In this paper, we investigate the goodness-of-fit of the Variance-Gamma (VG), NormalInverse Gaussian (NIG), and Heston models for several developed and emerging stock markets, in terms of their ability to represent empirical return... more
In this paper, we investigate the goodness-of-fit of the Variance-Gamma (VG), NormalInverse Gaussian (NIG), and Heston models for several developed and emerging stock markets, in terms of their ability to represent empirical return distributions. The goodnessof-fit of these models are evaluated using three goodness-of-fit test statistics, i.e. Chisquare, Kolmogorov-Smirnov, and Anderson-Darling. In particular, the Anderson-Darling test statistic is a good measure of distance between the theoretical and empirical distributions and a small value indicates a better fit. We show that while normality assumption and the Heston models are clearly rejected, VG and NIG models improve upon the normal distribution and Heston models in capturing the behavior of the empirical returns and yield much smaller test statistics in all the markets considered in our analysis.
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In this study a macroeconomic model is considered to predict the next month's monthly average exchange rates via machine learning based regression methods including the Ridge, decision tree regression, support vector regression and... more
In this study a macroeconomic model is considered to predict the next month's monthly average exchange rates via machine learning based regression methods including the Ridge, decision tree regression, support vector regression and linear regression. The model incorporates the domestic money supply, real interest rates, Federal Funds rate of the USA, and the last month's monthly average exchange rate to predict the next month's exchange rate. Monthly data with 148 observations from the US Dollar and Turkish Lira exchange rates are considered for the empirical testing of the model. Empirical results show that the Ridge regression offers accurate estimation for investors or policy makers with relative errors less than 60 basis points. Policy makers can obtain point estimates and confidence intervals for analyzing the effects of interest rate cuts on the exchange rates.
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The logistic type model, which requires the use of an optimization routine for the estimation of model parameters, is one of a number of widely used methods in modeling natural gas consumption. In this study, we derive a regression model... more
The logistic type model, which requires the use of an optimization routine for the estimation of model parameters, is one of a number of widely used methods in modeling natural gas consumption. In this study, we derive a regression model by considering the Euler discretization of the logistic type model and show that this regression based approach offers a simpler estimation procedure, in addition to better modeling natural gas consumption data. For comparison, the regression model derived from the logistic model is fitted to the same dataset published in Forouzanfar et al. (2010). Furthermore, in the regression approach, confidence intervals for point forecasts can be obtained, whereas the logistic function model is a deterministic function of time that does not provide confidence intervals.
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In this dissertation, we discuss the generation of low discrepancy sequences, randomization of these sequences, and the transformation methods to generate normally distributed random variables. Two well known methods for generating... more
In this dissertation, we discuss the generation of low discrepancy sequences, randomization of these sequences, and the transformation methods to generate normally distributed random variables. Two well known methods for generating normally distributed numbers are considered, namely; Box-Muller and inverse transformation methods. Some researchers and financial engineers have claimed that it is incorrect to use the Box-Muller method with lowdiscrepancy sequences, and instead, the inverse transformation method should be used. We investigate the sensitivity of various computational finance problems with respect to different normal transformation methods. Box-Muller transformation method is theoretically justified in the context of the quasi-Monte Carlo by showing that the same error bounds apply for Box-Muller transformed point sets. Furthermore, new error bounds are derived for financial derivative pricing problems and for an isotropic integration problem where the integrand is a func...
