# Break even Levels Local volatility

I came across a presentation where it is stated that using a local volatility model the PnL of an option is

and

What does he mean by spot/vol correl = -100%?

The LV model is a particular kind of model where the implied volatility of a European vanilla of given strike and maturity emerges a deterministic function of time, spot level and the local volatility function used $\sigma(\cdot, \cdot)$. $$\hat{\sigma}_{KT} = f(t, S_t; \sigma)$$ such that using Itô one could write \begin{align} \frac{ dS_t }{S_t } &= \mu dt + \sigma(t,S_t) dW_t^\Bbb{Q} \\ d\hat{\sigma}_{KT} &= \left( \frac{\partial f}{\partial t} + \frac{\partial f}{\partial S} (r-q) S_t + \frac{1}{2} \frac{\partial^2 f}{\partial S^2} \sigma^2(t,S_t) S_t^2 \right) dt + \frac{\partial f}{\partial S} \sigma(t,S_t) S_t dW_t^\Bbb{Q} \\ &:= \mu_{KT} dt + \nu_{KT} \hat{\sigma}_{KT} dW_t^\Bbb{Q} \end{align} from where you see that if the market behaves as postulated by the model $$\Bbb{E}\left[ \frac{\delta S}{S} \frac{\delta \hat{\sigma}_{KT}}{\hat{\sigma}_{KT}} \right] = \sigma(t,S_t) \nu_{TK} \delta t$$ and the Volga term in the P&L equation above vanishes in expectation, independently of the instrument considered, as required of a genuine market model (payoff-independent break-even levels).
Now looking at the spot/implied volatility correlation priced in by the local volatility model we have: $$\frac{d \langle \ln S, \hat{\sigma}_{KT} \rangle_t}{\sqrt{ d \langle \ln S \rangle_t d \langle \hat{\sigma}_{KT} \rangle_t } } = \frac{ \sigma^2(t,S_t) S_t \frac{\partial f}{\partial S} dt }{ \sigma^2(t,S_t) S_t \left\vert \frac{\partial f}{\partial S} \right\vert dt } = \text{sign}\left(\frac{\partial f}{\partial S}\right) = \text{sign}\left( \frac{{\partial \hat\sigma}_{KT}}{\partial \ln S} \right)$$ because of $S_t \geq 0, \forall t>0$