C15 - Statistical Simulation Methods: GeneralReturn

Exposure curves play significant role in modelling of property per risk excess of loss non-proportional reinsurance contracts, especially in the situations when not enough historical data is available for applying experience-based methods or if the underlying exposure changed significantly. The paper deals only with the first loss scale (FLS) approach which is frequently used in Europe. An alternative approach is based on ISO´s PSOLD methodology which is typical for the U.S. The first research into FLS approach was done by Ruth E. Salzmann in 1963 and some further curves have been developed since that time, however, their availability is limited. According to the authors´ knowledge only limited number of articles were published on this topic and no comprehensive publication which would describe the methodology to a larger extent exists. The paper provides a comprehensive description of the FLS exposure rating methodology, aims to summarise both historical and latest developments in this area and also includes various authors´ own practical considerations. The theory is illustrated on numerical examples.

Risk management for banking products can be challenging in general, but is even more risky in a global, low interest rate environment. This paper deals with the risk management of savings accounts, a bank product defined as a non-maturing account with embedded option that bears a relatively attractive rate of return. We focus on the interest rate risk of savings accounts. By constructing the replicating portfolio and simulating market rates and client rates, we show that under the severest scenario, some banks in the Czech Republic might face a significant capital shortage in next two years if market rates start to increase dramatically from recent low levels. We conclude that savings accounts are riskier liabilities than current accounts and term deposits for banks. Moreover, we propose imposing stricter regulation and supervision on these bank products since they might increase systemic risk of the Czech banking sector in coming years.

We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters' theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the BaxterKing filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough.

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model's parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model.

This paper focuses on operational risk measurement techniques and on economic capital estimation methods. A data sample of operational losses provided by an anonymous Central European bank is analyzed using several approaches. Multiple statistical concepts such as the Loss Distribution Approach and the Extreme Value Theory, including scenario analysis method, are considered. Custom plausible loss events defined in a particular scenario are merged with the original data sample and their impact on capital estimates and on the financial institution as a whole is evaluated. Two main questions are assessed - what is the most appropriate statistical method to measure and model operational loss data distribution and what is the impact of hypothetical plausible events on the financial institution. The g&h distribution was evaluated to be the most suitable one for operational risk modeling. The method based on the combination of historical loss events modeling and scenario analysis provides reasonable capital estimates and allows for the measurement of the impact of very extreme events on banking operations.

In this paper we extend the original heterogeneous agent model by introducing smart traders and changes in agents' sentiment. The idea of smart traders is based on the endeavor of market agents to estimate future price movements. By adding smart traders and changes in sentiment we try to improve the original heterogeneous agents model so that it provides a closer description of real markets. The main result of the simulations is that the probability distribution functions of the price deviations change significantly when smart traders are added to the model, and they also change significantly when changes in sentiment are introduced. We also use the Hurst exponent to measure the persistence of the price deviations and we find that the Hurst exponent is significantly increasing with the number of smart traders in the simulations. This means that the introduction of the smart traders concept into the model results in significantly higher persistence of the simulated price deviations. On the other hand, the introduction of changing sentiment in the proposed form does not change the persistence of the simulated prices significantly.