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AKAT, Muzaffer

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Now showing 1 - 6 of 6
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    Conference ObjectPublicationMetadata only
    An approximation of stochastic telegraph equations
    (AIP Publishing, 2012) Ashyralyev, A.; Akat, Muzaffer; International Finance; AKAT, Muzaffer
    In the present paper the two-step difference scheme for the telegraph equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference scheme for the numerical solution of two problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment.
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    ArticlePublicationOpen Access
    Market-neutral trading with fuzzy inference, a new method for the pairs trading strategy
    (Kaunas University of Technology, 2019) Bayram, M.; Akat, Muzaffer; International Finance; AKAT, Muzaffer
    Pricing of financial instruments and stock market predictions is a specific and relatively narrow field, which has been mainly explored by mathematicians, economists and financial engineers. Prediction to make profits in a martingale domain is a hard task. Pairs trading, a market neutral arbitrage strategy, attempts to resolve the drawback of unpredictability and yield market independent returns using relative pricing idea. If two securities have similar characteristics, so should their prices. Deviation from the acceptable similarity range in price is considered an anomaly, and whenever noticed, trading is executed assuming the anomaly will correct itself. This work proposes a fuzzy inference model for the market-neutral pairs trading strategy. Fuzzy logic lets mimicking human decision-making in a complex trading environment and taking advantage of arbitrage opportunities that the crisp models may miss to acquire for trade decision-making. Spread between two co-integrated stocks and volatility of the spread are used as decision-making inputs. The main focus of this study is the contribution of the fuzzy engine to the existing pairs trading strategies based on the spread measure. Widespread classical 'crisp' techniques are chosen and compared with the developed fuzzy' model. Significant enhancement on the performance of the trading strategies has been reported.
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    ArticlePublicationOpen Access
    On the numerical schemes for Langevin-type equations
    (Karaganda University, 2020) Akat, Muzaffer; Kosker, R.; Sirma, A.; International Finance; AKAT, Muzaffer
    In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.
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    ArticlePublicationOpen Access
    Numerical discretization of stochastic oscillators with generalized numerical integrators
    (Vinča Institute of Nuclear Sciences, 2021) Sirma, A.; Kosker, R.; Akat, Muzaffer; International Finance; AKAT, Muzaffer
    In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation of constants formula using generalized numerical integrators. For both of the displacement and the velocity components, we show that the scheme has an order of 3/2 in one step convergence and a first order in overall convergence. Theoretical statements are supported by numerical experiments.
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    Algorithmic pairs trading with expert inputs, a fuzzy statistical arbitrage framework
    (IOS Press, 2020) Bayram, M.; Akat, Muzaffer; Bulkan, S.; International Finance; AKAT, Muzaffer
    Pairs trading is a widespread market-neutral trading strategy aiming to utilize the relationship between pairs of financial instruments in efficient markets, where predictability of separate asset movements is theoretically not possible. The implication of trading pairs, following statistical analysis, is to buy the underpriced asset while short selling the overpriced. The predicted price relationship is determined through analysis of historical spread data between the members of the corresponding pair. The investor expects the price difference, in an efficient market, should converge and stocks return to their ‘fair value’, where the positions are closed and profit is realized. The main focus of this study is the contribution of the fuzzy engine to the existing pairs trading strategy. Widespread classical ‘crisp’ technique is chosen, utilized and compared with the developed ‘fuzzy’ model throughout the paper. In order to further improve this contribution, the expert opinions extracted from the Bloomberg database are also integrated into the fuzzy decision-making process. In most studies, transaction costs are simply ignored. As a final robustness check, the transaction costs are also considered. The improvement reached by the developed fuzzy technique is observed to be even more remarkable in this case.
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    An approximation of stochastic hyperbolic equations: case with Wiener process
    (Wiley, 2013-06) Ashyralyev, A.; Akat, Muzaffer; International Finance; AKAT, Muzaffer
    In the present paper, the two-step difference scheme for the Cauchy problem for the stochastic hyperbolic equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference schemes for the numerical solution of four problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment.