Articlegold2020

Fractional Riccati Equation and Its Applications to Rough Heston Model Using Numerical Methods

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Stochastic processes and financial applications Fractional Differential Equations Solutions Fuzzy Systems and Optimization

Abstract

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1968Fractional Brownian Motions, Fractional Noises and Applications 1987The Pricing of Options on Assets with Stochastic Volatilities 1996Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options 1999Option valuation using the fast Fourier transform 2018Volatility Is Rough 1998Long memory in continuous‐time stochastic volatility models

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