STOCHASTIC ASSET LIABILITY AND MANAGEMENT MODELLING USING LÃ©VY PROCESS - Laurencius Yonathan, Ferdinand
Insurance asset and liability management (ALM) is a process of formulating, implementing, and monitoring financial policies related to assets and liabilities intended to optimize the profitability and solvency of insurance companies. This process is vital because the insurance company accepts a significant transfer of risk from the insured, for example the risk of mortality in life insurance. The ALM formulation process involves modeling assets and liabilities. Considering the importance of model fitness on empirical data, in this thesis the simulation will utilize the Variance Gamma process as a comparison to the Black-Scholes model (geometric Brownian motion) which is more commonly used. Compared to the Black-Scholes model, the Variance Gamma process fits leptokurtic and heavy-tailed data better. The author also analyzes the value of zero-coupon bonds using the Cox-Ingersoll-Ross (CIR) stochastic short rate model. Meanwhile, the author also uses Thiele’s differential equation to calculate the policy value (insurance liability). The policy value calculation involves CIR short rate as well as the Gompertz mortality model which is fitted to the Indonesian Mortality Table IV. The asset and liability models are then implemented in a scenario simulation which aims to find initial portfolio composition which optimizes an objective function of the ratio between the expectation and Value-at-Risk of equity. Using the Monte-Carlo method, the simulation produces an optimal portfolio composition of 30%:49%:21%, respectively the proportion of cash, bonds, and stocks relative to the portfolio. Based on the goodness-of-fit test, the Variance Gamma and Black-Scholes models produce Akaike Information Criterion of -5,777.76 and -5,694.59 respectively. Although the Variance Gamma model fits better, the Black-Scholes model produces a larger optimal objective function value of 2.456 compared to 2.452. The Black-Scholes model also provides a lower default risk due to a theoretically higher expected value of stock price.