Before revision: We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both \beta parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model , and we show that the BFL14 result has to be adjusted for strikes above a certain critical value K^* where the convolution density admits a higher order saddlepoint .
After revision: We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both \beta parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model BFL14 result has to be adjusted for strikes above a certain critical value K^* where the convolution density admits a higher order saddlepoint .