Bayesian uncertainty quantification of local volatility model

Kai Yin and Anirban Mondal ()
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Kai Yin: Case Western Reserve University
Anirban Mondal: Case Western Reserve University

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 10, 290-324

Abstract: Abstract Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observed market data. Unlike most existing point-estimate methods, we cast the large-scale nonlinear inverse problem into the Bayesian framework, yielding a posterior distribution of the local volatility, which naturally quantifies its uncertainty. This extra uncertainty information enables traders and risk managers to make better decisions. To alleviate the computational cost, we apply Karhunen–Lòeve expansion to reduce the dimensionality of the Gaussian Process prior for local volatility. A modified two-stage adaptive Metropolis algorithm is applied to sample the posterior probability distribution, which further reduces computational burdens caused by repetitive numerical forward option pricing model solver and time of heuristic tuning. We demonstrate our methodology with both synthetic and market data.

Keywords: Local volatility; Bayesian statistics; uncertainty quantification; Karhunen–Lòeve expansion.; Primary: 62F15, 91B28, 60G15; Secondary: 65C05, 65D25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13571-022-00286-1

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