×

zbMATH — the first resource for mathematics

Pulled-to-par returns for zero-coupon bonds historical simulation value at risk. (English) Zbl 1444.91214
Summary: Due to bond prices pull-to-par, zero-coupon bond historical returns are not stationary, as they tend to zero as time to maturity approaches. Given that the historical simulation method for computing value at risk (VaR) requires a stationary sequence of historical returns, zero-coupon bonds’ historical returns cannot be used to compute VaR by historical simulation. Their use would systematically overestimate VaR, resulting in invalid VaR sequences. In this paper, we propose an adjustment of zero-coupon bonds’ historical returns. We call the adjusted returns “pulled-to-par” returns. We prove that when the zero-coupon bonds’ continuously compounded yields-to-maturity are stationary, the adjusted pulled-to-par returns allow VaR computation by historical simulation. We firstly illustrate the VaR computation in a simulation scenario, and then, we apply it to real data on eurozone STRIPS.
MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91G70 Statistical methods; risk measures
Software:
QRM; Dowd
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] International convergence of capital measurement and capital standards a revised framework comprehensive version (2006), Basel: Bank for International Settlements Bank for International Settlements, Basel
[2] STANDARDS Minimum capital requirements for market risk (2016), Basel: Bank for International Settlements, Basel
[3] Mehta, A.; Neukirchen, M.; Pfetsch, S.; Poppensieker, T., Managing market risk: today and tomorrow. McKinsey working papers on risk, 32 (2012), London: McKinsey & Company, London
[4] Abad, P.; Benito, S.; López, C., A comprehensive review of value at risk methodologies, Span Rev Financ Econ, 12, 1, 15-32 (2014)
[5] Fabozzi, FJ; Choudhry, M., The handbook of European fixed income securities (2004), Berlin: Wiley, Berlin
[6] Björk, T., Arbitrage theory in continuous time (2004), Oxford: Oxford University Press, Oxford · Zbl 1140.91038
[7] Sousa JB, Esquıvel ML, Gaspar RM, Real PC (2014) Historical VaR for bonds—a new approach. In: Coelho L, Peixinho R (eds) Proceedings of the 8th finance conference of the Portuguese finance network, pp 1951-1970
[8] Dowd, K., Measuring market risk (2007), Berlin: Wiley, Berlin
[9] McNeil, AJ; Frey, R.; Embrechts, P., Quantitative risk management: concepts, techniques, and tools (2005), Princeton: Princeton University Press, Princeton · Zbl 1089.91037
[10] Papoulis, A., Probability, random variables, and stochastic processes (1984), London: McGraw-Hill, London · Zbl 0191.46704
[11] Christoffersen, PF, Evaluating interval forecasts, Int Econ Rev, 39, 841-862 (1998)
[12] Daníelsson, J., Financial risk forecasting: the theory and practice of forecasting market risk, with implementation in R and matlab (2015), Berlin: Wiley, Berlin
[13] Afonso, A.; Rault, C., Short-and long-run behaviour of long-term sovereign bond yields, Appl Econ, 47, 37, 3971-3993 (2015)
[14] Alexander, C., Market risk analysis, value at risk models (2009), Berlin: Wiley, Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.