Efficient calibration, valuation and pricing with applications in interest rate and credit risk models

This thesis develops and extends advanced mathematical models for financial applications, with a focus on interest rate, affine term structure and credit risk models. Its aim is to contribute to both theoretical analysis and practical implementation of robust methods for parameter estimation, portfolio valuation and derivatives pricing.
The thesis first addresses the calibration of credit rating transition models that incorporate both cross-sectional dependence among obligors and serial dependence driven by economic cycles. Two maximum-likelihood-based algorithms are developed: a Laplace approximation combined with Kalman filtering for high-default portfolios, and a particle filter enhanced by importance sampling and Gaussian process regression for low-default portfolios. These methods allow calibration directly to observed default or migration counts and provide computationally efficient alternatives to conventional approaches.
The thesis then develops a Kalman particle filter for online parameter estimation in affine interest rate models. The proposed method combines a dynamic-kernel-enhanced particle filtering for unknown parameters, with Kalman filtering for latent states. This enables fast sequential updates and allows the model to accommodate regime changes. A theoretical convergence result is established for the posterior distributions of parameters and states.
Next, a Bayesian filtering and smoothing approach is introduced for dimension reduction in credit portfolio loss valuation. The method addresses the curse of dimensionality in valuation grids and improves the accuracy of expected loss and Value-at-Risk estimation compared with standard PCA-based techniques.
Finally, the thesis studies European-style option pricing on forward contracts within infinite-dimensional affine stochastic volatility models. We derive exponential moment conditions and develop semi-closed Fourier-based pricing formulas for vanilla options and hence allows for efficient pricing.