Modelling of tradeable securities with dividends

We propose a generalized framework for the modeling of tradeable securities with dividends which are not necessarily cash dividends at fixed times or continuously paid dividends. In our setup the dividend processes are only required to be semi-martingales. We give a definition of self-financing replication which incorporates dividend processes, and we show how this allows us to translate standard results for the pricing and hedging of derivatives on assets without dividends to the case of assets with dividends. We then apply this framework to analyze and compare the different assumptions that have been made in earlier dividend models. We also study the case where we have uncertain dividend dates, and we look at securities which are not equity-based such as futures and credit default swaps, since our weaker assumptions on the dividend process allow us to consider these other applications as well

Geography, culture, and religion: Explaining the bias in Eurovision song contest voting

This paper analyses votes cast in the Eurovision Song Contest in the period 1975 - 2003. We test whether accusations of 'political' voting among participants can be substantiated by looking at geographical influences. Our approach differs in two ways from earlier studies. First, we take into account a variety of variables to distinguish political voting from preferences based on cultural, linguistic, ethnic, and religious differences and similarities between countries. Secondly, we analyse the determinants of the voting behaviour separately per country, instead of looking at average effects over all participating countries. We find that geographical factors substantially affect the votes. Even after correction for cultural, linguistic and other factors many countries prefer or dislike the songs of surrounding countries. This leads to the suspicion that the geograph¬ical preferences reflect political voting. Also, we show that several countries favour songs of participants with the same religious background, while others prefer the contributions of countries with a different religion. Moreover, using data on the amount of Turkish immigrants across European countries, we document that countries with a substantial Turkish population favour the Turkish songs ('patriotic' voting). Furthermore, we study the repercussions of opening up the voting system to the general public by the introduction of televoting. It turns out that religious and patriotic voting have become considerably stronger since the introduction of the new voting system. Finally, we confront our em¬pirical findings to the publicly debated accusations of political voting made against certain blocks of countries. Although our analysis uncovers significant geographical patterns (suggesting political voting), we do hardly establish any empirical evidence for the claims against these particular countries

Pricing and Hedging Guaranteed Returns on Mix Funds

Abstract\ud In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment

Cash dividends and futures prices on discontinuous filtrations

We derive a general formula for the futures price process without the restriction that the assets used in the future margin account are continuous and of finite variation. To do so, we model tradeable securities with dividends which are not necessarily cash dividends at fixed times or continuously paid dividends. A future contract can then be modelled as an asset which pays dividends but has zero value in itself. We show that the futures price is not necssarily a martingale under the equivalent martingale measure, but that it remains a martingale under a new measure which is closely connected to multiplicative Doob-Meyer decompositions. Our definition of self-financing replication is different from some earlier ones, even for assets that do not pay dividends, and we argue that for discontinuous asset price processes it could be more natural than the usual formulation

A nonlinear filtering approach to changepoint detection problems:direct and differentialg-geometric methods

A benchmark change detection problem is considered which involves the detection of a change of unknown size at an unknown time. Both unknown quantities are modelled by stochastic variables, which allows the problem to be formulated within a Bayesian framework. It turns out that the resulting nonlinear filtering problem is much harder than the well-known detection problem for known sizes of the change, and in particular that it can no longer be solved in a recursive manner. An approximating recursive filter is therefore proposed, which is designed using differential-geometric methods in a suitably chosen space of unnormalized probability densities. The new nonlinear filter can be interpreted as an adaptive version of the celebrated Shiryayev-Wonham equation for the detection of a priori known changes, combined with a modified Kalman filter structure to generate estimates of the unknown size of the change. This intuitively appealing interpretation of the nonlinear filter and its excellent performance in simulation studies indicate that it may be of practical use in realistic change detection problems

Symmetries in jump-diffusion models with applications in option pricing and credit risk

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work it was shown that when invoked as a fundamental first principle, it provides a powerful alternative method for the derivation of prices and hedges of derivative securities, when prices of the underlying tradables are driven by Wiener processes. In this article we extend this work to the pricing problem in markets driven not only by Wiener processes but also by Poisson processes, i.e. jump-diffusion models. It is shown that in this case too, the focus on symmetry aspects of the problem leads to important simplifications of, and a deeper insight into the problem. Among the applications of the theory we consider the pricing of stock options in the presence of jumps, and Lévy-processes. Next we show how the same theory, by restricting the number of jumps, can be used to model credit risk, leading to a `market model' of credit risk. Both the traditional Duffie-Singleton and Jarrow-Turnbull models can be described within this framework, but also more general models, which incorporate default correlation in a consistent way. As an application of this theory we look at the pricing of a credit default swap (CDS) and a first-to-default basket option

Rapport Technische werkgroep economische scenario’s

Rapport over scenario's op het gebied van pensioenen

Advies Commissie Parameters 2022

Onderzoek van de Commissie Parameters 2022 naar de parameters, UFR-methode en economische en risico-neutrale scenario’s. Deze moeten worden gehanteerd bij diverse wettelijke toepassingen in zowel het huidige pensioenstelsel als in het nieuwe pensioenstelsel en de transitie daarnaartoe zoals voorgesteld in de Wet toekomst pensioenen