
Stock Option Pricing Inference - tcgv
https://thomasvilhena.com/2019/12/stock-option-pricing-inference
======
baron_harkonnen
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 variance
estimate. Likewise the estimations for the Cauchy are definitely off using
this technique (and precisely because of the Cauchy's infinite/undefined
variance you shouldn't use the mean, like the author does, to estimate the
center of the distribution).

Since the author uses mean for the estimate and sample sd in the other code
I'm confused why this isn't used as the estimate for the variance in the
guassian? If you want to demonstrate some sort of numerical optimization it
would be better to use a correct, more standard technique like minimizing the
negative log likelihood of the data given the parameters.

On top of all this there's very unnecessary amounts of superfluous R code in
here. With rnorm and rcauchy there's no need to role your own sampling
function

~~~
tcgv
Hi, I'm the author, thanks for the feedback!

> The ad hoc method of parameter estimation used here needs some explaining

I tried to imitate a "least squares regression" actually. I confess I wasn't
sure if this was the most appropriate approach. I will run the analysis again
using the more standard technique you suggested and compare the results.

> Since the author uses mean for the estimate and sample sd in the other code
> I'm confused why this isn't used as the estimate for the variance in the
> guassian?

The mean value from the density estimate was used for fitting both the
Gaussian and Cauchy models because they are symmetric functions, in an attempt
to reduce this one-dimensional (single variable) fitting error.

Later on the mean is removed when estimating prices since I was assuming a
driftless stochastic process for the underlying stock.

~~~
alimw
Is this what you mean by "log normalization"?
[https://www.spec2000.net/08-normalization.htm](https://www.spec2000.net/08-normalization.htm)

I haven't read much further, perhaps you make it explicit later on.

~~~
tcgv
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...](https://www.google.com/amp/s/quantivity.wordpress.com/2011/02/21/why-
log-returns/amp/)

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

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

------
kevas
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/Complete-Guide-Option-Pricing-
Formula...](https://www.amazon.com/Complete-Guide-Option-Pricing-
Formulas/dp/0071389970/ref=nodl_)

(2)
[http://www.espenhaug.com/articles.html](http://www.espenhaug.com/articles.html)

(3)
[http://www.espenhaug.com/manhat.html](http://www.espenhaug.com/manhat.html)

~~~
buschkowitz
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.

------
usmannk
Got worried when I saw the Gaussian approximation but I’m glad to see the
author’s evaluation.

> Despite the fact that the Gaussian distribution is widely used in fianacial
> models, it has some well known pitfalls, namely its inability to encompass
> fat tails observed in historical market data. As a result it will fail
> accurately describe extreme volatilty events, which can lead to possibly
> underpriced options.

~~~
sweeneyrod
Given that he is looking at one stock over a period of 6 months where AFAIK
nothing particularly unusual happened, I highly doubt any "extreme volatility
events" were relevant.

------
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 ;)

~~~
tcgv
> 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!

------
doublement
This is a fantastic post, and it looks like this blog is full of fantastic
posts. When I have some time I'm definitely going to play around with that
code.

~~~
tcgv
Thanks for that, I appreciate it!

