Estimating Value at Risk with the Kalman Filter Jaime Frade - - PowerPoint PPT Presentation

Estimating Value at Risk with the Kalman Filter

Jaime Frade

Department of Statistics Florida State University Anuj Srivastava STA5107

March 17, 2009

Jaime Frade (Florida State University) Estimating Value at Risk with the Kalman Filter March 17, 2009 1 / 8

Outline

1

Objective

2

Data of Model

3

Kalman Filter Process

4

Results: VaR: Calculations

5

Plot VaR:

6

Plots of Error:

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Objective

Goal In this project, the goal is to apply one technique of risk management which measures as a percent the maximum loss which is likely to be exceeded on the portfolio, given a certain probability and time horizon within a given confidence level under assumed market conditions. Using Value-at-Risk, VaR, will estimate the β’s of the assets of the portfolio with a Kalman Filter. Overall, the results showed more market sensitivity compared to historical simulation, depending on the assets of the portfolio

• r on the type of fund itself, for instance a hedge fund.

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Data of Model

Time horizon: (01/02/2004- 3/12/2009). Daily Stock last trade price for two individual companies, GE and IBM. S&P as my market variable. n = 1306 observations.

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Kalman Filter Process

Figure: Kalman Filter Process

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Results: VaR: Calculations

Procedure VaR Historical Simulation loss of 2.32% Kalman Filter loss of 2.74% Intrepretation: With 95% confidence, we expect that the worst daily loss will not exceed given percentage

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Plot VaR:

VaR = z

• w′ββ′wσ2

m

√ ∆t (1) Plot of daily VaR calculations based on porfolios of equal weights.

Figure: Sequence of VaR Calculations

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Plots of Error:

Plots of a comparsion of between using the predicted X(t+1)P and X(t+1)P−ADJ to predict the R(t+1)P(= Y(t+1)P)

Figure: Relizations of Error Plots

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