I would like to share my research and thoughts about stochastic volatility models and, in particular, about the log-normal stochastic volatility model that I have been developing in a series of papers (see introductory paper with Piotr Karasinski in 2012, the extension to include quadratic drift

The volatility of interest rates in 2022 has been indeed extreme. In Figure 1, I show the dependence the between the MOVE index (which measures the implied volatility of one-month options on UST bond futures and which is constructed similarly to the VIX index for implied volatilities of the S&P

Cryptocurrencies have been acknowledged as an emerging asset class with a relatively low correlation to traditional asset classes. One of the most important questions for allocators is how much to allocate to Bitcoin and to a portfolios cryptocurrency assets within a broad portfolio which includes

I am introducing my most recent research on log-normal stochastic volatility model with applications to assets with positive implied volatility skews, such as VIX index, short index ETFs, cryptocurrencies, and some commodities. Together with Parviz Rakhmonov, we have extended my early work on the

I am delighted to share the video from my QuantMinds presentation that I made in Barcelona in December 2021. Many thanks to QuantMinds organizers for allowing me to share this video. First, it was nice to attend the onsite conference in a while and to meet old friends and colleagues. I was

I am excited to share the latest paper with Prof. Alexander Lipton. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4035813 We find the semi-analytical solution to one of the unsolved problems in Quantitative Finance, which is to compute survival probabilities and barrier option values for

Everyone knows that the risk profile of systematic strategies can change considerably when equity markets turn down and volatilities spike. For an example, a smooth profile of a short volatility delta-hedged strategy in normal regimes becomes highly volatile and correlated to equity markets in