Partially convertible economies face a market-design problem: trade integration, cross-border investment, and domestic balance-sheet exposure increase the demand for currency hedging before full financial integration is complete. China adopted a distinctive architecture for this problem by fostering a deliverable offshore Renminbi market (CNH) alongside the segmented onshore market (CNY), rather than relying only on non-deliverable forwards. This creates two venues for closely related claims on the same currency. Spot prices are tightly linked, yet CNY and CNH forwards display a persistent and economically large discrepancy. We study that discrepancy in a joint equilibrium model for spot and forward trading with transaction costs and segmented supply. In the benchmark case with common constant supply and deterministic costs, spot parity implies a forward differential with the wrong sign relative to the data. Random offshore stress, modeled as a jump in trading costs, overturns this benchmark while preserving tight spot parity. The model yields a semi-explicit representation in the CNY/CNH application and a calibration of the observed forward discrepancy in terms of the market-implied likelihood and severity of offshore liquidity stress.

Carbon pricing has become a central pillar of modern climate policy, with carbon taxes and emissions trading systems (ETS) serving as the two dominant approaches. Although economic theory suggests these instruments are equivalent under idealized assumptions, their performance diverges in practice due to real-world market imperfections. A particularly less explored dimension of this divergence concerns the role of financial intermediaries in emissions trading markets. This paper develops a unified framework to compare the economic and environmental performance of tax- and market-based schemes, explicitly incorporating the involvement of financial intermediaries. By calibrating both instruments to deliver identical aggregate emission reduction targets, we assess their economic performance across alternative market structures. Our results suggest that although the two schemes are equivalent under perfect competition, the presence of intermediaries in ETS reduces both regulatory wealth and the aggregate wealth of economic agents relative to carbon taxation. These effects stem from intermediaries' influence on price formation and their appropriation of part of the revenue stream. The findings underscore the importance of accounting for intermediaries' behavior in the design of carbon markets and highlight the need for further empirical research on the evolving institutional structure of emissions trading systems.

For vanilla derivatives, which form the core of investment banks’ hedging portfolios, central clearing via central counterparties (CCPs) has become the prevailing standard. A fundamental role of a CCP is to ensure an efficient and effective resolution process in the event of a clearing member’s default. Upon such a default, the CCP is tasked with hedging and subsequently auctioning or liquidating the defaulted positions. While the counterparty credit risk associated with auctioning has been examined in prior studies from a valuation adjustments (XVA) perspective, this work focuses on evaluating the costs associated with hedging or liquidation. This is achieved by contrasting pre- and post-default market equilibria through a Radner equilibrium framework applied to portfolio allocation and price discovery in both scenarios. We establish the unique existence of Radner equilibria and provide both analytical and numerical solutions within elliptically distributed market settings. These insights equip CCPs with a rational basis for determining whether to hedge, auction, or liquidate defaulted portfolios in specific markets. Moreover, clearing members can leverage these findings to conduct what-if analyses, addressing inquiries from senior management and regulatory bodies. This study also underscores the advantages of central clearing over bilateral trading from a default resolution perspective.

High-frequency trading (HFT) and algorithmic trading (AT) have attracted considerable attention from the academic and regulatory communities, often highlighted for their contributions to enhancing market liquidity. However, the distinctive market framework in China may alter the operational dynamics of intraday trading, indicating that traditional HFT/AT paradigms might not fully apply. This study investigates the evolution of market quality in China from an HFT/AT perspective, using publicly available high-frequency data for six futures products traded on the Shanghai Futures Exchange and the Dalian Commodity Exchange. Our findings reveals improvements in contract continuity and liquidity diversification from a daily perspective. Furthermore, the intraday analysis-especially following the increased availability of more granular data to market participants-suggests the emergence of more sophisticated algorithmic traders who enhance liquidity provision and contribute to reduced slippage costs for investors and hedgers.

In this work, we study the extremal functions of the log-Sobolev functional on compact metric measure spaces satisfying the RCD^*(K,N) condition for K in ℝ and N in (2,∞ ) . We show the existence, regularity and positivity of non-negative extremal functions. Based on these results, we prove a Li-Yau type estimate for the logarithmic transform of any non-negative extremal functions of the log-Sobolev functional. As applications, we show a Harnack type inequality as well as lower and upper bounds for the non-negative extremal functions.

We present a one-period XVA model encompassing bilateral and centrally cleared trading in a unified framework with explicit formulas for most quantities at hand. We illustrate possible uses of this framework for running stress test exercises on a financial network from a clearing member's perspective or for optimizing the porting of the portfolio of a defaulted clearing member.

