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VaR Methodology for Non-Gaussian Finance by Marine Habart-Corlosquet, Jacques Janssen, Raimondo Manca

By Marine Habart-Corlosquet, Jacques Janssen, Raimondo Manca

Content material:
Chapter 1 Use of Value?at?Risk (VaR) innovations for Solvency II, Basel II and III (pages 1–16): Marine Habart?Corlosquet, Jacques Janssen and Raimondo Manca
Chapter 2 Classical Value?at?Risk (VaR) tools (pages 17–34): Marine Habart?Corlosquet, Jacques Janssen and Raimondo Manca
Chapter three VaR Extensions from Gaussian Finance to Non?Gaussian Finance (pages 35–62): Marine Habart?Corlosquet, Jacques Janssen and Raimondo Manca
Chapter four New VaR equipment of Non?Gaussian Finance (pages 63–114): Marine Habart?Corlosquet, Jacques Janssen and Raimondo Manca
Chapter five Non?Gaussian Finance: Semi?Markov versions (pages 115–158): Marine Habart?Corlosquet, Jacques Janssen and Raimondo Manca

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22] 24 VaR Methodology for Non-Gaussian Finance Here, we can see that the crucial problem in determining this VaR value is the calculation and then the estimation of the two basic parameters: trend and volatility. 1 having at time 0 shares each with a value €700 and knowing on the time period T = 1 that the mean return is €60 and the standard deviation is 40. 3. 4. 2). 5. 4. VaR extensions: tail VaR and conditional VaR The search for new indicators having, if possible, more pertinence than the VaR, begins with the consideration that the fixation of the security level is of course subjective, and so the idea is that we effectively fix this level in a reasonable way at value α; but instead of taking into account all the values larger than α, we take the mean of all the corresponding VaR values to obtain a new indicator, which is called Tail-VaR (TVaR), denoted by TVaRα ( X ), and defined as: TVaRα ( X ) = 1 1 VaRξ ( X )d ξ .

We give, here, some examples for the values of cn and d n . 4. , xNn } This new sample is ranked in an increasing way: y1' ≤ ... – The method presented is not used frequently as it has two main disadvantages: 1) The parameters are obtained by linear regression and so this estimation takes time. 2) The number of observations needed for the linear regression must be large. For example, for n = N = 50 – N being the number of n realizations done – we need 2,500 observations. Due this fact, it is not very easy to use daily data as we will need long-time data from of 10 years, but of course with high-frequency trading (HFT) this analysis is no longer true.

6). 39] CVaRα ( X ) = TVaRα ( X ) − VaRα ( X ). – Let us now consider another example in an insurance company. 6. 6. 40] where Φ = 1 − Φ . 5. VaR of an asset portfolio In the Markowitz theory, for a portfolio composed of several assets, the main difficulty for computing the VaR is the estimation of the variance-covariance matrix of the vector of assets constituting this portfolio. 1. VaR methodology Theoretically, it is not difficult to extend the VaR method for one asset to a portfolio composed of n assets.

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