Presentation on theme: "Insurance Liabilities and Option Prices"— Presentation transcript:
1 Insurance Liabilities and Option Prices A case study in market-consistent model calibrationAndrew Smith 8 September 2004
2 Agenda Example product – guaranteed annuity options Swaps and swaptionsAssumptions needed to bridge the gap between swaps and annuity guaranteesImportance of different assumptions
3 What is a Guaranteed Annuity Option? An add-on to an existing pension savings productWhen the savings product matures (with uncertain annuity value), the policyholder can choose to:Take the money and buy a life annuity in the open marketPurchase an annuity at a guaranteed rate - for example £1 per annum for every £9 maturity value. This is the guaranteed annuity optionGuaranteed annuity options are valuable if interest rates are low (because then market annuities are expensive) and expires worthless if interest rates rise.
4 Closest Match: Swaptions A receiver swaption entitles the bearer to:Receive a series of fixed cash flows (six monthly, between the strike date and swap maturity date)While paying a floating rateBut the bearer can walk away with no obligation on the strike date (eg if floating rates are expected to remain higher than the fixed cash flows)As for GAO’s, a swaption is more valuable as interest rates fall, and can expire worthless as interest rates rise
5 Market Data Swaption Volatilities at 30/06/2004 mostreliable dataSource: Royal Bank of Scotland
6 Zero Coupon Yield Volatilities: A Calibration Input A fitted model usually produces a smoother surface, described by a small number of parameters, and so does not capture all swaption prices. The reason for building this model is to price GAOs.Source: Bootstrap of swaption data
7 Market Consistent Prices (Step 1) 10 Year Annuity Certain, £1 Maturity Its more costly to guarantee a higher rate – but the shape of the curve (“smile”) is a chosen assumption, as only observed vols are at the money.
8 Swaps have a credit (+other) risk premium of 30-40 bp over strips Spot 30/06/2004Source: intercapital / datastream and DMO
9 Effect of using Risk-Free rates (mix swaption vols with gilt strip curve) Largest increase in GAO cost (as % swap based value) is for short dated out-of-the -money options.
10 Further Adjustments Required Stochastic mortality, expense and capital loads increase variability of annuity yields relative to swap comparison – likely that firms will have to reflect (at least) stochastic mortality in RBS in future, further increasing stated GAO costs.Quanto effects – bad news if the GAO is in the money at the same time as large fund maturity valuesTake-up rates likely to be a guess – but possible that firms will have to disclose a worst case.
11 ConclusionsRobust and well-established techniques exist for market-consistent valuation of short-dated market guaranteesTypical insurance guarantees require some interpolation or extrapolation to allow for a range of strikes and maturitiesConverting from inter-bank credit to risk-free is subtle and requires extra assumptions – stated liabilities increase by varying amounts.Allowance may be required for stochastic mortality, expense loads, capital cost, quanto effects and other “basis risks” between swap rates and annuity rates.Uncertainty over take-up rates has a huge effect, dominating everything else, and is very difficult to quantify.
12 Insurance Liabilities and Option Prices A case study in market-consistent model calibrationAndrew Smith 8 September 2004