bayesian sensitivity analysis for var & tvar
DESCRIPTION
Bayesian Sensitivity Analysis for VaR & TVaRTRANSCRIPT
Bayesian Sensitivity Analysis for
VaR & TVaR
Act. Edgar Anguiano
INTRODUCTION
VaR & TVaR are useful to measure huge
losses at low probabilities i.e. measures of
extreme events.
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INTRODUCTION
Nonetheless these values are difficult to
estimate precisely because they have high
sensitivity for low probabilities and sample
size.
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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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METHOD
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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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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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HYPOTHESIS
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STEPS
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DEFINITION OF THE PARAMETRIC SPACE
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DEFINITION OF THE PARAMETRIC SPACE
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DEFINITION OF THE PARAMETRIC SPACE
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DEFINITION OF P[θ] & P[θ|Zn]
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DEFINITION OF P[θ] & P[θ|Zn]
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SIMULATION OF θ|Zn
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SIMULATION OF θ|Zn
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SIMULATION OF θ|Zn
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SIMULATION OF θ|Zn
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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SENSITIVITY OF VaR & TVaR
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NUMERICAL EXAMPLE
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THE MODEL AND THE SAMPLE
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PARAMETRIC SPACE
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DEFINITION OF P[θ|Zn]
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SIMULATION OF θ|Zn
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SENSITIVITY OF
VaR & TVaR
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GOODNESS OF FIT OF VaRx|θ (p)
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GOODNESS OF FIT OF TVaRx|θ (p)
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GOODNESS OF FIT OF VaRx|θ (p)
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GOODNESS OF FIT OF TVaRx|θ (p)
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GOODNESS OF FIT OF VaRx|θ (p)
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GOODNESS OF FIT OF TVaRx|θ (p)
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GOODNESS OF FIT OF VaRx|θ (p)
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GOODNESS OF FIT OF TVaRx|θ (p)
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STATISTICS OF VaRx|θ (p)
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STATISTICS OF TVaRx|θ (p)
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STATISTICS OF VaRx|θ (p) & TVaRx|θ (p)
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STATISTICS
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STATISTICS
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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.
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.
QUESTIONS?
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