Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling

Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging to address within the traditional mathematical finance framework. Since deep hedging relies on market simulation, the underlying asset price process model is crucial. However, existing literature on deep hedging often relies on traditional mathematical finance models, e.g., Brownian motion and stochastic volatility models, and discovering effective underlying asset models for deep hedging learning has been a challenge. In this study, we propose a new framework called adversarial deep hedging, inspired by adversarial learning. In this framework, a hedger and a generator, which respectively model the underlying asset process and the underlying asset process, are trained in an adversarial manner. The proposed method enables to learn a robust hedger without explicitly modeling the underlying asset process. Through numerical experiments, we demonstrate that our proposed method achieves competitive performance to models that assume explicit underlying asset processes across various real market data.Comment: 8 pages, 7 figure

No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging

Deep hedging (Buehler et al. 2019) is a versatile framework to compute the optimal hedging strategy of derivatives in incomplete markets. However, this optimal strategy is hard to train due to action dependence, that is, the appropriate hedging action at the next step depends on the current action. To overcome this issue, we leverage the idea of a no-transaction band strategy, which is an existing technique that gives optimal hedging strategies for European options and the exponential utility. We theoretically prove that this strategy is also optimal for a wider class of utilities and derivatives including exotics. Based on this result, we propose a no-transaction band network, a neural network architecture that facilitates fast training and precise evaluation of the optimal hedging strategy. We experimentally demonstrate that for European and lookback options, our architecture quickly attains a better hedging strategy in comparison to a standard feed-forward network

Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study

Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to challenges posed by the curse of dimensionality. While deep learning-based PDE solvers have recently emerged as scalable solutions to this high-dimensional problem, their empirical and quantitative accuracy remains not well-understood, hindering their real-world applicability. In this study, we aimed to offer actionable insights into the utility of Deep PDE solvers for practical option pricing implementation. Through comparative experiments, we assessed the empirical performance of these solvers in high-dimensional contexts. Our investigation identified three primary sources of errors in Deep PDE solvers: (i) errors inherent in the specifications of the target option and underlying assets, (ii) errors originating from the asset model simulation methods, and (iii) errors stemming from the neural network training. Through ablation studies, we evaluated the individual impact of each error source. Our results indicate that the Deep BSDE method (DBSDE) is superior in performance and exhibits robustness against variations in option specifications. In contrast, some other methods are overly sensitive to option specifications, such as time to expiration. We also find that the performance of these methods improves inversely proportional to the square root of batch size and the number of time steps. This observation can aid in estimating computational resources for achieving desired accuracies with Deep PDE solvers.Comment: 11 pages, 6 figure

Effects of tongue cleaning on bacterial flora in tongue coating and dental plaque: a crossover study

BACKGROUND: The effects of tongue cleaning on reconstruction of bacterial flora in dental plaque and tongue coating itself are obscure. We assessed changes in the amounts of total bacteria as well as Fusobacterium nucleatum in tongue coating and dental plaque specimens obtained with and without tongue cleaning. METHODS: We conducted a randomized examiner-blind crossover study using 30 volunteers (average 23.7 ± 3.2 years old) without periodontitis. After dividing randomly into 2 groups, 1 group was instructed to clean the tongue, while the other did not. On days 1 (baseline), 3, and 10, tongue coating and dental plaque samples were collected after recording tongue coating score (Winkel tongue coating index: WTCI). After a washout period of 3 weeks, the same examinations were performed with the subjects allocated to the alternate group. Genomic DNA was purified from the samples and applied to SYBR® Green-based real-time PCR to quantify the amounts of total bacteria and F. nucleatum. RESULTS: After 3 days, the WTCI score recovered to baseline, though the amount of total bacteria in tongue coating was significantly lower as compared to the baseline. In plaque samples, the bacterial amounts on day 3 and 10 were significantly lower than the baseline with and without tongue cleaning. Principal component analysis showed that variations of bacterial amounts in the tongue coating and dental plaque samples were independent from each other. Furthermore, we found a strong association between amounts of total bacteria and F. nucleatum in specimens both. CONCLUSIONS: Tongue cleaning reduced the amount of bacteria in tongue coating. However, the cleaning had no obvious contribution to inhibit dental plaque formation. Furthermore, recovery of the total bacterial amount induced an increase in F. nucleatum in both tongue coating and dental plaque. Thus, it is recommended that tongue cleaning and tooth brushing should both be performed for promoting oral health