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

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