Yield Curve Extrapolation: Longest reliable point
Posted on 19-04-2011 | 0 comments
It is profoundly worrying that the most basic valuation question we might ask of an insurer -- what is the value today of a fixed liability cash flow at some future date?-- is still unanswered less than two years ahead of Solvency II implementation.
Policymakers, regulators, firms, actuaries and accountants have belatedly focussed on a number of difficult questions including the choice of risk-free asset, the method for extending valuation beyond traded maturities and the possible impact of market liquidity premia on the way the valuation question is answered. This comment focuses on one specific aspect of the extrapolation – the reliability of forward rate estimates and whether we should switch focus from the liquidity of assets to the reliability of forward rates derived from market prices.
It’s apparent that there is considerable discomfort with potential variation in yield curves and their impact on the balance sheet where firms are exposed to large duration mismatches. Putting aside the rights and wrongs of exposing the economic mismatch between assets and liabilities (and I’m in the accounting camp here), I think there is a lack of appreciation of the difficulty and estimation error in establishing a reliable forward interest rate curve even where markets are Active and meet the ‘Deep/Liquid/Transparent’ (DLT) requirement (if we could decide what ‘DLT’ really means). This is important because I think the preference for a reduced longest liquid point (‘LLP’) is driven by the desire to stabilise the forward curve between valuation dates rather than any objective view on liquidity. This objective is not unreasonable given that, in practice, for durations beyond 15-years there can be a reasonably wide range of credible forward rates that will closely fit market prices. So, if your objective is not simply to produce the best fit to market prices at a single point in time but to produce a good fit and manage changes between valuation dates in a credible fashion, it may be more useful to think in terms of a ‘longest reliable point’ (LRP). Here, we might choose to extend the curve from 15 or 20 years, not because of liquidity considerations but because we can better manage the trade-off between providing a good fit to market instruments out to – say – 30 years and, additionally, ensuring that the behaviour of the curve beyond the LRP is credible through time.
Here’s an example. This compares the government forward curves produced by Barrie & Hibbert and the US Fed for end-December 2008:
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A few points to note:
- Both curves provide an extremely close fit to bond prices
- The Fed (in common with other central banks) use methods which focus only on the traded part of the curve (why would they do otherwise?)
- Generally, the spline approach allows for a richer description of the market and provides a marginally better fit
- However, the B&H curve is additionally influenced by what we want to happen in the extrapolated part of the curve (which is not shown) and so the terminal gradient is managed, but this does not have a material impact on the overall fit to observed prices.
My conclusion is that we may want to think about shifting the discussion from a narrow focus on liquidity (which could be argued is a ‘red herring’) to a longest reliable observation on forward rates and management of the trade-off between fitting instruments beyond this LRP with stability of the curve over time.
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