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For LMSV option pricing the strategy that I have taken is to note that LMSV produces a different future average realized volatility compared to Markovian models and I then plug this volatility into a standard Black-Scholes.  It is thus important to remember elementary facts, such as if $\sigma$ denotes daily volatility, then we want $\sigma' = \sigma \sqrt{T}$ where $T=252$ for the annualized volatility.   In the same vein, recall that we work with the model $r_t = \exp(h_t/2) z$ where $z$ is $N(0,1)$.