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| Type | Master's Thesis |
| Scope | Discipline-based scholarship |
| Title | Application of a Double Exponential Jump Diffusion Process to Estimate the Impact of Solvency II on Insurance Companies Optimal Capital Structure Decision |
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| Institution | University of Zurich |
| Faculty | Faculty of Economics, Business Administration and Information Technology |
| Number of Pages | 91 |
| Date | 2015 |
| Abstract Text | Executive Summary Within the last decade, governments as well as (inter)national organisations increased their e orts to regulate the global nancial markets. This trend did not stop at the European insurance markets where the sector saw two fundamental new regulations: The so-called solvency directives. The European Parliament implemented revised solvency directives for European insurers back in 2002, called Solvency I Directives. By imposing minimum capital requirements Solvency I should ensure the market stability of the European insurance sector, but since the Solvency I Directives were implemented in di erent ways across Europe, and since they did not suciently re ect the complexity of the modern insurance business with its inherent risk factors, it was the EU Commission that agreed to fundamentally reform the Solvency I Directives. The outcome were the so-called Solvency II Directives with their risk-based three-pillar approach, which has its roots in the Basel II Directives for banking supervision. Similar to Solvency I, Solvency II obliges insurers with domiciles in the European Union and in the United Kingdom to hold a certain minimum capital in order to mitigate the risk of bankruptcy. Once implemented in 2016, the Solvency II Directives should result in a more harmonised and securer European insurance market. As regulations do intervene in nancial markets, they can also have negative or unwanted e ects. Hence, the thesis investigates these speci c regulations, the Solvency II Directives, and their impact on the choice of the debt-to-equity-ratio of the ten largest European insurance companies. The aim of this thesis therefore is to examine whether the debt-to-equity-ratio has deteriorated from one regime (that is before Solvency II has been approved by the European Parliament in April 2009) to another (i.e. after Solvency II has passed the European Parliament). In order to do so the author estimates a theoretical model, with empirical risk factors as input parameters, and compares the calculated optimal debt-to-equity ratios with those observed in the market and nally concludes whether the observed leverage on the market has deteriorated over time and across the di erent regimes. A sub-optimal debt-to-equity-ratio could, to provide an example, lead to higher capital costs since an insurer could hold a to high portion of equity which would have an impact on the tax shield and II therefore rise capital costs. The theoretical model, that serves to estimate the optimal debt-to-equity ratio, is the so-called Double Exponential Jump Di usion Model (DEJD) introduced by Kou and Chen (2009). It is an endogenous default model, based on Geometric Brownian Motion (GBM) that allows for two sided jumps. The DEJD model needs a variety of input parameters. Namely the volatility, the number of jumps, the magnitude of the jumps, the total payout ratio, the risk-free interest rate, the average coupon, the average maturity, taxes and the recovery rate in case of default. These input parameters have been estimated and collected for four di erent periods. That is, the DEJD model was applied on data estimated for January 2004 - March 2009 and April 2009 - June 2014, i.e. before and after the Solvency II directives passed the European Parliament. Furthermore, to account for the nancial crisis which may provide some risk factors that are biased and far from regular conditions, the model was estimated for two additional periods, i.e. January 2004 - December 2006 and July 2011 - June 2014. By applying the DEJD model on four di erent periods the author controls for market risk factors. As an example of such a market risk, one can think of rising stock price volatility. If volatility becomes larger insurers might increase their equity in order to account for the higher risk. To estimate some of the input parameters (volatility, number of jumps and jump magnitude) for the DEJD model, a Maximum Likelihood Estimation (MLE) on log-returns of the stock prices has been conducted. Since the Maximum Likelihood function contains double improper integrals as well as double in nite summations, the MLE to estimate the input parameters for the DEJD model was the most challenging and computationally a very costly part of this thesis. The MLE, which was implemented in R with the maximization algorithm Bound Optimization BY Quadratic Appoximation (BOBYQA), showed to be not fully optimized since the results obtained by the BOBYQA algorithm where di erent for di erent start parameters. Hence, by assuming a correct implementation of the Maximum Likelihood function in R, the Maximum Likelihood function seems to have several local Maxima. Using not fully optimized values as input parameters for the DEJD model certainly yields in results that should be, if at all, interpreted very carefully. Furthermore, the assumption for taxes and the recovery rate, two main drivers of the model of Kou and Chen (2009), were very strong since the tax rate of the country of domicile was applied on the whole company or, in the case of the III recovery rate for large insurance companies, hard to obtain, since large insurance companies rarely default. The weak indicators that have been found, that the capital structure deteriorated when Solvency II has been approved, would not withstand a proper statistical examination. First, the average shift that has been found is very small with a large variance and second, the ten examined insurance companies are too few to get signi cant results. However, the DEJD model showed to be useful to illustrate certain interdependencies and sensitivities to the debt-to-equity-ratio with respect the risk factors. In addition, it showed that further studies might use di erent algorithms to obtain fully optimized parameters from the MLE |
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