Insurance liabilities and option prices
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Insurance Liabilities and Option Prices. A case study in market-consistent model calibration. Andrew Smith 8 September 2004 [email protected] Agenda. Example product – guaranteed annuity options Swaps and swaptions

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Insurance liabilities and option prices

Insurance Liabilities and Option Prices

A case study in market-consistent model calibration

Andrew Smith8 September [email protected]



  • Example product – guaranteed annuity options

  • Swaps and swaptions

  • Assumptions needed to bridge the gap between swaps and annuity guarantees

  • Importance of different assumptions

What is a guaranteed annuity option

What is a Guaranteed Annuity Option?

  • An add-on to an existing pension savings product

  • When the savings product matures (with uncertain annuity value), the policyholder can choose to:

    • Take the money and buy a life annuity in the open market

    • Purchase an annuity at a guaranteed rate - for example £1 per annum for every £9 maturity value. This is the guaranteed annuity option

  • Guaranteed annuity options are valuable if interest rates are low (because then market annuities are expensive) and expires worthless if interest rates rise.

Closest match swaptions

Closest Match: Swaptions

  • A receiverswaption 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 rate

    • But 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

Market data swaption volatilities at 30 06 2004

Market DataSwaption Volatilities at 30/06/2004


reliable data

Source: Royal Bank of Scotland

Zero coupon yield volatilities a calibration input

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

Market consistent prices step 1 10 year annuity certain 1 maturity

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.

Swaps have a credit other risk premium of 30 40 bp over strips

Swaps have a credit (+other) risk premium of 30-40 bp over strips

Spot yield @ 30/06/2004

Source: intercapital / datastream and DMO

Effect of using risk free rates mix swaption vols with gilt strip curve

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.

Further adjustments required

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 values

  • Take-up rates likely to be a guess – but possible that firms will have to disclose a worst case.



  • Robust and well-established techniques exist for market-consistent valuation of short-dated market guarantees

  • Typical insurance guarantees require some interpolation or extrapolation to allow for a range of strikes and maturities

  • Converting 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.

Insurance liabilities and option prices1

Insurance Liabilities and Option Prices

A case study in market-consistent model calibration

Andrew Smith8 September [email protected]

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