Why Risk-Neutral Drift Is Used in PRIIPs Risk Scenarios

Summary

The document asks why regulatory risk calculations for packaged investment products use a risk-neutral price process with drift set to the risk-free rate. It refers to volatility-equivalent VaR calculations and a geometric Brownian motion model in which the risk-free rate determines drift. The question contrasts this convention with the real-world return investors might expect, including the need to earn a return above product costs.

The response explains that these scenarios are intended to support a Monte Carlo VaR calculation for a structured fund, using the interest rate swap curve to set the drift. Under risk-neutral valuation, market prices are framed without requiring a separate estimate of each asset’s expected return or each participant’s risk aversion. The brief answer does not discuss the distinction between pricing and forecasting in depth, nor the assumptions and limitations behind applying risk-neutral dynamics to regulatory risk measures.

Key ideas

• The regulatory scenario described models asset prices with drift set to the risk-free rate.
• The response associates the drift input with the interest rate swap curve.
• Risk-neutral pricing avoids choosing asset expected returns based on individual investor views.
• The rationale concerns consistent valuation conventions, not a direct forecast of realized returns.
• The explanation is brief and leaves the broader model assumptions unexamined.

Tags

# Why do regulators assume a risk-neutral world?


# 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.

## Answer by JejeBelfort (score 1)

https://quant.stackexchange.com/a/34161

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!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.