A review of current Rough Volatility Methods

Abstract

Recent literature has provided empirical evidence showing that the behaviour of volatility in financial markets is rough. Given the complicated nature of rough dynamics, a review of these methods is presented with the intention of ensuring tractability for those wishing to implement these techniques. The models of rough dynamics are built upon the fractional Brownian Motion and its associated powerlaw kernel. One such model is called the Rough Heston, an extension of the Classical Heston model, and is the main model of focus for this dissertation. To implement the Rough Heston, fractional Riccati ordinary differential equations (ODEs) must be solved; and this requires numerical methods. Three such methods in order of increasing complexity are considered. Using the fractional Adam's numerical method, the Rough Heston model can be effected to produce realistic volatility smiles comparable to that of market data. Lastly, a quick and easy approximation of the Rough Heston model, called the Poor Man's Heston, is discussed and implemented.