Robust Estimation and Simulation of Distributional VAR in Multi-State Models
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Winkler, Robert Kevin
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Abstract
This research focuses on the computational modeling and inference of the behavior of a heterogeneous collection of financial instruments, for example residential mortgages, which assume various possible states. The states of these instruments are influenced both by the individual characteristics of the instruments as well as the effects of external influences that may be stochastic in nature. Simulation of the evolution, over time, of the distribution of the instruments’ states or other variables that are dependent upon object states is used to make statistical inferences concerning the future characteristics of the population of objects. A framework for modeling these types of problems and the movement of financial instruments between various states is described. Several examples of application areas for this framework are mentioned and an extensive example from computational finance is used to demonstrate the methodology. The specific example explored involves the calculation of capital holding requirement that would be sufficient to insure that the credit losses associated with a portfolio of mortgages would be adequate to cover those losses with a pre-specified level of certainty. This will be referred to as the Economic Capital Value-at-Risk (ECVAR) problem. This example was chosen because of the economic significance of the mortgage market and the benefit of leveraging information about the state of each mortgage over time in calculating ECVAR. The U.S. mortgage market is substantial with more than $13.7 trillion in outstanding debt as of 2015. The slump in this market figured prominently in economic decline that resulted in the Great Recession of 2007 through 2009. Yet, despite the size and importance of this market, many of the models used for the risk management of mortgage portfolios failed to adequately identify the extent of potential losses in this market. Such models, generally termed value-at-risk or VAR models generally appeared to be biased downward (i.e. underestimating the potential losses). Such biases were present because models sometimes replaced random variables with estimates of the expected values of the variables resulting in understating the variance and the length of tails of the estimated loss distribution. Other factors that contributed to mortgage credit loss model failures included too much reliance on estimated variance measures and reliance on over aggregation of data and/or models that can lead to the appearance of less dispersion in the loss distribution by overstating diversification effects in a portfolio of mortgages or a mortgage-backed security. By focusing on the loan-level, joint estimation of mortgage payment states (including voluntary mortgage prepayments as well as defaults), less biased estimates of the tails of loss distribution can be obtained. Additionally, through the use of Monte Carlo simulation, information on the distribution of the losses in the tail of the loss distribution can be collected and examined for purposes of statistical inference. This approach may be termed Distributional Value-at-Risk (DVAR) and is similar to Conditional Value-at-Risk (CVAR) but supports calculation of higher level moments in the tails of the loss distribution in addition to being able to compute CVAR.
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This dissertation has been embargoed for 5 years and will not be available until April 2021 at the earliest.
Keywords
Value at risk, VAR, Credit risk, Mortgage