Exploring the commodity market: pricing Asian options with stochastic convenience yields and jump diffusions, and the study of the trading-date seasonality

The main underlying theme of this PhD thesis is the study of the commodity market. We first begin by pricing Asian options based on the Schwartz (1997) model. Asian options have been widely used in the global commodity market for its unique feature of using the average price instead of the price at maturity to determine the payoff function. We attempt to price Asian options written on commodity related future contracts under the model of three stochastic factors, namely, the spot price, the convenience yield, and the interest rate. We obtain closed-form solutions of geometric average Asian options, which will serve as control variates to price arithmetic average Asian options by Monte Carlo simulation. Our results show significant improvements in terms of simulation accuracy. We also manipulate the parameters of the model to see how the options prices behave accordingly. Next, a jump diffusion process is introduced to the model. Although analytical solution is unobtainable, a new numerical method is found to price arithmetic average Asian options with jumps, which lead to observable accuracy improvements. During our journey to further explore the behaviour of the commodity futures prices, we found a new seasonality pattern. The traditional idea of seasonality in the future market relates to the maturity date of a future contract. However, we find a new seasonal pattern in the futures prices that relates to the trading dates. We decide to explore such phenomenon in three energy commodity markets, namely, natural gas, gasoline, and crude oil. To conduct our initial empirical research, we design the so-called backward curve, as opposite to the forward curve, to visually illustrate the pattern of the trading-date seasonality. We find that when the prices of a collection of future contracts with the same maturity month can be averaged over the different years, the seasonality of trading dates is obvious to observe. We also find an interesting change of behaviour in the natural gas futures prices. Then, we conduct multiple statistical tests to further confirm our findings, which include the Kruskal-Wallis test, the autocorrelation test, and the power spectrum test. The results show strong evidence to support the existence of the trading-date seasonality. In light of what we find in the second chapter, we decide to look further into the new seasonality that relates to the trading dates, by constructing a trading strategy that is designed specifically to profit from the new seasonal pattern in three commodity markets. The results show promising profit over the long run for all three commodities, with relatively low risks. Then, we establish a model based on the Sorensen (2002) model, with the introduction of an arbitrage factor to capture the trading-date seasonality. We calibrate the model using the Kalman filter in the state space form, and the results suggest that the vast majority of the parameters are highly statistically significant in explaining the movement of the futures prices in the three commodity markets

Mapping Soil Alkalinity and Salinity in Northern Songnen Plain, China with the HJ-1 Hyperspectral Imager Data and Partial Least Squares Regression

In arid and semi-arid regions, identifying and monitoring of soil alkalinity and salinity are in urgently need for preventing land degradation and maintaining ecological balances. In this study, physicochemical, statistical, and spectral analysis revealed that potential of hydrogen (pH) and electrical conductivity (EC) characterized the saline-alkali soils and were sensitive to the visible and near infrared (VIS-NIR) wavelengths. On the basis of soil pH, EC, and spectral data, the partial least squares regression (PLSR) models for estimating soil alkalinity and salinity were constructed. The R2 values for soil pH and EC models were 0.77 and 0.48, and the root mean square errors (RMSEs) were 0.95 and 17.92 dS/m, respectively. The ratios of performance to inter-quartile distance (RPIQ) for the soil pH and EC models were 3.84 and 0.14, respectively, indicating that the soil pH model performed well but the soil EC model was not considerably reliable. With the validation dataset, the RMSEs of the two models were 1.06 and 18.92 dS/m. With the PLSR models applied to hyperspectral data acquired from the hyperspectral imager (HSI) onboard the HJ-1A satellite (launched in 2008 by China), the soil alkalinity and salinity distributions were mapped in the study area, and were validated with RMSEs of 1.09 and 17.30 dS/m, respectively. These findings revealed that the hyperspectral images in the VIS-NIR wavelengths had the potential to map soil alkalinity and salinity in the Songnen Plain, China

Trading time seasonality in commodity futures: an opportunity for arbitrage in the natural gas and crude oil markets?

In this paper we investigate energy futures contracts and the presence of a type of seasonality, that has been given very little to no attention in the literature – we call it trading time seasonality. Such seasonality is exposed through the futures trading time, not its maturity time, nor the underlying spot price. As we show, it can be linked to seasonality in the pricing kernel, but the latter can’t explain it fully. Its relationship to arbitrage and CAPM violation is investigated, and its presence is confirmed for natural gas and crude oil futures markets using descriptive analysis, Kruskal—Wallis testing and CAPM methodology. We provide an informal discussion around possible reasons for the effect and identify seasonal hedging pressure and market sentiments as such

Combating Mode Collapse in GANs via Manifold Entropy Estimation

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEEComment: Accepted by AAAI'2023 (Oral); Code is released at https://github.com/HaozheLiu-ST/ME

Remote Sensing of Soil Alkalinity and Salinity in the Wuyu’er-Shuangyang River Basin, Northeast China

