On the 1st of January 2016, the Solvency II Directive regulating the European insurance industry came into force. Along with a host of reporting requirements, quantitative algorithms for calculating key quantities are provided in the Solvency II documentation. One of these key quantities is the Solvency Capital Requirement (SCR) providing an insurance company with a "soft" floor in terms of capital that it needs to hold. A vital element in calculating the SCR for an insurance company is the so-called Standard formula based on Gaussian risks which is used iteratively to aggregate the different risk elements in the business. An alternative to the Standard formula was proposed by Bølviken and Guillen who introduced log-normal distributions to better capture the skewness often present in insurance risks. They used classical moment matching to approximate the distribution of a sum of log-normal risks. In this thesis we will consider another log-normal alternative making use of moment-generating functions. This method will then be shown to offer superior accuracy compared to the Standard formula and the method of Bølviken and Guillen.