The document presents a Bayesian sensitivity analysis methodology for estimating Value at Risk (VaR) and Tail Value at Risk (TVaR). The methodology aims to explain the variability of VaR and TVaR as functions of the parameter θ, which is estimated using maximum likelihood. It allows considering not only variation in the model but also variation in the estimation of the model parameters. The analysis guarantees risk measures that are marginally higher than the real values, ensuring sufficient funds to cover potential extreme losses. In conclusion, the technique provides a relevant way to assess risk while accounting for uncertainty in both the model and parameter estimates.

1. Bayesian Sensitivity Analysis
for
VaR & TVaR
Act. Edgar Anguiano

2. INTRODUCTION
VaR & TVaR are useful to measure huge
losses at low probabilities i.e. measures of
extreme events.
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3. INTRODUCTION
Nonetheless these values are difficult to
estimate precisely because they have high
sensitivity for low probabilities and sample
size.
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4. INTRODUCTION
Also these measures come into the error of
estimation of θ, where θ is usually estimated
by the maximum likelihood method,
therefore the estimation is the most
probable value but not the real one.
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5. METHOD
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6. OBJECTIVE
Explains the variability of VaR & TVaR as
functions of θ.
Guarantee safe founds to face losses of
some extreme event.
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7. QUESTIONS TO ANSWER
•What is the expected value?
• What is the most probable value?
• What is the variance?
• What is the most probable maximum value?
•Do the estimators have a probability distribution?
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8. HYPOTHESIS
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9. STEPS
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10. DEFINITION OF THE PARAMETRIC SPACE
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11. DEFINITION OF THE PARAMETRIC SPACE
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12. DEFINITION OF THE PARAMETRIC SPACE
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13. DEFINITION OF P[θ] & P[θ|Zn]
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14. DEFINITION OF P[θ] & P[θ|Zn]
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15. SIMULATION OF θ|Zn
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16. SIMULATION OF θ|Zn
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17. SIMULATION OF θ|Zn
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18. SIMULATION OF θ|Zn
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19. SENSITIVITY OF VaR & TVaR
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20. SENSITIVITY OF VaR & TVaR
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21. SENSITIVITY OF VaR & TVaR
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22. SENSITIVITY OF VaR & TVaR
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23. SENSITIVITY OF VaR & TVaR
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24. SENSITIVITY OF VaR & TVaR
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25. SENSITIVITY OF VaR & TVaR
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26. NUMERICAL EXAMPLE
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27. THE MODEL AND THE SAMPLE
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28. PARAMETRIC SPACE
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29. 29

30. DEFINITION OF P[θ|Zn]
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31. SIMULATION OF θ|Zn
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32. SENSITIVITY
OF
VaR & TVaR
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33. GOODNESS OF FIT OF VaRx|θ (p)
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34. GOODNESS OF FIT OF TVaRx|θ (p)
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35. GOODNESS OF FIT OF VaRx|θ (p)
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36. GOODNESS OF FIT OF TVaRx|θ (p)
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37. GOODNESS OF FIT OF VaRx|θ (p)
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38. GOODNESS OF FIT OF TVaRx|θ (p)
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39. GOODNESS OF FIT OF VaRx|θ (p)
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40. GOODNESS OF FIT OF TVaRx|θ (p)
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41. STATISTICS OF VaRx|θ (p)
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42. STATISTICS OF TVaRx|θ (p)
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43. STATISTICS OF VaRx|θ (p) & TVaRx|θ (p)
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44. STATISTICS
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45. STATISTICS
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46. CONCLUSION
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Was shown that this methodology is useful for
understanding the variations of VaR and TVaR as
function of θ and the technique takes into account not
only the variation of the model, but also take into
consideration the variation of the estimation of the
model.

47. CONCLUSION
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Also, the method guarantees a stressed risk measure
that are just enough above the real one.
Then, in conclusion this technique is relevant in order
to guarantee safe founds to face losses of some
extreme event.

48. 48
Source

49. QUESTIONS?
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