Risk-Neutral Calibration, Hedging Dynamics, and Model Risk

# Parameter estimation using martingale measures - include real world data?


# Parameter estimation using martingale measures - include real world data?












Please note: I posted this in nuclearphynance first, but didn't get any replies.

For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic Volatility, etc...) using implied vols of the plain vanillas. This seems totally fine as these are usually the hedging instruments. But what is market standard for pricing plain vanillas? Is there anything else than estimating the hedging cost (historically)? How is this usually done? If a bank sells plain vanillas and underestimates the future vol, they'll get a problem, won't they?

The above was meant as an example to a more general problem on which I'd like to find/read some survey paper/opinion (didn't find much yet): Platen writes in his paper ("Alternative Defaultable Term Structure Models") the following:

"One can say that risk-neutral pricing is a kind of relative pricing. As soon as some market participant places some derivative price in the market, others can use it to calibrate their risk-neutral model and form consistent prices for fur- ther derivatives. This does not prevent a development where over long periods of time such prices can be way out from what may be realistically sustainable, as observed prior to the recent subprime crisis."

This coincides with my first remark. What is the general problem of using historical data/economic estimates in a risk neutral model framework? As I see it, if real world expectations like default intensities are used for pricing the hedging instruments correctly, his argument should be pointless. Still, if you have a totally wrong opinion on how things evolve (say AIG on credit), you'll get into trouble.

Thanks for sharing your opinion!

## Answer by Brian B (score 1, accepted)

https://quant.stackexchange.com/a/3176

In reality, you needn't bring exotics into consideration to think about this issue. Consider the case of a shop that has fundamental analysts but also trades options on those equities. The fact that the fundamental analysts trade stocks means they think those prices are somehow "wrong". So of course it seems from their point of view that the options traders are working off poor assumptions.

Of course, to the options traders, all that is really necessary is that the dynamics of the hedging instruments follow the model sufficiently well for the hedge ratios to work, regardless of direction.

Now consider your exotics book. The vanilla hedging instruments need not have the "right" volatility for the book to make money, but any changes in their volatility had better follow the dynamics specified by the model.

If the model only has deterministic volatility, then a good manager will neutralize vega (vol sensitivity) in the portfolio as a whole, in order to avoid PL swings due to circumstances outside his trading writ. The same is true in credit, though in that case the neutralization is necessarily far more approximate.

In practice there are relatively few such "good managers", and zillions of traders have gotten promotions and big bonuses because their portfolio had the right emergent exposure at the right time. It's nice to gamble with the house's money.