Deep calibration of rough stochastic volatility models

Abstract

Sparked by Alòs, León, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models such as Heston (1993), these non-Markovian models with fractional volatility drivers allow to parsimoniously recover key stylized facts of market implied volatility surfaces such as the exploding power-law behaviour of the at-the-money volatility skew as time to maturity goes to zero. Standard model calibration routines rely on the repetitive evaluation of the map from model parameters to Black-Scholes implied volatility, rendering calibration of many (rough) stochastic volatility models prohibitively expensive since there the map can often only be approximated by costly Monte Carlo (MC) simulations (

Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models

“…The Heston model is considered in our numerical experiments in Section 5. It was also considered by [9,18] in different neural network contexts.…”

“…few layers) as in [55] with a larger number of neurons. On the other hand, multiple findings indicate [9,47] that adding hidden layers beyond 4 hidden layers does not significantly improve network performance.…”

“…One of the striking advantages of this approach is that it speeds up the (on-line) calibration Rough Volatility models to the realm of just a few milliseconds. There have been several recent contributions on neural network calibrations of stochastic models [9,13,36,49,17]. Clearly, much depends on the finesse of the particular network design with respect to the performance of these networks.…”

Calibrating Rough Volatility Models: A Convolutional Neural Network Approach

“…Convolutional neural networks, referred to from here as CNNs, are known to be very powerful machine learning tools with a vast array of applications including (but of course not limited to) image classification [Hinton et al 2012], [Back et al 1997], [Simonyan et al 2015]; speech recognition ], [Abdel-Hamid et al 2013]; and self-driving cars [Chen et al 2015], [Iandola et al 2017]. Very recently Bayer and Stemper [Bayer et al 2018] used neural networks to learn implied volatility surfaces; the network is then used as part of a wider calibration scheme for options pricing. To the best of our knowledge, however, this paper is the first to explore the use of CNNs to predict the Hölder exponent of a given stochastic process.…”

Stacked Monte Carlo for Option Pricing

“…This of course generated an appetite for variance reduction techniques, whereby more stability can be achieved with similar computation time and level of accuracy. There has recently also been a lot of interest in leveraging the power of machine learning tools, mainly on the use of neural networks to solve pricing [10,13,30,19,24,29] and calibration [6,23,32] problems.…”