Value-at-Risk (VaR ) is an industrial
standard for monitoring market risk in an
investment portfolio. It measures potential
osses within a given confidence level. VaR
was first used by major financial
institutions in the early 1990’s, and widely
developed after the release of J.P. Morgan’s
Riskmetrics Technical Document in 1996. The
efficient calculation, implementation,
interpretation and optimization of VaR are a
challenge in the practice of risk management
when the number of market factors in the
portfolio is high.
In this thesis, we are concerned with the
quadratic analytical estimation of VaR and
we present a methodology for an approximation
to VaR that is based on the principal
components of a sensitivity-adjusted
covariance matrix. The result is an explicit
expression in terms of portfolio deltas,
gammas, and the mean and covariance matrix.
It can be viewed as a non-linear extension
of the linear model given by the
delta-normal-VaR of RiskMetrics, a standard
calculation for the risk in the financial
sector. We obtain an asymptotic expansion
for VaR in the limit when the confidence
level approaches 1 and precise estimates of
the reminder. We then optimize the
approximated VaR with respect to the
gradient or delta of the portfolio, a
quantity which can be changed by trading the
underlying assets (stocks), without entering
into any derivative transactions. This
analysis provides an optimal trading
strategy of the portfolio that minimizes the
risk.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/11248 |
| Date | 01 August 2008 |
| Creators | Quintanilla, Maria Teresa |
| Contributors | Sulem, Catherine |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 713758 bytes, application/pdf |
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