A regularized unconstrained optimization in the bond portfolio valuation and hedging

Abstract

In this chapter, a numerical approach to the valuation and hedging of a portfolio of bond and options is presented in the case of strong dependency of bond principal on the market interest rate metric. Collateralized Mortgage Obligations (CMO) represents one of the important classes of such bond type. To improve the CMO valuation methodology and to develop a robust procedure for the construction of the optimal hedge for CMO, we introduce an optimization approach to minimize the dispersion of the portfolio spread distribution by using available on market options. In doing so, we design an optimal hedge with respect to the set of available benchmarks and we obtain the two new valuation metrics that represent the quality of hedge with respect to this set. Our two main outputs are the mean and the standard deviation of the individual spreads for the optimal portfolio. These metrics can be used in comparison analysis in addition to the standard OAS valuation. © 2009 Springer Netherlands.