Financial Derivatives

Adaptive Nesterov Accelerated Distributional Deep Hedging for Efficient Volatility Risk Management ArXiv ID: 2502.17777 “View on arXiv” Authors: Unknown Abstract In the field of financial derivatives trading, managing volatility risk is crucial for protecting investment portfolios from market changes. Traditional Vega hedging strategies, which often rely on basic and rule-based models, are hard to adapt well to rapidly changing market conditions. We introduce a new framework for dynamic Vega hedging, the Adaptive Nesterov Accelerated Distributional Deep Hedging (ANADDH), which combines distributional reinforcement learning with a tailored design based on adaptive Nesterov acceleration. This approach improves the learning process in complex financial environments by modeling the hedging efficiency distribution, providing a more accurate and responsive hedging strategy. The design of adaptive Nesterov acceleration refines gradient momentum adjustments, significantly enhancing the stability and speed of convergence of the model. Through empirical analysis and comparisons, our method demonstrates substantial performance gains over existing hedging techniques. Our results confirm that this innovative combination of distributional reinforcement learning with the proposed optimization techniques improves financial risk management and highlights the practical benefits of implementing advanced neural network architectures in the finance sector. ...

Multi-Layer Deep xVA: Structural Credit Models, Measure Changes and Convergence Analysis ArXiv ID: 2502.14766 “View on arXiv” Authors: Unknown Abstract We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long’s (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of $\mathcal{“O”}(h^{“1/4-ε”})$ rather than the usual $\mathcal{“O”}(h^{“1/2”})$. Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses. ...

Examples and Counterexamples of Cost-efficiency in Incomplete Markets ArXiv ID: 2407.08756 “View on arXiv” Authors: Unknown Abstract We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [“BS24”]. These examples and counterexamples do not only illustrate the results obtained in [“BS24”], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [“DS06, Chapter 3”], there obtained using duality. ...

Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall ArXiv ID: 2311.15333 “View on arXiv” Authors: Unknown Abstract Crépey, Frikha, and Louzi (2023) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit theorems for the renormalized estimation errors associated with both algorithms as well as their averaged versions. Our findings are substantiated through a numerical example. ...

Fuel Hedging in the Airline Industry: The Case of Southwest Airlines ArXiv ID: ssrn-578663 “View on arXiv” Authors: Unknown Abstract Set in June 2001, the case places the student in the role of Scott Topping, Director of Corporate Finance at Southwest Airlines. Scott is responsible for the a Keywords: Corporate Finance Strategy, Hedging (Fuel), Risk Management, Financial Derivatives, Airline Economics, Equity (Transportation Sector) Complexity vs Empirical Score Math Complexity: 1.0/10 Empirical Rigor: 3.0/10 Quadrant: Philosophers Why: The paper is a qualitative case study focused on corporate finance decision-making with minimal mathematical modeling, and while it includes some financial data and volatility metrics, it lacks backtesting or implementation details. flowchart TD A["Research Goal: <br>Should SWA use fuel hedging?"] --> B["Data Inputs: <br>1. Historical Oil Prices<br>2. Futures/Options Prices<br>3. SWA Fuel Consumption"] B --> C["Methodology: <br>Valuation of Hedging Strategies"] C --> D["Computational Process: <br>Monte Carlo Simulation<br>of Oil Price Scenarios"] D --> E{"Key Findings/Outcomes"} E --> F["SWA Hedging reduced volatility<br>and saved costs vs. peers"] E --> G["Risk Management Framework<br>justifies active hedging policy"] E --> H["Recommendation: <br>Maintain/Expand Hedging Program"]

Introduction to Fast Fourier Transform inFinance ArXiv ID: ssrn-559416 “View on arXiv” Authors: Unknown Abstract The Fourier transform is an important tool in Financial Economics. It delivers real time pricing while allowing for a realistic structure of asset returns, taki Keywords: Fourier transform, asset pricing, financial economics, time series analysis, real-time pricing, Financial Derivatives Complexity vs Empirical Score Math Complexity: 8.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper involves advanced mathematical concepts like Fourier transforms, complex numbers, and convolution, but it is a conceptual pedagogical piece focusing on methodology rather than providing empirical data, backtests, or implementation details for real-world trading. flowchart TD A["Research Goal: Use Fourier Transform<br>for Real-Time Financial Pricing"] --> B["Key Methodology: Fast Fourier Transform<br>FFT Algorithm"] B --> C["Data Inputs: Asset Return Time Series<br>& Market Data"] C --> D["Computational Process: FFT of<br>Return Distributions to Price Derivatives"] D --> E["Key Findings: Efficient Real-Time Pricing<br>Model for Financial Derivatives"]