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In this study, the profitability of different pairs selection and spread trading methods are compared using the complete dataset of commodity futures from Dalian Commodity Exchange (DCE), Shanghai Futures Exchange (SHFE) and Zhengzhou... more
In this study, the profitability of different pairs selection and spread trading methods are compared using the complete dataset of commodity futures from Dalian Commodity Exchange (DCE), Shanghai Futures Exchange (SHFE) and Zhengzhou Commodity Exchange (CZCE). Pairs trading methods that are already known in the literature are compared in terms of the risk-adjusted returns via in-sample and out-of-sample backtesting and bootstrapping for robustness. The empirical results show that pairs trading in the Chinese commodity futures market offers high returns, whereas, the profitability of these strategies primarily depends on the identification of suitable pairs. The observed high returns are a compensation for the spread divergence risk during the potentially longer holding periods, which implies that the maximum drawdown is more crucial compared to other risk-adjusted return measures such as the Sharpe ratio. Complementary to the existing literature, for our market, it is shown that if shorter maximum holding periods are introduced for the spread positions, then the pairs trading profits decrease. Therefore, the returns do not necessarily imply market inefficiency when the higher maximum drawdown associated with the holding period of the spread position is taken into account.
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In this paper, we investigate the goodness-of-fit of three option pricing models, namely VarianceGamma (VG), Normal-Inverse Gaussian (NIG), and Heston models, with respect to the benchmark cases of the Black-Scholes model and student-t... more
In this paper, we investigate the goodness-of-fit of three option pricing models, namely VarianceGamma (VG), Normal-Inverse Gaussian (NIG), and Heston models, with respect to the benchmark cases of the Black-Scholes model and student-t distribution. We compare the physical probability measures under these models with the empirical return distributions of twenty developed and emerging stock markets. We also extend our analysis by applying a Markov regime switching model to index returns to identify normal and turbulent periods. Empirical finding si ndicate that the VG model represents the empirical distributions better than the other models considered. Furthermore, once normal and turbulent periods are identified the fit of all three models, and especially the VG model, improves significantly, in terms of lower Chi-square and Anderson-Darling goodness-of-fit statistics in most of the markets.
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In this paper, we utilize a mean reverting stochastic process to model the dynamic behaviour of natural gas consumption, where a Brownian motion drives the noise. We employ daily data on natural gas consumption from Istanbul, Turkey to... more
In this paper, we utilize a mean reverting stochastic process to model the dynamic behaviour of natural gas consumption, where a Brownian motion drives the noise. We employ daily data on natural gas consumption from Istanbul, Turkey to estimate our model and evaluate the forecast performance by backtesting of the model at different forecast horizons using relative mean squared errors. We document that time-series observations on natural gas consumption exhibits stationarity, strong seasonality, mean reversion, and serial correlation. Based on our approach, the conditional distribution of natural gas consumption is derived, and it can be used for forecasting and pricing contingent claims on natural gas consumption.
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In this article we investigate the goodness-of-fit of the Heston stochastic volatility model for the Shanghai composite index and five Chinese stocks from different industries with the highest trading volume. We have jointly estimated the... more
In this article we investigate the goodness-of-fit of the Heston stochastic volatility model for the Shanghai composite index and five Chinese stocks from different industries with the highest trading volume. We have jointly estimated the parameters of the Heston stochastic volatility for the daily, weekly and monthly timescales model by employing a kernel density of the empirical returns to minimize the mean-squared deviations between the theoretical and empirical return distributions. We find that the Heston model is able to characterize the empirical distribution of Chinese stock returns at the daily, weekly and monthly timescales.
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In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of... more
In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of Financial Economics, 73, 525–565 and derive the statistical arbitrage condition in the multi-asset Black–Scholes economy building upon the single asset case studied in Goncu, A (2015). Statistical arbitrage in the Black Scholes framework. Quantitative Finance, 15(9), 1489–1499. Statistical arbitrage profits can be generated if there exists at least one asset in the economy that satisfies the statistical arbitrage condition. Therefore, adding a no-statistical arbitrage condition to no-arbitrage pricing models is not realistic if not feasible. However, with an example we show that what excludes statistical arbitrage opportunities in the Black–Scholes economy, and possibly in other complete market models, is the presence of uncertainty or stochasticity in the model parameters. Furthermore, we derive analytical formulas for the expected value and probability of loss of the statistical arbitrage portfolios and compute optimal boundaries to sell the risky assets in the portfolio by maximizing the expected return with a constraint on the probability of loss.
