Estimating Effective Duration of Inforce SPDA Liabilities

[Actuarial Enthusiast]

I am looking for ways to estimate effective duration for a block of inforce SPDA liabilities. I have a MoSes model so I can generate liability cash flows which are interest sensitive and path dependent. Let us assume here that I've calibrated the dynamic lapse function properly--which is another topic but not the point of my post. I assume no future premiums--which is another complication for an FPDA model.

'Theoretical Liability Effective Duration'
To calculate a theoretical effective duration, I need to run a set of risk neutral scenarios using a starting reference curve (US Treasury, LIBOR swap, etc.) and then calculate the PV of liability cash flows (no reserves, no surplus, no GAAP Stat IRFS Tax accounting). For a single scenario, the PV uses the stream of 90-day rates generated in that scenario. The sum of the PVs for each scenario are then divided by the number of scenarios to come up with the reference liability value (V(0)). I then shock the original reference curve up 25bp, re-run the set of interest rate scenarios, re-calculate the stream of distributable earnings for the liability, re-calculate the PVs, sum up the PVs and divide by the number of scenarios to get value V (+25bp). I do the same for a level drop in the reference curve and get V(-25bp). I then have effective duration of -[V(+25bp) - V(-25bp)]/[2*V(0)*0.005].



My 2 questions to the discussion board are this,

1. Is my definition of the 'theoretical effective duration' more or less correct?

2. Given than the number of scenarios required to get the reference liability values to converge can be large (1,000 by convention but might be closer to 10,000 or 100,000) , what are some techniques I can use to estimate effective duration while reducing the number of scenarios I have to run?

Regards,
AE

[Freebird]

Originally Posted by Actuarial Enthusiast

My 2 questions to the discussion board are this,

1. Is my definition of the 'theoretical effective duration' more or less correct?

2. Given than the number of scenarios required to get the reference liability values to converge can be large (1,000 by convention but might be closer to 10,000 or 100,000) , what are some techniques I can use to estimate effective duration while reducing the number of scenarios I have to run?

Regards,
AE

This sort of relates to a separate post of mine (http://www.actuarialoutpost.com/actu...d.php?t=235671), in which I am asking a question regarding risk-neutral scenarios. Please feel free to comment on mine, and I will do the same for yours.
1). I see nothing wrong with the approach, but are you using an asset liability model to do the calculation, or a liability-only model with an interest rate assumption applied to reserves on the asset side? That's sort of the gist of my post. When I have done that kind of liability duration calculation in the past, using TAS, I used an asset liability model and a 50 bp shift (not 25). However, the size of the interest rate shift shouldn't make any difference, as long as your formula is correct. Speaking of which, your formula looks okay to me for effective duration, but I don't remember the exact details.
2). I didn't have to use more than 1,000 scenarios to get convergence for a fixed def ann block. As I recall, it was somewhat less than 1,000, but I don't remember the number. Have you already determined that you need more than 1,000 to get convergence? I don't have any links for you, but I know the Academy (SOA?) has been doing a study on modeling efficiency. You may find what you need there. Good luck!

[Eimon Gnome]

Originally Posted by Actuarial Enthusiast

My 2 questions to the discussion board are this,

1. Is my definition of the 'theoretical effective duration' more or less correct?

2. Given than the number of scenarios required to get the reference liability values to converge can be large (1,000 by convention but might be closer to 10,000 or 100,000) , what are some techniques I can use to estimate effective duration while reducing the number of scenarios I have to run?

Regards,
AE

1] Looks very good. You'll have a solid estimate if you follow that game plan.

2a] Convergence with 1,000 should not be a problem. Turn off the asset side when you are looking at the liabilities. It's not an ALM exercise - you just want info on the liabilities. Sometimes this gets a bit sticky, since it invariably comes up that "we have a portfolio rate credit strategy". Dump that. Forget the "portfolio". I'm sure you can come up with a proxy using something that works from a modeled index - say the 3 year average of the 10 year treasury plus 100bps. That will be fine enough.

[2b] On rare occasions, you may need a whole lot of scenarios to get an accurate read. This is typical if you have a way out of the money option in the liabilities, with a really sever payoff. The other is when you have some cliff like option - like a digital. Those can require a fair number of scenarios before you get an accurate read. But SPDAs rarely contain these exotics, so most likely you are safe.

[Colymbosathon ecplecticos]

Originally Posted by Actuarial Enthusiast

I then have effective duration of -[V(+25bp) - V(-25bp)]/[2*V(0)*0.005].

You have an extra factor of 2 in your denominator.