  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. The result follows from the
heat kernel on hyperbolic space for $n=3$ combined with the Bellaiche [Bel81]
heat kernel expansion and Laplace's method, and we give numerical results which
corroborate our asymptotic formulae. Similar to the Black-Scholes case, we find
that there is a phase transition from one "most-likely" path to two most-likely
paths beyond some critical $K^*$.
