Calibrating Local Volatility Models with Stochastic Drift and Diffusion

Orcan Ogetbil, Narayan Ganesan and Bernhard Hientzsch

Papers from arXiv.org

Abstract: We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems, and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign, each modeled by a G1++ process. For stochastic volatility, we model the variance for the exchange rate by a CIR process. We include tests to show the convergence and the accuracy of the proposed algorithms.

Date: 2020-09, Revised 2023-05
New Economics Papers: this item is included in nep-ore
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Published in International Journal of Theoretical and Applied Finance, 25(02):2250011, 2022

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2009.14764

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