
4:59 AM (6 hours ago)


Ladies and Gentlemen,
I have shown a simple way to incorporate long memory — the fact that waiting times for volatility jumps in all financial price series are MittagLeffler distributed — into a closed form option pricing model. The model is a modification of Steven Heston’s 1993 model, and I have been talking about how nonMarkovian effects cannot be evaded in finance. Here are some results comparing Heston model with my model (fractional Heston, i.e. a stochastic volatility model where the square root process in Heston model is replaced by a TIMEFRACTIONAL stochastic differential equation).
Attached are the results (and code but not data which are large) of ~28 stocks where I fit the entire volatility surface worth call options by Heston and fracHeston model on a ‘StartDate’ and then use the parameters of the fit for 9 subsequent days recording the mean error of fit. The attached file contains the mean of these errors and the pvalue of the ttest between them.
This particular set of data shows that the mean Heston error is 0.159 ( in quoted price so 16 cents on average) and the the fractional Heston error is actually a tiny bit higher at 0.163. There is no significance to this difference in this dataset (pval=0.9). This is a soso result. It’s good in the sense that here is a modification of the Heston model that is nontrivial that is a reasonable option pricing model and is competitive with Heston model. It’s disappointing because this is not a slam dunk in improvement in this level of granularity (overall volatility surface over 10 days on ~28 stocks). Nevertheless, this is a great breakthrough in the history of finance. Long memory has a closed form stochastic volatility option pricing formula filling a gigantic gap in quantitative finance, one that is not much harder to code or longer to execute than the Heston model.
3 Attachments
Preview attachment bulkCompareHestonVsLMHeston.R
Advertisements
Leave a Reply