Thanks a lot for your reply. Insurance guarantees are very long term options on the pension investment of our clients we sell in order to protect policyholder's investment. We are therefore seller of options - very risky!
How to price these options (which can be very exotic, with cliquet and loopback features) is more art than science. In particular, interest rate sensitivity is key when it comes to discount cash flows that will potentially take place in 30 to 50 years.
One thing that actuaries really require (believe it or not) is that the IR volatility assumption used for pricing these options should not vary with time and should be quite conservative (ie. somewhat high). These assumed volatilities are typically calculated taking a (60%-65%) percentile of historical Black implied volatilities for different levels of maturities/term. You can imagine there is some "mean-reverting in the long term" rationale behind this practice.
No matter what level of interest rates, we would hence price liars with the same vol, missing the fact that for swap's rate decrease, Black volatilities tend to increase and vice-versa (this is the "leverage" effect I was referring to...now I see that in IR jargon it is called level effect!
).
Given we hedge DV01 of this option, the assumed liabs volatility becomes crucial when it comes to convexity P&L estimation. Marking to market the assets in fact create huge P&L swings depending on interest rate movements (if long term swap rates decrease a lot, like they are doing in EUR and JPY, Black vols increase a lot potentially surpassing the fixed liability ones and viceversa).
My idea is that if we were to assume normal volatilities on the liabs at least once we convert them into Black ones (ie. dividing for the forward rate) we would be able to replicate the level effect we have on the asset side and potentially hedging it.
Hope this clarifies the things a little bit better.
