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.

  • $\begingroup$ 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? $\endgroup$ – JejeBelfort May 11 '17 at 14:19
  • $\begingroup$ @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. $\endgroup$ – Ric May 11 '17 at 14:35
  • $\begingroup$ @JejeBelfort but you are right, they don't mention the word Brownian motion anywhere. $\endgroup$ – Ric May 11 '17 at 14:37
  • $\begingroup$ Indeed. I will try to formulate an answer shortly $\endgroup$ – 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!

  • $\begingroup$ 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. $\endgroup$ – Ric May 11 '17 at 14:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.