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Calculating Value at Risk for Bond Portfolios by Selecting Basic Scenarios in the Historical Simulation Method

Chaghazardi, Ali | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53316 (44)
  4. University: Sharif University of Technology
  5. Department: Management and Economics
  6. Advisor(s): Zamani, Shiva; Arian, Hamid Reza
  7. Abstract:
  8. In many methods of calculating Value-at-Risk (VaR), we need to calculate the value of the portfolio several times for different scenarios. Because an explicit formula is not available to calculate the value of some fixed income assets, calculating VaR for portfolios containing these assets imposes a heavy computational burden. In this study, we introduce a new method for calculating VaR for such portfolios. In this method, some of the existing scenarios are selected as basic scenarios and the value of the portfolio is calculated only for each of them. Next, using the calculated values, the portfolio values for other scenarios are estimated by interpolation (or extrapolation). Finally, by obtaining a discrete distribution of the expected portfolio value changes for the next day, VaR can be easily estimated. In this way, the number of recalculations of the portfolio value is reduced and consequently a much less computational load is imposed. To implement the proposed method, a portfolio of callable and puttable bonds is simulated, and interest rates reported by the US Treasury Department from 2011 to 2020 are considered. In order to evaluate the performance of the proposed method, unconditional coverage test (Kupiec, 1995), independence test and conditional coverage test (Christoffersen, 1998) are used. Also, the method of Gibson and Pritsker (2000), which can be considered as one of the most complete methods in this field, has been considered for comparison with the proposed new method. The first advantage of our proposed method over Gibson and Pritsker method is being much simpler to implement and understand. To compare the results of these two methods, Ranking Model (Sener et al. 2012) and Diebold-Mariano test (Diebold and Mariano, 1995) are used. At high confidence levels for calculating VaR (e.g., 99%), the results show the relative superiority of the proposed new method over the Gibson and Pritsker method. However, as the level of confidence decreases, the difference between the performances of two methods decreases. In order to enhance the accuracy of VaR estimation, we applied some techniques similar to the filtered historical simulation method. To this end, GARCH (1.1), ARMA-GARCH (1.1) and EWMA filters are used for updating the volatility of interest rates at different maturities. According to the results, the implementation of these techniques improves the performance of the proposed method as well as the Gibson and Pritsker method. This improvement is more noticeable for the days which show more volatility. In the final part of the study, ideas for improving the performance of the Gibson and Pritsker method are presented. Furthermore, some other ideas for improving the performance of the Gibson and Pritsker method are presented which show acceptable results
  9. Keywords:
  10. Value at Risk ; Yield Curve ; Putable Bonds ; Fixed Income ; Bonds with Embedded Options ; Updating Volatility

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