# Why do regulators assume a risk-neutral world?

It is clear that when pricing derivatives we do this in the risk-neutral measure for known reasons. In the calculation of the VaR equivalent Volatility (VEV) in the KID-SRRI calculation (see page 9 here) as well as int the coming regulation of PRIIPs (see this question or this document page 7) the model for the price of the product looks like this $$S_t = S_0 \exp \left ( (r-\sigma^2/2)t + \sigma B_t \right),$$ where r is the risk-free rate.

I am aware that choosing any drift would be difficult but what could be reasons that the regulator chose a risk-neutral setting? Certainly we would need some kind of reward to earn at least the costs of such products.

• Weird, I have been quickly through both of the documents you have quoted but none of them refers to this (Black-Scholes) model. The only potential reference is on page 21 of the second document you quoted where it is written: "historical lognormal returns rt". Could you be more explicit please? – JejeBelfort May 11 '17 at 14:19
• @JejeBelfort in my opinion: if you assume a normal distribution which they do and a drift of a certain form (which they do) then the model is the above - isn't it? They have the term $-\sigma^2/2$ there too. So it should be a geometric Brownian motion. – Richard May 11 '17 at 14:35
• @JejeBelfort but you are right, they don't mention the word Brownian motion anywhere. – Richard May 11 '17 at 14:37
• Indeed. I will try to formulate an answer shortly – JejeBelfort May 11 '17 at 14:45

If I am not mistaken, I might have found something related to this in Box 8 of p11 of the first quoted document.

Essentially, you need to compute a Monte Carlo VaR for your structured funds portfolio. Therefore, they advise you to retrieve the drift (ie: risk free rate) from the interest swap curve.

The rationale behind the use of this risk-free rate is the essence of risk-neutral pricing: instruments prices should be the same irrespectively from the risk-aversion of each of the market participants. The latter do not need to estimate the expected drift of each asset by imposing their view. The risk-neutral pricing does it for them!

• Yes, if we use the same risk-neutral drift for all products, then we don't have to estimate for each product separately. Neither can different manufacturers choose one. Most probably this is the only solution for a risk-based comparison. I hope to find more arguments in this discussion. Thanks for your input. – Richard May 11 '17 at 14:53