Monte Carlo simulation approaches to the valuation and risk management of unit-linked insurance products with guarantees

With the introduction of the Solvency II regulatory framework, insurers face the challenge of managing the risk arising from selling unit-linked products on the market. In this thesis two approaches to this problem are considered: Firstly, an insurer could project the value of their liabilities to some future time using Monte Carlo simulation in order to reserve adequate capital to cover these with a high level of confidence. However, the complex nature of many liabilities means that valuation is a task requiring further simulation. The resulting `nested-simulation' is computationally inefficient and a regression-based approximation technique known as least-squares Monte Carlo (LSMC) simulation is a possible solution. In this thesis, the problem of configuring the LSMC method to efficiently project complex insurance liabilities is considered. The findings are illustrated by applying the technique to a realistic unit-linked life insurance product. Secondly, an insurer could implement a hedging strategy to mitigate their exposure from such products. This requires the calculation of market risk sensitivities (or `Greeks'). For complex, path-dependent liabilities, these sensitivities are typically estimated using simulation. Standard practice is to use a `bump and revalue' method. As well as requiring multiple valuations, this approach can be unreliable for higher order Greeks. In this thesis some alternative estimators are developed. These are implemented for a realistic unit-linked life insurance product within an advanced economic scenario generator model, incorporating stochastic interest rates and stochastic equity volatility

Applications of the Scaled Laplace Transform in some Financial and Risk Models

In this work, we propose several approximations for the evaluation of some risk measures and option prices based on the inversion of the scaled version of the Laplace transform which was suggested by Mnatsakanov and Sarkisian (2013). The classical risk model is considered for the evaluation of probability of ultimate ruin. Approximations of the inverse function of the ruin probability is proposed and its natural extension to the computation of Value at Risk, a benchmark risk measure for insurance and finance sectors, is proposed. The recovery of the distributions of bivariate models and bivariate aggregate claims amount on insurance policies is suggested. The proposed method is also applied to the Black-Scholes model for the estimation of option prices. Simulation studies and results are presented to demonstrate the performance of the proposed method