Dominance tracking index for measuring pension fund performance with respect to the benchmark

This paper focuses on the performance of Lithuanian life-cycle second-pillar pension funds. Every such fund first specifies its benchmark and then attempts to follow the benchmark in some way. This is a form of regulation, meaning that every such fund is somehow regulated and controlled by the central bank authorities. The goal of this paper is twofold: (i) to analyse the returns of the pension funds with respect to their benchmarks and (ii) to determine whether less strict regulation leads to a better outperformance of the fund with respect to the benchmark. In order to achieve this, we introduced a new performance measure called the dominance-tracking index, which combines the ideas of almost stochastic dominance relations and tracking errors. While the tracking error and its modifications measure the strength of the regulation, almost stochastic dominance provides information about preferences between the funds and their benchmarks. Therefore, the new index was constructed in such a way as to take into account both approaches. The empirical section of the study then presents the results separately for the considered pension managers and participants’ age groups as usual in the life-cycle pension funds analysis. Finally, by taking into account various periods, we studied the effects of the COVID-19 crisis. Keywords: pension fund; management; regulation; life-cycle strategy; benchmark; stochastic dominance; almost stochastic dominance; risk assessment; COVID-19

Dominance Tracking Index for Measuring Pension Fund Performance with Respect to the Benchmark

This paper focuses on the performance of Lithuanian life-cycle second-pillar pension funds. Every such fund first specifies its benchmark and then attempts to follow the benchmark in some way. This is a form of regulation, meaning that every such fund is somehow regulated and controlled by the central bank authorities. The goal of this paper is twofold: (i) to analyse the returns of the pension funds with respect to their benchmarks and (ii) to determine whether less strict regulation leads to a better outperformance of the fund with respect to the benchmark. In order to achieve this, we introduced a new performance measure called the dominance-tracking index, which combines the ideas of almost stochastic dominance relations and tracking errors. While the tracking error and its modifications measure the strength of the regulation, almost stochastic dominance provides information about preferences between the funds and their benchmarks. Therefore, the new index was constructed in such a way as to take into account both approaches. The empirical section of the study then presents the results separately for the considered pension managers and participants’ age groups as usual in the life-cycle pension funds analysis. Finally, by taking into account various periods, we studied the effects of the COVID-19 crisis

On the pricing of illiquid options with Black-Scholes formula

Detecting the fair, ie. no-arbitrage, price of an option is a very interesting and challenging task of quantitative finance. It results mostly from the fact that the option payoff is nonlinear and the price can be very sensitive to the changes of underlying factors (especially ATM options). From the other point of view, ATM vanilla options are often traded and liquid, while deep ITM and OTM options are mostly illiquid and it is difficult to estimate the model parameters. Another issue is how to obtain the market assumptions about riskless rate relevant for the option maturity and the future expected dividends. In this paper we focus on a particular problem of extracting parameters to value options on dividend paying stocks via BS model using real data from German option market

Implied volatility and state price density estimation: arbitrage analysis

This paper deals with implied volatility (IV) estimation using no-arbitrage techniques. The current market practice is to obtain IV of liquid options as based on Black–Scholes (BS type hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. Therefore, it follows that the BS model can be related simultaneously to the whole set of IVs as given by maturity/moneyness relation of tradable options. Then, it is possible to get IV curve or surface (a so called smile or smirk). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary. However, it can lead to arbitrage opportunity if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim to analyse the behavior of IV and SPD with respect to different choices of bandwidth parameter h, time to maturity and kernel function. A set of bandwidths which violates no-arbitrage conditions is identified. We document that the change of h implies interesting changes in the violation interval of moneyness. We also perform the analysis after removing outliers, in order to show that not only outliers cause the violation of no-arbitrage conditions. Moreover, we propose a new measure of arbitrage which can be considered either for the SPD curve (arbitrage area measure) or for the SPD surface (arbitrage volume measure). We highlight the impact of h on the proposed measures considering the options on a German stock index. Finally, we propose an extension of the IV and SPD estimation for the case of options on a dividend-paying stock

Pension fund optimal allocations

We address the problem of a private pension plan sponsor who has to decide the best pension funds that should be offered to the pension plan members. Starting from the analysis of the population of the plan in order to identify a set of representative subscribers, we focus on an individual optimal portfolio allocation in a pension perspective. Then, the optimal allocation for each representative will become a pension fund. For each representative, we propose a multistage stochastic program (MSP) which includes a multi-criteria objective function. The optimal choice is the portfolio allocation that minimizes the Average Value at Risk Deviation of the final wealth and satisfes a wealth target in the final stage. Stochasticity arises from investor's salary process and asset returns. The stochastic processes are assumed to be correlated. Numerical results show optimal dynamic portfolios with respect to investor's preferences and then the best pension funds the provider can offer