We study the impact of wrong-way risk (WWR) on the credit valuation adjustment (CVA) of a portfolio of interest rate swaps (IRSs), using an intensity-based reduced form model. To model WWR in IRSs we create a dependence between he underlying market risk factor of the IRS and the survival probability of the
counterparty. The focus lies on modeling the credit part of the CVA, choosing the most suitable default model. Using a Monte Carlo (MC) framework, we correlate the Brownian increments of the stochastic processes that describe the interest rate and the hazard rate. Assuming the correlation parameter is chosen based on historical data, we solve the problem of leaking correlation. Two
stochastic processes for the credit part are chosen, the CIR++ and the JCIR++, such that the influence of the model choice can be separated from the impact of WWR. With a case study, we vary the correlation parameter to quantify the impact of WWR on CVA of the portfolio. We show that the introduced dependence has a significant impact on the CVA, that depends on the calibration, the portfolio and the chosen correlation. Solving the leaking correlation problem can increase the impact of WWR on the CVA, especially using JCIR++ dynamics.

This thesis showcases a rather contemporary method of solving a generalized system of stochastic differential equations (SDE's) comparable to the SABR model. The solution is derived from a stochastic-local volatility (SLV) model in which the local volatility (LV) component is kept general. This generality is maintained throughout all derivations, eventually yielding a model containing an undefined LV function. This function can then be specified however the user of the model deems suitable, as long as minor constraints are satisfied. Obviously, this is a very valuable quality of the model as it is highly customizable. The solution consists of a set of pricing functions that seemingly possess all the aforementioned desirable properties, i.e. fast in evaluation, computational tractability, flexibility etc., with little disadvantages. The generalized SLV model that is used is typically denoted in the form of two SDE's, though in the majority of this thesis an atypical three SDE form is used. This extended system is used to isolate the LV component, in turn enabling for appropriate application of an SDE transformation called the Lamperti transform, which will provide the key to solving the entire system. The Lamperti transform is a highly versatile method for transforming SDE's into new equations typically more suitable for simulation and parameter estimation procedures, and its inner-workings and various applications will be the main focus of this thesis.

This thesis captures the calibration of a FX hybrid model: The FX Black-Scholes Hull-White model. The main focus is on the calibration of the parameters in the Hull-White process: The mean reversion and the volatility parameter. The latter is commonly calibrated as a time-dependent parameter, whilst the mean reversion parameter is not. This thesis covers the calibration of the mean reversion as a time-dependent parameter. A known method from the Literature is researched, where we calibrate the mean reversion independently from the volatility parameter to the ratio of two swaptions with the same expiry but different tenor. In our research this method is extended to the negative interest rate environment by assuming that the swap rate follows a shifted lognormal distribution instead of a lognormal distribution. We show that a specific set of swaptions can be chosen, so that the calibration problem is simplified. This choice leads to sequential calibration of convex optimization problems. Numerical results of calibration to artificial and market data are presented, where we compare our method to picking the mean reversion parameter arbitrarily. The findings suggest that the choice of mean reversion parameter affects the calibration procedure. Therefore, we argue that a calibration method for the mean reversion would be appropriate. Besides the focus on the Hull-White process, the calibration of the volatility parameter in the FX Black-Scholes process of the hybrid model is investigated. For the calibration of the FX volatility parameter ATM options on FX rates are used. Numerical results of calibration to artificial and market data are shown. A typical problem of calibration in the industry is discussed: Precision for late maturities. The results in this thesis suggest that this problem could be solved. For research on homogeneity constraints on the time-dependent parameters, the performance of delta-hedging is investigated. The delta-hedging is performed in a simple Black-Scholes world with time-dependent volatility. We show that given a fixed amount hedges beforehand and interest rate zero, there exists an optimal distribution of time points that will lead to equal variance on the profit and loss for every volatility function that has equal implied volatility from t0 to maturity T. Using this strategy, the homogeneity of the volatility parameter has no impact on the performance of delta-hedging. Therefore, in this thesis no homogeneity constraints are used for the calibration of the time-dependent parameters.

The yield curve represents market supply and demand implied expectations of future interest rates and is calibrated from the most liquidly traded interest rate derivatives like cash deposits, forward rate agreeents, swaps and futures. Due to the daily margining mechanism of futures contracts, interest rate futures require the substraction of a convexity adjustment in order for them to be used in curve calibration. It is common practice to use externally computed convexity adjustments, which treats the convexity adjustment as a black-box parameter. We will argue the inherent relationship between the convexity adjustment and cap/floor volatility smiles and derive a nested calibration algorithm for the simultaneous calibration of the yield curve to futures and the convexity adjustment to cap/floor volatility surfaces. This introduces dependencies of the yield curve to option volatilities and we will argue that for simple interest rate derivatives the implied vegas are negligible. .

Efficiently managing hedging portfolios on behalf of pension funds is key in achieving the target hedging strategy, which can significantly impact coverage ratios. A new optimization approach to fixed income portfolio management for pension funds is proposed that finds interest rate risk hedging strategies while incorporating additional requirements. These are relevant requirements for pension funds such as country allocations, low transaction costs and reasonable investment costs. In doing so, pension fund regulations and common practices are investigated in a rigorous mathematical framework. The hedging strategies are shown to perform well when back-testing. In addition, simulation of the interest rate and cash flows in a Defined Benefits pension scheme displays the good performance of the strategies. These strategies are further tailored to specific pension funds by considering the trade-off between yield and risk, which could contribute to increasing a pension fund’s coverage ratio. Alternatively, a procedure is also proposed to generate more diversified albeit less optimal hedging portfolios using the optimization approach.