Corpus ID: 235732105

Deep calibration of the quadratic rough Heston model

  title={Deep calibration of the quadratic rough Heston model},
  author={Mathieu Rosenbaum and Jianfei Zhang},
The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model. We show that the model is able to reproduce very well both SPX and VIX implied volatilities. We typically obtain VIX option prices within the bid-ask spread and an excellent fit of the SPX at-the-money skew. Moreover, we also explain how to use the trained… Expand


Deep calibration of rough stochastic volatility models
This work showcases a direct comparison of different potential approaches to the learning stage and presents algorithms that provide a suffcient accuracy for practical use and provides a first neural network-based calibration method for rough volatility models for which calibration can be done on the y. Expand
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem
Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible toExpand
Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models
A neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. Expand
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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,Expand
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This work investigates the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup and suggests parsimonious but suitable network architectures capable of capturing the non-Markoviantity of time-series. Expand
Lifting the Heston model
  • E. Jaber
  • Mathematics, Economics
  • Quantitative Finance
  • 2019
How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting atExpand
Multifactor Approximation of Rough Volatility Models
This paper designs tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure and applies this procedure to the specific case of the rough Heston model. Expand
Roughening Heston
Rough volatility models are known to fit the volatility surface remarkably well with very few parameters. On the other hand, the classical Heston model is highly tractable allowing for fastExpand
The Characteristic Function of Rough Heston Models
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 toExpand
Rough volatility: Evidence from option prices
ABSTRACT It has been recently shown that spot volatilities can be closely modeled by rough stochastic volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian motionExpand