Sticky Strike

We are pricing an option for an underlying $S$ with initial price $S_0 = 12$. However, we are not under the assumptions of Black-Scholes. More specifically, we assume that the implied volatility follows a sticky-strike model.

$$\\$$

For an option at strike $K = 13$, the implied volatility is $\sigma = 0.3$. At time $1$, the underlying price is $S_1 = 15$. What is the implied volatility of the $K = 13$ strike option?