After the financial crisis, the standards for the valuation of financial derivatives were reviewed and several adjustments were made to these valuations, of which Credit Value Adjustment (CVA) is the most important one. CVA represents the price of counterparty credit risk that should be added to the default-free fair price of a financial derivative. Nowadays, banks and other financial institutions have dedicated CVA desks that are responsible for estimating CVA and its sensitivities to many market parameters for each counterparty. It is therefore important to have accurate and efficient methods to compute CVA and its sensitivities. This can, however, be a challenge.

Multiple methods to compute CVA sensitivities already exist in the literature, but these methods have certain drawbacks, such as a high computational expense or a payoff dependency. An efficient approach for computing CVA sensitivities is the Likelihood Ratio Method. One of the main advantages is its payoff independence, making the method applicable to sensitivities of any payoff, even payoffs with discontinuities. Furthermore, the Likelihood Ratio Method stands out by its ability to derive multiple sensitivities within a single Monte Carlo simulation. In this research, an innovative approach is developed, which involves using the Hull-White short rate model to model interest rates while applying the Likelihood Ratio Method. A drawback of the Likelihood Ratio Method is its susceptibility to high variance. To mitigate this issue, variance reduction techniques are explored, including antithetic sampling, control variates, and Quasi-Monte Carlo methods.

The performance of the Likelihood Ratio Method is compared to the Bump & Reprice method in computing first-order CVA sensitivities of three different over-the-counter derivatives. It is shown that for a certain range of model parameter values, the Likelihood Ratio Method is able to match the Bump & Reprice sensitivities. However, the Likelihood Ratio Method exhibits high variance for some extreme parameter values.

Since the gamma distribution is one of the most important models, and no convenient statistical tools for this distribution are available, the aim of this project is to construct an R package for the gamma distribution. In this package five functions are created, that can be used to either generate gamma distributed random variables, to estimate the parameters of a gamma distribution and to construct statistical limits for the gamma distribution. In this report, the methods to do so are explained, implemented in R, and the performance of the methods have
been tested. Lastly, an example is given to illustrate the application of the package.