I would like to share the youtube video of my online seminar at Minnesota Center for Financial and Actuarial Mathematics and presentation slides.
I discuss the motivation behind introducing Karasinki-Sepp log-normal stochastic volatility (SV) model in our IJATF paper with Parviz Rakhmonov. I briefly highlight the advantages of this model over existing SV models. Then I focus on new features of the model.
For the first time, I formulate the dynamic of log-normal SV model consistent with the forward variance by construction. This formulation enables to automatically fit the model to a given term structure of variance swap strikes implied from market prices. I show that there is a small modification of the closed-form solution presented in our paper so that the existing solution can be applied here as well.
Also for the first time, I introduce the rough formulation of the log-normal SV model. I note that our exponential affine expansion for the classic log-normal SV model can also be applied for the rough version, but it results in a system of multi-variate system of integral equations which is numerically tedious. We need to resort tom Monte-Carlo simulations of this model and Deep Learning for model calibration. This is work in progress so stay tuned.
Finally, I present the model calibration to the time series of implied volatilities of options on Bitcoin traded on Deribit. I touch upon the calibration of mean-reversion parameters using empirical auto-correlation function discussed in our paper. The rest of model parameters: the current level and long-term mean volatility, volatility beta, and volatility-of-volatility are fitted in time series calibration.
Below I show that the model error (the average difference between market and model implied volatility) is less than 1% most of the times. The volatility beta serves as the expected skeweness indicator switching from large negative values during risk-aversion and positive values during risk-seeking periods. This time series construction can serve as a base for relative value analysis and quant trading strategies.
I mention that Python implementation of model is available in stochvolmodels package at Github. See an example of running the log-normal SV model and example of model calibration using the new formulation of term structure consistent with impled variance.
Disclosure
This research is a personal opinion and it does not represent an official view of my current and last employers.
This paper and the post is an investment advice in any possible form.