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How to design back-testing (validation) for such modified Vasicek model?

Consider a classical Black Scholes model , $$\frac{dS}{S} = \mu dt + \sigma dW$$ , where $dW$ is a Brownian motion, that $W(t_1) - W(t_0) \sim N(0, t_1 - t_0)$. The back-testing strategy is ...