# Why is the market price of risk a non-entity according to Bergomi?

I am reading Bergomi's book Stochastic Volatility Modelling. In the chapter 6 dedicated to the Heston model, page 202, he describes the traditional approach to first generation stochastic volatility models :

1. You start with historical dynamics for the instantaneous variance : $$dV_t = \mu(t,S_t,V_t,p)dt + \alpha dZ_t^{\mathbf{P}}$$ where $$p$$ are model parameters ($$Z^{\mathbf{P}}$$ is hence a Brownian motion in the "historical" probability $$\mathbf{P}$$)

2. In risk-neutral dynamics the drift of $$V$$ is altered by the "market price of risk" $$\lambda$$ which is an arbitrary function of $$t$$, $$S_t$$ and $$V_t$$ : $$dV_t = (\mu(t,S_t,V_t,p) + \lambda(t,S_t,V_t,p))dt + \alpha dZ_t^{\mathbf{Q}}$$ ($$Z^{\mathbf{Q}}$$ is a Brownian motion in a risk-neutral probability $$\mathbf{Q}$$)

3. (Quoting Bergomi) A few lines down the road, jettison "mark price of risk" and conveniently decide that risk-neutral drift has same functional form a historical drift except parameters now have stars : $$dV_t = \mu(t,S_t,V_t,p^{\star})dt + \alpha dZ_t^{\mathbf{Q}}$$

4. Calibrate starred parameters $$p^{\star}$$ on vanilla smile.

Bergomi writes : "discussions surrounding the market price of risk and the uneasiness generated by its a priori arbitrary form and hasty disposal are pointless -- the market price of risk is a non-entity." He points out right after that $$V_t$$ is an artifical object as for different $$t$$ the quantity $$V_t$$ represents a different forward variance and that its drift is then only a reflection of the term-structure of forward variances.

What does he mean by all of that ?

In fact, in never understood the market price of risk even in the context of the Black-Scholes model : we aim at risk-neutral pricing (we care about market models for which a risk-neutral measure exist, no always necessarily for models where a unique risk-neutral measure exist) so why even bother to give model dynamics in the historical measure and not give them immediately in a risk neutral measure ?

For instance : would you try to derive Heston PDE with delta and option hedging, at some point you would come across the market price of risk while if you would start in a risk neutral measure and use Feynman-Kac you wouldn't bother with market price of risk at all.