Abstract
This paper investigates how the market implicitly prices very long-dated cash-flows. We do this empirically, using daily market data on the 3½% War Loan, a UK infinite maturity coupon bond. We price the War Loan as an American option with 100 years of maturity. To this end, we perform daily calibrations to observed swaption prices using the Hull-White (1990) one-factor term structure model. The mean-reversion and volatility parameters resulting from the calibrations are then used in a finite difference method, which is equivalent to the Hull-White (1994 and 1996) trinomial tree procedure. We calculate the constant long-term yield beyond the last observed yield, which equates the results of the finite difference procedure with the observed prices of the War Loan. We find that prior to the financial crisis the constant long-term yield was situated above the last observed yield, whereas after the crisis it was situated below the last observed yield.
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