THREE ESSAYS ON MORTGAGE BACKED SECURITIES: HEDGING INTEREST RATE AND CREDIT RISKS
Fu, Michael C.
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This dissertation includes three essays on hedging the interest rate and credit risks of Mortgage-Backed Securities (MBS). Essay one addresses the problem of how to efficiently estimate interest rate sensitivity parameters of MBS. To do this in Monte Carlo simulation, we derive perturbation analysis (PA) gradient estimators in a general setting. Then we apply the Hull-White interest rate model and a common prepayment model to derive the corresponding specific PA estimators, assuming the shock of interest rate term structure takes the form of a trigonometric polynomial series. Numerical experiments comparing finite difference (FD) estimators with our PA estimators indicate that the PA estimators can provide better accuracy than FD estimators, while using much lower computational cost. Using the estimators, we analyze the impact of term structure shifts on various mortgage products. Based these analysis, we propose a new product to mitigate interest rate risk. Essay two addresses the problem of how to measure interest rate yield curve shift more realistically, and how to use these risk measures to hedge the interest rate risk of MBS. We use a Principal Components Analysis (PCA) approach to analyze historical interest rate data, and acquire the volatility factors we need in Heath-Jarrow-Morton interest rate model simulation. Then we propose a hedging algorithm to hedge MBS, based on PA gradient estimators derived upon these PCA factors. Our results show that the new hedging method can achieve much better hedging efficiency than traditional duration and convexity hedging. Essay three addresses the application a new regression method on credit spread data. Previous research has shown that variables in traditional structural model have limited explanatory power in credit spread regression. We argue that this is partially due to the non-constancy of the credit spread gradients to state variables. We use a Random Coefficient Regression (RCR) model to accommodate this problem. The explanatory power increases dramatically with the new RCR model, without adding new independent variables. This is the first work to address the dependence between credit spread sensitivities and state variables of structural in a systematic way. Also our estimates are consistent with prediction from Merton’s structural model.