Stock Option Pricing Inference
thomasvilhena.com
Stock Option Pricing Inference
1–10 of 17 posts
Re: Stock Option Pricing Inference
#2This 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.
Re: Stock Option Pricing Inference
#3Got 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.
Re: Stock Option Pricing Inference
#4The 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
Re: Stock Option Pricing Inference
#5Note 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)
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(1) https://www.amazon.com/Complete-Guide-Option-Pricing-Formula...
Re: Stock Option Pricing Inference
#6The 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, 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.
Re: Stock Option Pricing Inference
#7This 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.
Thanks for that, I appreciate it!
Re: Stock Option Pricing Inference
#8Got 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.
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.
Re: Stock Option Pricing Inference
#9The 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, 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 othe…
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.
Re: Stock Option Pricing Inference
#10Earlier quoted context omitted.
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 othe…
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...