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We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices, where the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset... more
We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices, where the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via buy and hold until a barrier strategy, where the investor sells the risky asset when it hits a deterministic boundary. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.
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PurposeThe purpose of this paper is to compare the ability of popular temperature models, namely, the models given by Alaton et al., by Benth and Benth, by Campbell and Diebold and by Brody et al., to forecast the prices of... more
PurposeThe purpose of this paper is to compare the ability of popular temperature models, namely, the models given by Alaton et al., by Benth and Benth, by Campbell and Diebold and by Brody et al., to forecast the prices of heating/cooling degree days (HDD/CDD) futures for New York, Atlanta, and Chicago.Design/methodology/approachTo verify the forecasting power of various temperature models, a statistical backtesting approach is utilised. The backtesting sample consists of the market data of daily settlement futures prices for New York, Atlanta, and Chicago. Settlement prices are separated into two groups, namely, “in‐period” and “out‐of‐period”.FindingsThe findings show that the models of Alaton et al. and Benth and Benth forecast the futures prices more accurately. The difference in the forecasting performance of models between “in‐period” and “out‐of‐period” valuation can be attributed to the meteorological temperature forecasts during the contract measurement periods.Research li...
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ABSTRACT Empirical phenomenon in financial markets such as volatility smiles and term structure of implied volatilities made stochastic volatility models more attractive. In this paper, we consider a two-factor stochastic volatility model... more
ABSTRACT Empirical phenomenon in financial markets such as volatility smiles and term structure of implied volatilities made stochastic volatility models more attractive. In this paper, we consider a two-factor stochastic volatility model with slow and fast mean reverting factors for which a first order asymptotic approximation formula in terms of the homogenized Black-Scholes solution is given by Fouque et al. (2004) [1]. We compare the simulation efficiency of importance sampling estimators derived from the zeroth and first order terms in the asymptotic expansion formula with the benchmark crude Monte Carlo estimator. We implement the zeroth order importance sampling estimators for the barrier option pricing by the use of the discrete barrier option pricing formula with the continuity correction. Results show that using the importance sampling estimator based on the zeroth order term together with some of the well known randomized quasi-Monte Carlo sequences is computationally the most efficient method for pricing the European and barrier options considered.
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In this study, empirical moments and the cointegration for all the liquid commodity futures traded in the Chinese futures markets are analyzed for the periods before and after Covid-19, which is important for trading strategies such as... more
In this study, empirical moments and the cointegration for all the liquid commodity futures traded in the Chinese futures markets are analyzed for the periods before and after Covid-19, which is important for trading strategies such as pairs trading. The results show that the positive change in the average returns of the products such as soybean, corn, corn starch, and iron ore futures are significantly stronger than other products in the post Covid-19 era, whereas the volatility increased most for silver, petroleum asphalt and egg futures after the pandemic started. The number of cointegrated pairs are reduced after the pandemic indicating the differentiation in returns due to the structural changes caused in the demand and supply conditions across commodities.
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Research Interests: Applied Mathematics, Simulated Annealing, Monte Carlo, Numerical Analysis, Sampling, and 9 moreVariance, Mathematical Model, Importance Sampling, Mathematical and Computer Modelling, Conditional Expectation, Numerical Analysis and Computational Mathematics, Optimal Bayesian Estimation, Monte Carlo Method, and Variance Reduction Techniques
Research Interests: Applied Mathematics, Simulated Annealing, Monte Carlo, Numerical Analysis, Sampling, and 9 moreVariance, Mathematical Model, Importance Sampling, Mathematical and Computer Modelling, Conditional Expectation, Numerical Analysis and Computational Mathematics, Optimal Bayesian Estimation, Monte Carlo Method, and Variance Reduction Techniques
ABSTRACT This article is the first study to price temperature-based weather derivatives based on the daily average temperatures of Chinese cities, namely Beijing, Shanghai and Shenzhen. A dynamic model with a piecewise constant volatility... more
ABSTRACT This article is the first study to price temperature-based weather derivatives based on the daily average temperatures of Chinese cities, namely Beijing, Shanghai and Shenzhen. A dynamic model with a piecewise constant volatility function, proposed by Alaton et al. (2002), is used for pricing Heating Degree Days (HDD) and Cooling Degree Days (CDD) options. Price estimates for these options are obtained using Monte Carlo simulation and analytical approximation methods.
