Dear Sirs.

I share with you the (first?) results on the performance of my model in terms of pricing.

1) Sample

Trades of S&P500 calls of Tuesday 15/1/2019 (a randomly chosen day, because it is provided by iVolatility.com free of charge as a data example) for a total of 5498 trades after having applied 2 filters, i.e. 0.9 <= St0/K <= 1.1 and expiration < 6 months (18/1, 15/2, 15/3, 18/4, 21/6).

2) Limitations

Dividend yield not included and r = 0.01 for all expiration dates for greater ease.

3) Calibration

I calibrated my model, which has (only!) 2 parameters to be calibrated, i.e. sigmat0 and alpha. I also calibrated Black-Scholes (BS), which has unique parameter sigma to be calibrated.

The calibration for each model was done by searching the values of above parameters that minimize the MSE between the market price and the model price by means of the fminsearch Matlab function, which uses the Nelder-Mead method.

The number of steps of my model (tree) was set to 100.

4) Results

BS: sigma = 0.1513, MSE = 13.85, running time = few seconds.

My tree: sigmat0 = 0.1558, alpha = 0.0423, MSE = 4.15, running time = about 9 minutes.

The sample mean market price is 34.37.

Matlab R2009b was used on my (few years old) PC with Intel Core i5 processor.

5) Comments

Another study, i.e. Master thesis of 2 inidividuals, with other data of another index, Swedish OMX30, reports BS MSE of 15.83 and Heston MSE of 3.30 with a lower sample mean market price of 24.09. So, I think that my model's performance is about as good as Heston's, if not better, in spite of only 2 parameters against Heston's 5! I also had a look at other similar studies, and, more or less, the performance of my model seems to be similar or better than performances of much more complex models with much more parameters.

Perhaps, as a next step, I will use the values of above calibrated parameters to calculate MSE of the following day trades and of the day a week later, in order to see if out-of-sample performance remains good.

What is your opinion regarding these results and possible further analyses? Comments? Thanks!

Finally, I enclose .pdf file of my paper on my model (Please let me know if you wish to have Matlab calibration code files and Excel data files, because I don't seem to be able to attach Matlab files).

Thanks for your attention and speak to you soon!

PS. Since the above, I also calibrated BS and my model to S&P500 calls trades of 2 other days:

16/1/2019

BS: sigma = 0.1471, MSE = 9.39.

My tree: sigmat0 = 0.1514, alpha = 0.0408, MSE = 1.9107.

The sample mean market price is 30.19.

23/1/2019 (expiration < 9 months)

BS: sigma = 0.1626, MSE = 22.28.

My tree: sigmat0 = 0.1694, alpha = 0.0446, MSE = 3.3646.

The sample mean market price is 47.40.