i understand that the local volatility function can be computed from the implied volatility surface.(i.e there is no calibration to option prices, we just need the full implied volatility surface only)

In the standard Local vol BS Model, there is also a drift and dividend term, how do we know what values they should be?

Would they be product specific?

Best Regards, Ben

  • $\begingroup$ The drift under the risk neutral measure Q is common to any model you'll use since it is what guarantees that the discounted prices of self-financing portfolios are Q-martingales. More specifically you would always have: $dS_t/S_t = \mu(t) dt + dX_t$ where $(X_t)_{t>0}$ is a martingale. Assuming continuous paths for instance, you'll get $X_t = \sigma dW_t$ under BS, $X_t = \sigma(t,S_t) dW_t$ under LV, $X_t =\sigma_t dW_t$ under SV with another SDE for $\sigma_t$ (or more frequently $v_t = \sigma_t^2$ e.g. in Heston). $\endgroup$ – Quantuple Jul 30 '18 at 7:13

To be honest I am not sure you understand:

  1. Calibrating to vanilla option prices is equivalemt to calibrating to implied volatilities. Vanilla option prices = implied vol surface

  2. The real world drift does not matter and is certainly not derivative product specific, it's the drift of the underlying asset. For options pricing the risk-neutral drift matters, and that is also not dependent on the type of derivative.You can infer the risk neutral drift from put call parity.

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