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This work presents an extensive case study on modelling the DAX (Deutscher Aktienindex) index and United States Oil Fund (USO) exchange‐traded fund (Etf) time series with the financial agent‐based system learning financial agent‐based simulator (L‐FABS) that exploits simulated annealing as a learning method. The USO Etf time series is highly correlated with oil price behaviour, and the DAX index is based on the weighted and accumulated behaviour of the share prices of some of the largest companies traded on the Frankfurt Stock Exchange. These two time series are driven by completely different economic factors and thus provide two diverse empirical settings to evaluate the effectiveness of our methodology. Our experimentation shows that a relatively simple computational representation of real financial markets is effective in capturing the overall behaviour of the time series with varying approximation levels while the prediction target is moved into the future. The reported experimental investigation of L‐FABS shows that it is robust notwithstanding the learning method used and the data sets exploited. L‐FABS indeed produced a relatively low approximation error in several settings even when evaluated with respect to other modelling approaches, for example, 0.88% and 1.61% errors on average for 1 day ahead experiments in, respectively, DAX index and USO Etf. [ABSTRACT FROM AUTHOR]

In an arbitrage-free securities market, all state-contingent claims and the stochastic discount factors can be approximated appropriately by index options with a semi-nonparametric method. These index options are constructed by efficient algorithms and uniform approximation error under these efficient algorithms are derived. This paper suggests a method to examine state-contingent claims and stochastic discount factors using index options in financial market regardless the market is complete or not. [ABSTRACT FROM AUTHOR]

Local volatility model is widely used in the fields of risk management, options pricing, etc. The model can not only describe the "smile" and the term structure of volatility, but can also ensure the completeness of the market. The core goal of local volatility research is to calculate the implied volatility. In this paper, the implied volatility surfaces arc built with both parametric and non-parametric methods to obtain smoother volatility surfaces. Parametric method can ensure the absence of arbitrage. Meanwhile, a closed form of solving the local volatility model with non-parametric method is proposed, which can eliminate the approximation error. In addition, the pricing of Shanghai 50ETF option in China based on the local volatility model is studied by comparing effects of the models from aspects of in-the-sample, out-of-the sample and hedging pricing errors. The empirical results show that the non-parametric method is better than the parametric method for errors in-the-samplc; the parametric method has better results for out-of-sample and hedging effects. Particularly, both the options pricing and hedging effects of the implied volatility modeling methods are better than nn-modeled method in the aspects that the pricing errors can be decreased by more than half and the mean square error can be reduced by 1~2 orders of magnitude. [ABSTRACT FROM AUTHOR]

The rough Heston model has recently been shown to be extremely consistent with the observed empirical data in the financial market. However, the shortcoming of the model is that the conventional numerical method to compute option prices under it requires great computational effort due to the presence of the fractional Riccati equation in its characteristic function. In this study, we contribute by providing an efficient method while still retaining the quality of the solution under varying Hurst parameter for the fractional Riccati equations in two ways. First, we show that under the Laplace–Adomian-decomposition method, the infinite series expansion of the fractional Riccati equation's solution corresponds to the existing expansion method from previous work for at least up to the fifth order. Then, we show that the fourth-order Padé approximants can be used to construct an extremely accurate global approximation to the fractional Riccati equation in an unexpected way. The pointwise approximation error of the global Padé approximation to the fractional Riccati equation is also provided. Unlike the existing work of third-order global Padé approximation to the fractional Riccati equation, our work extends the availability of Hurst parameter range without incurring huge errors. Finally, numerical comparisons were conducted to verify that our methods are indeed accurate and better than the existing method for computing both the fractional Riccati equation's solution and option prices under the rough Heston model. [ABSTRACT FROM AUTHOR]