The characteristic function of rough Heston models
| Autor: | Omar El Euch, Mathieu Rosenbaum |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Hurst exponent
Economics and Econometrics 050208 finance Fractional Brownian motion Applied Mathematics 05 social sciences Computational Finance (q-fin.CP) 01 natural sciences Mathematical Finance (q-fin.MF) Heston model FOS: Economics and business 010104 statistics & probability Quantitative Finance - Computational Finance Quantitative Finance - Mathematical Finance Accounting 0502 economics and business Riccati equation Applied mathematics 0101 mathematics Volatility (finance) Derivatives pricing Social Sciences (miscellaneous) Finance Mathematics |
| DOI: | 10.48550/arxiv.1609.02108 |
| Popis: | It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log-price in rough Heston models. In the classical Heston model, the characteristic function is expressed in terms of the solution of a Riccati equation. Here we show that rough Heston models exhibit quite a similar structure, the Riccati equation being replaced by a fractional Riccati equation. Comment: 35 pages, 1 figure |
| Databáze: | OpenAIRE |
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