• This document describes how I used mathematical methods for the estimation of implied volatility curve, a crucial engineering problem raised in our High Frequency Trading (HFT) strategy. I apologize for using many of jargons and unformatted figures. This is because the materials were not prepared for an academic purpose, but just for internal usage. • All data used in this document are about ...

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a ...

This study investigates whether the direction of U.S. implied volatility, VIX index, can be forecast. Multiple forecasts are generated based on standard econometric models, but, more importantly, several machine learning techniques. Their statistical significance is assessed by a plethora performance evaluation measures, while real-time investment strategies devised to appraise implications und...

We study the probability mass at the origin in the SABR stochastic volatility model, and derive several tractable expressions for it, in particular when time becomes small or large. In the uncorrelated case, tedious saddlepoint expansions allow for (semi) closed-form asymptotic formulae. As an application–the original motivation for this paper–we derive small-strike expansions for the implied v...