Explicit implied volatilities for multifactor local-stochastic\n volatility models

2013/06/23 by Matthew Lorig, Lorig, Matthew, Stefano Pagliarani +3
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Financial Markets and Investment Strategies

paper · pdf · doi:10.48550/arxiv.1306.5447

Abstract

We consider an asset whose risk-neutral dynamics are described by a general\nclass of local-stochastic volatility models and derive a family of asymptotic\nexpansions for European-style option prices and implied volatilities. Our\nimplied volatility expansions are explicit; they do not require any special\nfunctions nor do they require numerical integration. To illustrate the accuracy\nand versatility of our method, we implement it under five different model\ndynamics: CEV local volatility, quadratic local volatility, Heston stochastic\nvolatility, 3/2 stochastic volatility, and SABR local-stochastic volatility.\n

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