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Activity Number: 519 - SPEED: Methodological Advances in Time Series: BandE Speed Session, Part 2
Type: Contributed
Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 11:15 AM
Sponsor: Business and Economic Statistics Section
Abstract #307884
Title: Bayesian Estimation of Local Volatility with Gaussian Process
Author(s): Kai Yin* and Anirban Mondal
Companies: Case Western Reserve University and Case Western Reserve University
Keywords: Local Volatility ; Bayesian ; Gaussian Process ; MCMC; Uncertainty Quantification; Inverse Problem
Abstract:

Volatility is a very important quantity in empirical finance with a great impact on trading and pricing to avoid providing arbitrage into the market. Here we focus on estimating local volatility. Calibrating a local volatility to market prices is often very challenging as it is an inverse problem that involves estimating an unknown function from a noisy market data. While uncertainty quantification is vital for volatility, in the past there has not been much research effort in estimating the local volatility function from the option price data using probabilistic models. We propose a full Bayesian non-parametric method to estimate local volatility from the option prices. Bayesian method casts the inverse solution as the posterior distribution of the local volatility and uncertainty is attached naturally. A Gaussian process prior is used to model the local volatility as a function of price and time. The posterior is intractable as the likelihood will include the Dupires’s PDE, hence MCMC is used to sample from the posterior. Direct MCMC is very expensive due to solving the PDE in each iteration using finite difference method. To reduce the computational burden of Markov Chain Monte


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