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Value-at-Risk for Nonlinear Financial Instruments - Linear Approximation or Full Monte Carlo?
Company: University of St. Gallen
Company Url: Click here to open
Year Of Publication: 2001
Month Of Publication: December
Pages: 19
Download Count: 3263
View Count: 37195
Comment Num: 0
Language: EN
Source: working paper
Who Can Read: Free
Date: 10-4-2002
Publisher: Administrator
Summary
We implement different methods of computing VaR for portfolios containing nonlinear financial instruments. We show that simple linear approximation models (e.g. the Delta-Exact VaR) are reasonably accurate in many cases. For some heavily optioned portfolios, however, only simulation methods such as Monte Carlo simulation with full revaluation are appropriate. In particular, we find that: ? For portfolios without substantial option components, the (linear) Delta-Normal and particularly the Delta-Exact VaR represent a good approximation for the Monte Carlo VaR. The results deteriorate somewhat for increasing VaR time horizons and confidence levels. ? For portfolios with more pronounced nonlinearities, such as pure option portfolios, Delta-Exact VaR and Monte Carlo VaR tend to differ substantially, especially for longer VaR time horizons and high confidence levels. Portfolios containing other highly nonlinear instruments such as straddles or strangles also produce large approximation errors. ? Furthermore, the difference between the relative Delta-Exact VaR and the Monte Carlo VaR increases for options with a short time to maturity.
Author(s)
Ammann, Manuel Sign in to follow this author
Reich, Christian Sign in to follow this author
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