Presentation on theme: "Insurance Liabilities and Option Prices"— Presentation transcript:
1Insurance Liabilities and Option Prices A case study in market-consistent model calibrationAndrew Smith 8 September 2004
2Agenda Example product – guaranteed annuity options Swaps and swaptionsAssumptions needed to bridge the gap between swaps and annuity guaranteesImportance of different assumptions
3What 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.
4Closest 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
5Market Data Swaption Volatilities at 30/06/2004 mostreliable dataSource: Royal Bank of Scotland
6Zero 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
7Market 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.
8Swaps have a credit (+other) risk premium of 30-40 bp over strips Spot 30/06/2004Source: intercapital / datastream and DMO
9Effect 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.
10Further 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.
11ConclusionsRobust 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.
12Insurance Liabilities and Option Prices A case study in market-consistent model calibrationAndrew Smith 8 September 2004