Pricing Inference

thomasvilhena.com

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Re: Stock Option Pricing Inference

#11

Post by alimw »

tcgv wrote: post #10
alimw wrote: post #9

Earlier quoted context omitted.

Is this what you mean by "log normalization"? https://www.spec2000.net/08-normalization.htm I haven't read much further, perhaps you make it explicit later on.

I took the natural logarithm of the stock's daily returns. Then when estimating option prices I performed the reverse operation: > exp(1) ^ dist[["x"]] In this link you can find more information: - https://www.google.com/amp/s/quantivity.wordpress.com/2011/0...

OK well that is not commonly called "log normalization". It is called "using log returns".

Re: Stock Option Pricing Inference

#12

Post by tcgv »

alimw wrote: post #11
tcgv wrote: post #10

Earlier quoted context omitted.

I took the natural logarithm of the stock's daily returns. Then when estimating option prices I performed the reverse operation: > exp(1) ^ dist[["x"]] In this link you can find more information: - https://www.google.com/amp/s/quantivity.wordpress.com/2011/0...

OK well that is not commonly called "log normalization". It is called "using log returns".

Fixed that, thanks! (should take effect in a while)

Re: Stock Option Pricing Inference

#13

Post by buschkowitz »

kevas wrote: post #5

Note that the author is pricing European options, not American options. The standard BSM formula is for European options, not American. If anyone wants to dive deep into a lot of the different models out there, check out The Complete Guide to Option Pricing Formulas by Espen Haug(1). His site has some wonderful material too(2). I especially like his ‘Exotic Option Fantasy Land’(3) —— (1) https://www.amazon.com/Comple…

Thanks for the interesting link to Espen Haug!

For non-financial engineers, there is a subtle difference between the two option flavors. Holders of an American option can exercise their right to buy/sell the underlying asset at any time while European option holders can only exercise at expiration date.

Re: Stock Option Pricing Inference

#14

Post by pillefitz »

Cool stuff. What's hindering you from making money at this point?

I just started a job implementing asset pricing algorithms for energy contracts similar to what you did, even though a bit more involved (using stochastic dynamic programming and quite complex models for coming up with price paths).

Being completely new to trading I naturally wondered what the catch is, i.e. why I couldn't employ the same techniques for making private profits. Shoot me a mail if you'd like to discuss ideas ;)

Re: Stock Option Pricing Inference

#15

Post by tcgv »

pillefitz wrote: post #14

Cool stuff. What's hindering you from making money at this point? I just started a job implementing asset pricing algorithms for energy contracts similar to what you did, even though a bit more involved (using stochastic dynamic programming and quite complex models for coming up with price paths). Being completely new to trading I naturally wondered what the catch is, i.e. why I couldn't employ the same techniques fo…

> Cool stuff. What's hindering you from making money at this point?

Thanks! That's the goal in the long term.

Besides being a spare-time endeavour, I believe I'm still in the learning phase, studying different statistical finance concepts and techniques, making experiments like this one, assessing the results.

Then the next step I think is to come up with some strategies, perform backtests with historical data and build a real-time automated trading infrastructure.

I have a few friends working in Investment Banks but they're more into traditional portfolio management than automated trading, so they don't help much.

I will organize my thoughts and shoot you a mail once a get the time!

Re: Stock Option Pricing Inference

#16

Post by tcgv »

baron_harkonnen wrote: post #4

The ad hoc method of parameter estimation used here needs some explaining. It looks like the author is trying to minimize the distance between the two lines on the y-axis which is not traditionally how you fit parameters to a distribution and will lead to weird results. Notice that if you estimated a Gaussian the traditional way: by just computing mean and sample variance you do get wider tails caused by a higher var…

Hi again,

So I ran the analysis again using the standard MLE technique you suggested and got the following results:

- Gaussian Model: σ = 0.0473

- Cauchy Model: σ = 0.1443

Quite an improvement from the original least squares regression approach I used!

You can find the updated plots below:

- [Probability Distributions] https://imgur.com/da8dRzm

- [Option prices chart] https://imgur.com/5hey110

Re: Stock Option Pricing Inference

#17

Post by tcgv »

tcgv wrote: post #16
baron_harkonnen wrote: post #4

The ad hoc method of parameter estimation used here needs some explaining. It looks like the author is trying to minimize the distance between the two lines on the y-axis which is not traditionally how you fit parameters to a distribution and will lead to weird results. Notice that if you estimated a Gaussian the traditional way: by just computing mean and sample variance you do get wider tails caused by a higher var…

Hi again, So I ran the analysis again using the standard MLE technique you suggested and got the following results: - Gaussian Model: σ = 0.0473 - Cauchy Model: σ = 0.1443 Quite an improvement from the original least squares regression approach I used! You can find the updated plots below: - [Probability Distributions] https://imgur.com/da8dRzm - [Option prices chart] https://imgur.com/5hey110

For reference, I just updated the code and plots in the article. I also did some minor changes to the text and fixed an issue with the generation of random samples, which had a small impact in the estimations.

Left some notes at the end describing these changes, along with a reference to the original version.

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