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Purpose–The purpose of this paper is to propose a feasible model for the daily average temperatures of Beijing, Shanghai and Shenzhen, in order to price temperature-based weather derivatives; also to derive analytical approximation... more
Purpose–The purpose of this paper is to propose a feasible model for the daily average temperatures of Beijing, Shanghai and Shenzhen, in order to price temperature-based weather derivatives; also to derive analytical approximation formulas for the sensitivities of these contracts. Design/methodology/approach–This study proposes a seasonal volatility model that estimates daily average temperatures of Beijing, Shanghai and Shenzhen using the mean-reverting Ornstein-Uhlenbeck process. It then uses the analytical approximation and Monte Carlo methods to price heating degree days and cooling degree days options for these cities. In addition, it derives and calculates the option sensitivities on the basis of an analytical approximation formula. Findings–There exists a strong seasonality in the volatility of daily average temperatures of Beijing, Shanghai and Shenzhen. To model the seasonality Fourier approximation is applied to the squared volatility of daily temperatures. The analytical approximation formulas and Monte Carlo simulation produce very similar prices for heating/cooling degree days options in Beijing and Shanghai, a result that also verifies the convergence of the Monte Carlo and approximation estimators. However, the two methods do not produce converging option prices in the case of HDD options for Shenzhen. Originality/value–The article provides important insight to investors and hedgers by proposing a feasible model for pricing temperature-based weather contracts in China and derives analytical approximations for the sensitivities of heating/cooling degree days options.
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Purpose–The purpose of this paper is to propose a feasible model for the daily average temperatures of Beijing, Shanghai and Shenzhen, in order to price temperature-based weather derivatives; also to derive analytical approximation... more
Purpose–The purpose of this paper is to propose a feasible model for the daily average temperatures of Beijing, Shanghai and Shenzhen, in order to price temperature-based weather derivatives; also to derive analytical approximation formulas for the sensitivities of these contracts. Design/methodology/approach–This study proposes a seasonal volatility model that estimates daily average temperatures of Beijing, Shanghai and Shenzhen using the mean-reverting Ornstein-Uhlenbeck process. It then uses the analytical approximation and Monte Carlo methods to price heating degree days and cooling degree days options for these cities. In addition, it derives and calculates the option sensitivities on the basis of an analytical approximation formula. Findings–There exists a strong seasonality in the volatility of daily average temperatures of Beijing, Shanghai and Shenzhen. To model the seasonality Fourier approximation is applied to the squared volatility of daily temperatures. The analytical approximation formulas and Monte Carlo simulation produce very similar prices for heating/cooling degree days options in Beijing and Shanghai, a result that also verifies the convergence of the Monte Carlo and approximation estimators. However, the two methods do not produce converging option prices in the case of HDD options for Shenzhen. Originality/value–The article provides important insight to investors and hedgers by proposing a feasible model for pricing temperature-based weather contracts in China and derives analytical approximations for the sensitivities of heating/cooling degree days options.
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Weather derivatives provide better risk management alternatives for industries, which are exposed to weather-based risks. Dynamic pricing of weather derivatives requires a suitable underlying temperature model. This paper is the first to... more
Weather derivatives provide better risk management alternatives for industries, which are exposed to weather-based risks. Dynamic pricing of weather derivatives requires a suitable underlying temperature model. This paper is the first to model the average daily temperatures and ...