A simple approximating formula of implied volatility in general local volatility model

In this paper, we use the technique of Taylor expansion to obtain a very analytical and highly applicable approximating formula for implied volatility for general local volatility models, including time-inhomogeneous model case. Our formula is a slightly modification of proposition 5.3 in Pierre Henry-Labordere (2008) [17], and an approximation method is also devised so that the implied variance can be expressed as a very simple series. Numerical results confirm high efficiency and accuracy of our approximating formula, and demonstrate our significant improvement over Pierre Henry-Labordere result.