Ahmet Göncü

Pricing temperature‐based weather derivatives in China

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.

On pricing discrete barrier options using conditional expectation and importance sampling Monte Carlo

Estimators for the price of a discrete barrier option based on conditional expectation and importance sampling variance reduction techniques are given. There are erroneous formulas for the conditional expectation estimator published in the literature: we derive the correct expression for the estimator. We use a simulated annealing algorithm to estimate the optimal parameters of exponential twisting in importance sampling, and compare it with a heuristic used in the literature. Randomized quasi-Monte Carlo methods are used to further increase the accuracy of the estimators.

Statistical Arbitrage with Pairs Trading

We analyze statistical arbitrage with pairs trading assuming that the spread of two assets follows a mean-reverting Ornstein-Uhlenbeck process around a long-term equilibrium level. Within this framework, we prove the existence of statistical arbitrage and derive optimality conditions for trading the spread portfolio. In the existence of uncertainty in the long-term mean and the volatility of the spread, statistical arbitrage is no longer guaranteed. However, the asymptotic probability of loss can be bounded as a function of the standard error of the model parameters. The proposed framework provides a new filtering technique for identifying best pairs in the market. Backtesting results are given for the five pairs of stocks considered in Zeng and Lee (2014).

Statistical arbitrage in the Black–Scholes framework

In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expected value, variance, and probability of loss for the discounted cumulative trading profits. No-statistical arbitrage condition is derived for the Black-Scholes framework, which imposes a constraint on the Sharpe ratio of the stock. Furthermore, we verify our theoretical results via extensive Monte Carlo simulations.In this study, we prove the existence of statistical arbitrage opportunities in the Black–Scholes framework by considering trading strategies that consist of borrowing at the risk-free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expected value, variance and probability of loss for the discounted cumulative trading profits. The statistical arbitrage condition is derived in the Black–Scholes framework, which imposes a constraint on the Sharpe ratio of the stock. Furthermore, we verify our theoretical results via extensive Monte Carlo simulations.

Uniform point sets and the collision test

Monte Carlo and quasi-Monte Carlo methods are popular numerical tools used in many applications. The quality of the pseudorandom sequence used in a Monte Carlo simulation is essential to the accuracy of its estimates. Likewise, the quality of the low-discrepancy sequence determines the accuracy of a quasi-Monte Carlo simulation. There is a vast literature on statistical tests that help us asses the quality of a pseudorandom sequence. However, for low-discrepancy sequences, assessing quality by estimating discrepancy is a very challenging problem, leaving us with no practical options in high dimensions. In this paper, we will discuss how a certain interpretation of the well-known collision test for pseudorandom sequences can be used to obtain useful information about the quality of low-discrepancy sequences. Numerical examples will be used to illustrate the applications of the collision test.

A stochastic model for commodity pairs trading

In this study, we introduce an optimal pairs trading model and verify its performance in the commodity futures markets. Empirical evidence from commodity futures indicates the existence of significant mean reversion together with high peak and fat tails for the distribution of spread residuals. Therefore, we assume an Ornstein–Uhlenbeck process with the noise term driven by a Lévy process with generalized hyperbolic distributed marginals. Our model not only provides trading signals, but also can be considered as a pair screening technique to rank all potential pairs for trade priority in terms of the distance to the expected profit-maximizing thresholds. Empirical examples and backtesting results obtained from commodity futures data show strong support for the profitability of the model even in the presence of transaction costs.

Efficient simulation of a multi-factor stochastic volatility model

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.

Comparison of temperature models using heating and cooling degree days futures

Purpose - The purpose of this paper is to compare the ability of popular temperature models, namely, the models given by Alaton Design/methodology/approach - To 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”. Findings - The 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 limitations/implications - In future studies, it may be useful to utilize the historical data for meteorological forecasts to assess the forecasting power of the new hybrid model considered. Practical implications - Out-of-period backtesting helps reduce the effect of any meteorological forecast on the formation of futures prices. It is observed that the performance of models for out-of-period improves consistently. This indicates that the effects of available weather forecasts should be incorporated into the considered models. Originality/value - To the best of the authors knowledge this is the first study to compare some of the popular temperature models in forecasting HDD/CDD futures. Furthermore, a new temperature modelling approach is proposed for incorporating available temperature forecasts into the considered dynamic models.

Estimating sensitivities of temperature-based weather derivatives

Pricing of temperature-based weather derivatives has been studied in the literature; however, there is no analysis of the estimation of the sensitivities of weather derivatives in a stochastic model of temperatures. We use pathwise derivative and kernel methods to derive Monte Carlo estimators for the sensitivity (Greeks) of temperature-based weather derivatives. These sensitivities can be used by investors for choosing the most suitable weather contracts for partial hedging or speculation. Temperature data from New York, Atlanta and Chicago are used in the discussion of numerical results.

A Comparative Goodness-of-Fit Analysis of Distributions of Some Lévy Processes and Heston Model to Stock Index Returns

In this paper, we investigate the goodness-of-fit of three Levy processes, namely Variance-Gamma (VG), Normal-Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions, and probability distribution of the Heston model to index returns of twenty developed and emerging stock markets. Furthermore, we extend our analysis by applying a Markov regime switching model to identify normal and turbulent periods. Our findings indicate that the probability distribution of the Heston model performs well for emerging markets under full sample estimation and retains goodness of fit for high volatility periods, as it explicitly accounts for the volatility process. On the other hand, the distributions of the Levy processes, especially the VG and NIG distributions, generally improves upon the fit of the Heston model, particularly for developed markets and low volatility periods. Furthermore, some distributions yield to significantly large test statistics for some countries, even though they fit well to other markets, which suggest that properties of the stock markets are crucial in identifying the best distribution representing empirical returns.