Catálogo de publicaciones - libros

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk-based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). We introduce several alternative product designs and analyze their impact on the insurer’s financial situation. We also introduce a measure for Capital Efficiency that considers both, profits and capital requirements, and compare the results of the innovative products to the traditional product design with respect to Capital Efficiency in a market consistent valuation model.

In this chapter, we study the effect of the fee structure of a variable annuity on the embedded surrender option. We compare the standard fee structure offered in the industry (fees set as a fixed percentage of the variable annuity account) with periodic fees set as a fixed, deterministic amount. Surrender charges are also taken into account. Under fairly general conditions on the premium payments, surrender charges and fee schedules, we identify the situation when it is never optimal for the policyholder to surrender. Solving partial differential equations using finite difference methods, we present numerical examples that highlight the effect of a combination of surrender charges and deterministic fees in reducing the value of the surrender option and raising the optimal surrender boundary.

A significant number of life insurance contracts are based on deterministic investment strategies—this justifies to restrict the set of admissible controls to deterministic controls. Optimal deterministic controls can be identified by Hamilton-Jacobi-Bellman techniques, but for the corresponding partial differential equations only numerical solutions are available and so the general existence of optimal controls is unclear. We present a non-constructive existence result and derive necessary characterizations for optimal controls by using a Pontryagin maximum principle. Furthermore, based on the variational idea of the Pontryagin maximum principle, we derive a numerical optimization algorithm for the calculation of optimal controls.

In traditional portfolio theory, risk management is limited to the choice of the relative weights of the riskless asset and a diversified basket of risky securities, respectively. Yet in industry, risk management represents a central aspect of asset management, with distinct responsibilities and organizational structures. We identify frictions that lead to increased importance of risk management and describe three major challenges to be met by the risk manager. First, we derive a framework to determine a portfolio position’s marginal risk contribution and to decide on optimal portfolio weights of active managers. Second, we survey methods to control downside risk and unwanted risks since investors frequently have nonstandard preferences, which make them seek protection against excessive losses. Third, we point out that quantitative portfolio management usually requires the selection and parametrization of stylized models of financial markets. We, therefore, discuss risk management approaches to deal with parameter uncertainty, such as shrinkage procedures or resampling procedures, and techniques of dealing with model uncertainty via methods of Bayesian model averaging.

Korn and Wilmott [9] introduced the worst-case scenario portfolio problem. Although Korn and Wilmott assume that the probability of a crash occurring is unknown, this paper analyzes how the worst-case scenario portfolio problem is affected if the probability of a crash occurring is known. The result is that the additional information of the known probability is not used in the worst-case scenario. This leads to a -quantile approach (instead of a worst case), which is a value at risk-style approach in the optimal portfolio problem with respect to the potential crash. Finally, it will be shown that—under suitable conditions—every stochastic portfolio strategy has at least one superior deterministic portfolio strategy within this approach.

Currently, several large life insurance companies apply the replicating portfolio technique for valuation and risk management of their liabilities. In [7], the two most common approaches, cash-flow matching and terminal value matching, have been investigated from a theoretical perspective and it has been shown that optimal terminal value replicating portfolios are not suitable to replicate liability cash-flows by construction. Thus, their usage for asset liability management is rather restricted, especially for out-of-sample cash profiles of liabilities. In this paper, we therefore enhance the terminal value approach by an additional linear regression of the corresponding optimal dynamic numéraire strategy to overcome this drawback. We show that terminal value matching together with an approximated dynamic strategy has in-sample and out-of-sample performance very close to the optimal cash-flow matching portfolio and, due to computational advantages, can thus be used as an alternative for cash-flow matching, especially in risk and asset liability management.

Computation is based on models and applies algorithms. Both a model and an algorithm can be sources of risks, which will be discussed in this paper. The stems from erroneous results, the topic of the first part of this paper. We attempt to give a definition of , and propose how to avoid it. Concerning the underlying model, our concern will not be the “model error”. Rather, even the reality (or a perfect model) can be subjected to structural changes: Nonlinear relations of underlying laws can trigger sudden or unexpected changes in the dynamical behavior. These phenomena must be analyzed, as far they are revealed by a model. A computational approach to such a will be discussed in the second part. The paper presents some guidelines on how to limit computational risk and assess structural risk.

We suggest practical and simple methods for Monte Carlo estimation of the (small) probabilities of large losses using importance sampling. We argue that a simple optimal choice of importance sampling distribution is a member of the generalized extreme value distribution and, unlike the common alternatives such as Esscher transform, this family achieves bounded relative error in the tail. Examples of simulating rare event probabilities and conditional tail expectations are given and very large efficiency gains are achieved.

The Hartman–Watson distribution is an infinitely divisible probability law on the positive half-axis whose density is difficult to evaluate near zero. We compare three different methods to evaluate this density and show that the straightforward implementation along Yor’s explicit formula can be improved significantly by resorting to dedicated Laplace inversion algorithms. In particular, the best method seems to be an approach that is specifically designed for distributions from the Bondesson class, to which the Hartman–Watson distribution belongs. The latter approach can furthermore be extended to yield an efficient Laplace inversion algorithm for evaluating the distribution function of the Hartman–Watson law.

We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including Lévy and affine processes. As an application, we compute the implied copula of the NIG Lévy process which exhibits notable time-dependence.