近十年,人工智能(AI)飞速发展.从精确的图像文本识别技术到先进的内容生成方法,AI几乎无所不能,这些惊人的技术进步几乎重塑了世界经济.在金融领域,由于AI的广泛应用,金融市场变得更加高效.目前,通过AI可以对大量异构的金融数据进行实时分析,同时AI技术也可用于对市场欺诈行为进行监测.不过,AI的应用也存在一些潜在的风险和挑战.事实上,通过机器学习方法(尤其是深度神经网络)构建的决策模型,往往如"黑盒"一般,其具体决策行为不容易被直观地解释.在高频交易的背景下,AI驱动的自动化交易系统可能会实施一些市场操纵策略,这样的违规交易行为却可能很难被监测和取证.本文将介绍一种特殊的市场操纵行为——幌骗(Spoofing),同时说明一个以降低交易成本为目标的AI系统可能会实施幌骗策略.作为应对,本文也将从技术和监管角度讨论可行的监控和预防措施,以阻止恶意AI算法对市场秩序的破坏,维护投资者的信心.

The optimal strategy of a potential spoofer is described and applied to Level 2 data on TMX

We test the robustness of the regime switching model for pegged markets introduced by Drapeau et al. [How rational are the option prices of the Hong Kong dollar exchange rate? J. Derivatives, 2021, 28(3), 140–161]. In particular, there are two disputable underlying assumptions: (1) a Black and Scholes model with low volatility for the pre-depegging regime and (2) a thin tail distribution—Exponential type—for the time of the depegging. For the pre-depegging regime, we consider a bounded model within the peg—from Ingersoll and Rady. For the depegging time, we consider fat tail distributions more in line with catastrophic events—Pareto/Fréchet. We derive the option prices formula for each combination of these models. We then calibrate to option data from USD-HKD as well as EUR-CHF. In comparison to the benchmark model in Drapeau et al. [How rational are the option prices of the Hong Kong dollar exchange rate? J. Derivatives, 2021, 28(3), 140–161], it turns out that the relevant resulting characteristics—probability of a depegging before maturity, appreciation/depreciation at the depegging time as well as post-depegging volatility—are strongly robust in terms of model choice for this regime switching approach. However, from a term structure perspective, fat tail distributions fit the data significantly better and provide more rational depegging probabilities for short and long maturities.

This paper investigates the hedging performance of a pegged foreign exchange market in a regime switching (RS) model introduced by Drapeauet al.We compare two prices, an exact solution and first-order approximation and provide bounds for the error. We provide exact RS delta, approximate RS delta as well as mean variance hedging strategies for this specific model and compare their performance. To improve the efficiency of the pricing and calibration procedure, a Fourier approach to this regime-switching model is developed in our work. It turns out that: (1) the calibration of the volatility surface with this regime switching model outperforms the classical SABR model on real data; (2) the Fourier approach is significantly faster than the direct approach; (3) in terms of hedging, the approximate RS delta hedge is a viable alternative to the exact RS delta hedge while significantly faster.

We provide q-moment estimates on annuli for weak solutions of the singular p-Laplace equation where p and q are conjugates. We derive q-uniform integrability for some critical parameter range. As applications, we derive a mass conservation as well as a weak convergence result for a larger critical parameter range. Concerning the latter point, we further provide a rate of convergence of order tq−1 of the solution in the q-Wasserstein distance.

The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other properties, we show that it is bounded from below in terms of convex combinations of expected shortfalls, and also from above by the smallest law invariant, coherent and comonotonic risk measure, for which we give the explicit formulation of the corresponding distortion function. As a benchmark to the industry standard expected shortfall we further provide its comparative asymptotic behavior in terms of extreme value distributions. Based on these results, we finally compute explicitly the expectile based expected shortfall for some selected class of distributions.

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.

In this study, we have analyzed a market impact game between n risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium.

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first-order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide an explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least-squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.

In this paper, we study the prices of the options on Hong Kong's linked exchange rate. The study was motivated by the apparent contradiction that options with strike prices outside the narrow trading band have positive prices. We developed a simple regime-switching model of the exchange rate and provided a formula for the prices of its options. The option pricing formula allows us to back out the implied probability of the failure of the linked exchange rate regime. With the option price data for the period from June 1, 2005 to July 31, 2018, we find that the market's belief about the likelihoods of the failure, as implied by the option prices, is too high to be justified by the possibility of the failure alone. This is first shown qualitatively, without using any model, with ratio of empirical over implied volatilities and the implied range of strike prices. Then, using the model, we find that, close to 40% of the sample period, the market thinks the failure probability is greater than 10%. When contrasted with the fact that the regime has not failed since 1983, the p-value of that event is less than 0.1%. Our finding suggests that, while the failure of the linked exchange rate regime is a significant risk factor, it cannot explain the risk premium seen in the option prices.

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with explicit examples how to quantify the costs of incompleteness when using utility indifference pricing, as well as a way to find optimal solutions for recursive utilities.

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including the average value-at-risk as a special case. First we focus on the case where the uncertainty is modeled by a nonlinear expectation penalizing distributions that are "far" in terms of optimal-transport distance (Wasserstein distance for instance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value-at-risk is a tail risk measure.

Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the confidence level goes to $1$ in terms of extreme value distributions. We use concentration inequalities to illustrate that the estimation of value at risk requires larger sample size than expected shortfall and expectile for heavy tail distributions when $\alpha$ is close to $1$. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile and some simulation results for some classical distributions.