eThesis - Kauppakorkeakoulun sähköiset gradut

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This thesis aims to provide contribution to further development of Value at Risk (VaR) models utilized in the risk measurement and management of financial instruments. More specifically, this study concentrates on VaR measurement of swaptions by employing Historical Simulation and its variations. Furthermore, the objective is to find out whether or not it is worth the added measurement system complexity to incorporate fluctuations in the observed shape of swaption volatility smile as a risk factor into VaR estimation process.

A set of interest rate and swaption implied volatility data from the period between March 8, 2011 and February 1, 2013 is used in this study to generate VaR estimates, the validity of which are evaluated using a variety of backtesting methods that compare the estimates with actual profit and loss figures. The VaR estimates are computed for swaption contracts including maturity-tenor -pairs of 1x2, 1x5, 5x2, 5x5, 10x2 and 10x5. Moreover, the considered contract strike rates in addition to at-the-money (ATM) level comprise the following: +25 bps, +50 bps, +100 bps and +200 bps with respect to the ATM levels. The different main VaR models employed are Historical Simulation (HS), Filtered Historical Simulation (FHS) and Time-Weighted Historical Simulation (TW). These models are applied with modifications regarding the method used for incorporating different implied volatility fluctuations into the simulation. The VaR estimates are generated using a historical observation period of 250 trading days, which leaves 228 trading as the backtesting period.

The backtesting results show partial support with mixed evidence for the validity of the considered VaR models. None of them is able to pass each of the backtests with all tested swaption contracts, but some models could be considered sufficiently accurate in terms of regulatory boundaries. Overall, TW models seem to yield best results, but the estimates suffer from clustering of VaR exceptions, which leads to rejection by Christoffersen's (1998) test of conditional coverage. All of the considered models perform adequately well when tested with short positions, but the number of VaR breaches for long positions is in most cases clearly above the acceptable region.