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On the White Board - January 2010
Jan 15, 2010
Approximating VaR for Securitized Products
The traditional approach to Monte Carlo VaR involves repeatedly simulating the state of the market (that is, a set of market risk factors), and valuing the securities under every such simulated realization. In the context of Mortgage-Backed Securities (MBS), valuation involves a time intensive simulation process incorporating the effect of path-dependent prepayments. Computing Monte Carlo VaR using the traditional approach might be feasible (assuming substantial computing power) for portfolios of a small number of MBS, but would be impractical when we consider the simulation of large portfolios within typical timeframes.
The MBS full valuation approach creates a large number of scenarios for the risk factors and then, for each scenario, performs a complete revaluation of the portfolio, leading to the profit/loss distribution of the portfolio. Although the full valuation approach might well be the correct first step in a VaR computation exercise, the sheer computational overhead of such a procedure renders it prohibitively expensive for the MBS asset class. This begs the question - could we do this faster, with negligible loss of accuracy? Estimating the (black box) hypothetical pricing function with a quadratic approximation that incorporates a data-driven learning scheme provides one such solution.
Figure 1
Figure 1 depicts the full valuation prices along with the approximated prices resulting from the quadratic pricing scheme for a Subprime MBS Senior Tranche for a sample size of 100 simulations. The closeness of the approximated price series and the true price series suggests that at least for Monte Carlo VaR computation, the approximation provides a viable alternative to the full valuation approach. For a more robust estimate such as in the context of stressed VaR computations, the approximation scheme could take as input an appropriately perturbed risk factor space (i.e., stressed scenarios) so as to encompass a sufficiently wide range of risk factor scenarios. This would yield a potentially more robust solution where the approximation would adapt to larger moves of the underlying factors.
Although not a panacea, it does provide a simple solution to the computational hurdles.