Perfect hedging in rough Heston models
| Autor: | Omar El Euch, Mathieu Rosenbaum |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
fractional Brownian motion Implied volatility 01 natural sciences FOS: Economics and business 010104 statistics & probability 60J25 0502 economics and business Econometrics 60G22 0101 mathematics Mathematics fractional Riccati equations 050208 finance Fractional Brownian motion Stochastic volatility Rough volatility rough Heston model 05 social sciences Probabilistic logic limit theorems Variance (accounting) 91G20 Mathematical Finance (q-fin.MF) Heston model Quantitative Finance - Mathematical Finance Risk Management (q-fin.RM) Volatility smile forward variance curve Pricing of Securities (q-fin.PR) Statistics Probability and Uncertainty Volatility (finance) 26A33 Hawkes processes Quantitative Finance - Pricing of Securities Quantitative Finance - Risk Management |
| Zdroj: | Ann. Appl. Probab. 28, no. 6 (2018), 3813-3856 |
| DOI: | 10.48550/arxiv.1703.05049 |
| Popis: | Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to perfect hedging (at least theoretically). From a probabilistic point of view, our study enables us to disentangle the infinite-dimensional Markovian structure associated to rough volatility models. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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