  Using classical Taylor series techniques, we develop a unified approach to
pricing and implied volatility for European-style options in a general
local-stochastic volatility setting. Our price approximations require only a
normal CDF and our implied volatility approximations are fully explicit (ie,
they require no special functions, no infinite series and no numerical
integration). As such, approximate prices can be computed as efficiently as
Black-Scholes prices, and approximate implied volatilities can be computed
nearly instantaneously.
