Should market-implied volatilities be adjusted when calibrating to government bond yields?
Posted on 17-11-2009 by Viktor Knava | 0 comments
Market-consistent economic scenario generators (ESGs) are typically calibrated to a term structure of risk-free interest rates, market-implied volatilities, and correlations between the returns on different asset classes.
In this context market-implied volatilities are those volatilities that, when combined with the banks’ assumptions about the risk-free term structure and used in the appropriate option-pricing models (Black-Scholes model for equity options and Black model for interest rate swaptions), reproduce the market price of the derivative.
Banks will usually price derivatives using a risk-free term structure that is based on the swap curve; however CEIOPS’ Consultation Paper 40 states that “Government bonds rates of AAA rated governments should be considered as the benchmark for credit risk-free rates. Swap rates are not credit risk-free and for this reason unadjusted swap rates should not be used to discount technical provisions”.
In their responses to CEIOPS’ Consultation Paper 39 which deals with the Best Estimate calculation of the Technical Provisions, a number of respondents argue that market-implied volatility data first needs to be “translated” to volatilities appropriate for use with a risk-free curve based on government bond yields.
The implicit assumption behind an adjustment to market-implied volatility data is that the valuation is intended to reproduce derivative prices that are actually quoted in the market, based on the market’s assumptions about the risk-free term structure. On the other hand, not adjusting market-implied volatilities will result in derivative prices that are based on the market’s assumptions about asset price uncertainty and the costs of hedging, but the insurance enterprise’s own assumptions about risk-free interest rates. Effectively, we are pricing a notional option written by the government, rather than a bank.
The right approach to take will clearly depend on the theoretical purpose of the valuation; If the aim is to reproduce a liability price which an investment bank may charge to hedge out an insurance liability, and the ESG is calibrated to a reference rate other than the market swap rate, then it is theoretically correct to adjust the market-implied volatilities.
One may however argue that, having decided to use government bond yields as the risk-free rate of interest, the insurance enterprise should use this rate to value not just certain cashflows but also those which are subject to market risk, such as embedded options and guarantees.
Coincidentally this is the practice commonly adopted in the UK market, where companies valuing options and guarantees embedded in with-profits contracts typically base their term structure of risk-free interest rates on government bond yields, but without any adjustment to market volatility data.
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