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Financial Risk Management. Forecasting Risks and Correlations. Following P. Jorion, Value at Risk, McGraw-Hill. Chapter 8. Daniel HERLEMONT. Volatility.
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Financial Risk Management

Forecasting Risks and Correlations Following P. Jorion, Value at Risk, McGraw-Hill Chapter 8

Daniel HERLEMONT

Volatility

VAR increases with volatility

Unobservable, time varying, clustering

Moving average rt daily returns:

1 σ = M 2 t

M

∑r

2 t −i

i =1

Implied volatility (smile, smirk, etc.) Daniel HERLEMONT

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Time Variation in Risk

Daniel HERLEMONT

Modeling Time Varying Risk

Moving Average

σ t2 =

1 M

M

∑r

2 t −i

i =1

Daniel HERLEMONT

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GARCH Estimation

Generalized Autoregressive heteroskedastic Heteroskedastic means time varying variance

Daniel HERLEMONT

Daniel HERLEMONT

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The RiskMmetrics Approach - EWMA Exponentially Weighted Moving Average

ht = λ ⋅ ht −1 + (1 − λ ) rt 2−1 λ - is decay factor

rt 2−1 + λrt 2− 2 + λ2 rt 2−3 + K ht = 1− λ

λ is in the range 0.94 (daily) to 0.97 (monthly) The same apply for time varying correlations modeling

Daniel HERLEMONT

Correlations

Daniel HERLEMONT

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