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.

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Source

QUESTIONS?

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