The Songnen Plain of the Northeast China is one of the three largest soda saline-alkali regions worldwide. To better understand soil alkalinization and salinization in this important agricultural region, it is vital to explore the distribution and variation of soil alkalinity and salinity in space and time. This study examined soil properties and identified the variables to extract soil alkalinity and salinity via physico-chemical, statistical, spectral, and image analysis. The physico-chemical and statistical results suggested that alkaline soils, coming from the main solute Na2CO3 and NaHCO3 in parent rocks, characterized the study area. The pH and electric conductivity (EC ) were correlated with both narrow band and broad band reflectance. For soil pH, the sensitive bands were in short wavelength (VIS) and the band with the highest correlation was 475 nm (r = 0.84). For soil EC, the sensitive bands were also in VIS and the band with the highest correlation was 354 nm (r = 0.84). With the stepwise regression, it was found that the pH was sensitive to reflectance of OLI band 2 and band 6, while the EC was only sensitive to band 1. The R2Adj (0.73 and 0.72) and root mean square error (RMSE) (0.98 and 1.07 dS/m) indicated that, the two stepwise regression models could estimate soil alkalinity and salinity with a considerable accuracy. Spatial distributions of soil alkalinity and salinity were mapped from the OLI image with the RMSE of 1.01 and 0.64 dS/m, respectively. Soil alkalinity was related to salinity but most soils in the study area were non-saline soils. The area of alkaline soils was 44.46% of the basin. Highly alkaline soils were close to the Zhalong wetland and downstream of rivers, which could become a severe concern for crop productivity in this area

Improving GAN Training via Feature Space Shrinkage

Due to the outstanding capability for data generation, Generative Adversarial Networks (GANs) have attracted considerable attention in unsupervised learning. However, training GANs is difficult, since the training distribution is dynamic for the discriminator, leading to unstable image representation. In this paper, we address the problem of training GANs from a novel perspective, \emph{i.e.,} robust image classification. Motivated by studies on robust image representation, we propose a simple yet effective module, namely AdaptiveMix, for GANs, which shrinks the regions of training data in the image representation space of the discriminator. Considering it is intractable to directly bound feature space, we propose to construct hard samples and narrow down the feature distance between hard and easy samples. The hard samples are constructed by mixing a pair of training images. We evaluate the effectiveness of our AdaptiveMix with widely-used and state-of-the-art GAN architectures. The evaluation results demonstrate that our AdaptiveMix can facilitate the training of GANs and effectively improve the image quality of generated samples. We also show that our AdaptiveMix can be further applied to image classification and Out-Of-Distribution (OOD) detection tasks, by equipping it with state-of-the-art methods. Extensive experiments on seven publicly available datasets show that our method effectively boosts the performance of baselines. The code is publicly available at https://github.com/WentianZhang-ML/AdaptiveMix.Comment: Accepted by CVPR'2023. Code and Demo are available at https://github.com/WentianZhang-ML/AdaptiveMi

Pricing Asian options with stochastic convenience yield and jumps

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. In the case of no jumps, we obtain a closed-form solution for a geometric average Asian option. This analytic result enables us to employ this option as a suitable control variate when pricing the corresponding arithmetic average Asian option. Discussion of further applications and comparative statics are presented. To cover the case with jumps, we condition on the jump times first and then average over the sequences of jump times

Study on Massive-Scale Slow-Hash Recovery Using Unified Probabilistic Context-Free Grammar and Symmetrical Collaborative Prioritization with Parallel Machines

Slow-hash algorithms are proposed to defend against traditional offline password recovery by making the hash function very slow to compute. In this paper, we study the problem of slow-hash recovery on a large scale. We attack the problem by proposing a novel concurrent model that guesses the target password hash by leveraging known passwords from a largest-ever password corpus. Previously proposed password-reused learning models are specifically designed for targeted online guessing for a single hash and thus cannot be efficiently parallelized for massive-scale offline recovery, which is demanded by modern hash-cracking tasks. In particular, because the size of a probabilistic context-free grammar (PCFG for short) model is non-trivial and keeping track of the next most probable password to guess across all global accounts is difficult, we choose clever data structures and only expand transformations as needed to make the attack computationally tractable. Our adoption of max-min heap, which globally ranks weak accounts for both expanding and guessing according to unified PCFGs and allows for concurrent global ranking, significantly increases the hashes can be recovered within limited time. For example, 59.1% accounts in one of our target password list can be found in our source corpus, allowing our solution to recover 20.1% accounts within one week at an average speed of 7200 non-identical passwords cracked per hour, compared to previous solutions such as oclHashcat (using default configuration), which cracks at an average speed of 28 and needs months to recover the same number of accounts with equal computing resources (thus are infeasible for a real-world attacker who would maximize the gain against the cracking cost). This implies an underestimated threat to slow-hash protected password dumps. Our method provides organizations with a better model of offline attackers and helps them better decide the hashing costs of slow-hash algorithms and detect potential vulnerable credentials before hackers do