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on Risk Management |
| By: | Christopher Blier-Wong; Jean-Gabriel Lauzier |
| Abstract: | Regulatory and contractual constraints on individual exposures are standard in insurance and reinsurance markets, but a poorly designed constraint can distort the economic incentives of risk-averse agents. In the unconstrained problem, the classical comonotonic improvement theorem guarantees Pareto-optimal allocations that are nondecreasing in the aggregate loss. A constraint that is not stable under risk reduction can destroy this property. We show by example that Value-at-Risk caps lead to optimal allocations that are non-comonotonic in the aggregate loss. We identify componentwise convex-order solidity as a sufficient condition on the feasible set that restores the comonotonic improvement under constraints. If replacing any agent's allocation by a less risky one preserves feasibility, then every feasible allocation admits a feasible comonotonic improvement for all convex-order-consistent preferences. This criterion covers many constraints typical in risk management, but excludes Value-at-Risk caps and idiosyncratic deductibles. We illustrate the implications of our main result in a mean-variance risk-sharing application. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.24546 |
| By: | Damiaan Chen (De Nederlandsche Bank); Roel Beetsma (University of Amsterdam); Sweder van Wijnbergen (University of Amsterdam) |
| Abstract: | We explore to what extent real returns on investment portfolios can be hedged against inflation risk by using existing financial market instruments. We find that inflation-linked bonds offer only limited protection against inflation risk and that nominal debt and stocks play at least comparable roles in this respect. These findings apply to both a static and a dynamic setting. The demonstrated limits of hedging inflation risk are of particular relevance for long-term investors, such as pension funds with participants concerned about the real value of their pension benefits. |
| Keywords: | unhedgeable inflation risk, incomplete markets, welfare loss, mean-variance frontiers, minimum risk portfolio, nominal and index-linked bonds |
| JEL: | C61 E21 G11 G23 |
| Date: | 2025–10–10 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250059 |
| By: | Yunqi Liang; Hasan Ugur Koyluoglu; Fuat Alican; Yigit Ihlamur |
| Abstract: | We propose a Gaussian-copula-based framework that learns deal-level dependence directly from observed joint success frequencies across founder, geography, and market attributes. Holding marginal deal success probabilities fixed, deal-level correlation preserves expected portfolio outcomes but shifts the portfolio distribution toward heavier right tails and higher kurtosis. In portfolio simulations, correlation reduces the probability of modest success counts while sharply amplifying extreme upside outcomes, especially in structurally concentrated portfolios. Our findings suggest that extreme venture capital outcomes may partly reflect correlation-induced tail amplification rather than solely higher average deal quality, with potential implications for portfolio construction and risk management. We note that the observed dataset reflects selected deals with observable outcomes, which inflates apparent success rates relative to the true population base rate; however, the core finding that correlation reshapes the distributional shape while leaving the mean unchanged is structurally robust to the level of marginal success probabilities. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23087 |
| By: | Davide Rindori |
| Abstract: | Traditional multi-population models, such as the Li-Lee framework, rely on the assumption of mean-reverting country-specific deviations. However, recent data from high-longevity clusters suggest a systemic break in this paradigm. We identify a stationarity paradox where mortality residuals in countries like Sweden and West Germany exhibit persistent unit roots, leading to a systematic mispricing of longevity risk in linear models. To address these non-linearities, we propose Hybrid-Lift, a neural-actuarial framework that combines Hierarchical LSTM networks with a Mean-Bias Correction (MBC) anchoring mechanism. Positioned as a governance-friendly model challenger rather than a replacement of classical approaches, the framework exhibits selective superiority on out-of-sample validation (2012-2020): it outperforms Li-Lee by 17.40% in Sweden and 12.57% in West Germany, while remaining comparable for near-linear regimes such as Switzerland and Japan. We complement the predictive model with an integrated governance suite comprising SHAP-based cross-country influence mapping, a dual uncertainty framework for regulatory capital calibration (Swiss ES 99.0% of +1.153 years), and a reverse stress test identifying the critical shock threshold for solvency buffer exhaustion. This research provides evidence that neural networks, when properly anchored by actuarial principles, can serve as effective model challengers for longevity risk management under the SST and Solvency II standards. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.06438 |
| By: | Wenjun Jiang; Qingqing Zhang; Yiying Zhang |
| Abstract: | This paper investigates two optimal insurance contracting problems under distributional uncertainty from the perspective of a potential policyholder, utilizing a Bregman-Wasserstein (BW) ball to characterize the ambiguity set of loss distributions. Unlike the $p$-Wasserstein distance, BW divergence enables asymmetric penalization of deviations from the benchmark distribution. The first problem examines an insurance demand model where the policyholder adopts an $\alpha$-maxmin preference with Value-at-Risk (VaR). We derive the optimal indemnity function in closed form and study, both analytically and numerically, how the asymmetry inherent in BW divergence influences the optimal indemnity structure. The second problem employs a robust optimization framework, where the policyholder aims to secure robust insurance indemnity by minimizing the worst-case convex distortion risk measure while adhering to a guaranteed VaR constraint. In this context, we provide explicit characterizations of both the optimal indemnity and the worst-case distribution in closed form through a combined approach using the Lagrangian method and modification arguments. To illustrate the practical implications of our theoretical findings, we include a concrete example based on Tail Value-at-Risk (TVaR). |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27837 |
| By: | Pierpaolo Uberti |
| Abstract: | In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk reduction can be achieved without relying on risk measurement and risk minimization. To this end, we propose a generalization of the numerical rank and the condition number of a matrix, specifically the return matrix in this application. This generalization considers the entire matrix spectrum instead of focusing only on the smallest eigenvalue, as the condition number does. The approach directly provides an order among a finite number of risky scenarios. Risk reduction is obtained by identifying the riskiest scenarios and reducing investment exposures corresponding to them. The validity of this theoretical proposal is supported by a comprehensive experiment performed on real data. The capacity of the proposed approach to effectively reduce risk is proven by measuring the variability of out-of-sample returns for benchmark portfolios-constructed by minimizing standard risk measures-compared to the strategy of reducing exposure in high-risk scenarios. Finally, preventing large losses with limited active management-thereby controlling the impact of transaction costs-not only reduces risk but also preserves the average return and, consequently, the portfolio's Sharpe ratio. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.28124 |
| By: | Wolfgang Schadner |
| Abstract: | This paper observes that the Black--Scholes call price can be written as the survival probability of an inverse Gaussian distribution, equivalently as a probability in variance space. Inverting this representation yields an analytically explicit formula for implied volatility in terms of the corresponding inverse Gaussian quantile function, with volatility on the left-hand side and only observable option inputs on the right-hand side. Numerical tests recover implied volatility to machine precision and, in a controlled setting, show the formula to be faster than a state-of-the-art benchmark. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.24480 |
| By: | Martijn Boermans; Laurens Swinkels |
| Abstract: | Governments across the world have issued inflation-linked debt to finance their deficits. Recent advances in asset pricing models recognize that there may be clientele effects that affect relative prices, especially in bond markets. We study investor demand for inflation-linked bonds using detailed bond portfolio data. Our analysis reveals pronounced market segmentation: insurance companies, with predominantly nominal liabilities, underinvest in inflation-linked securities, while pension funds overinvest. Investors hedging inflation risk exhibit a strong preference for bonds indexed to domestic rather than foreign inflation. A regulatory reform announcement provides quasi-experimental evidence that the demand for inflation-linked bonds may be shaped by regulatory requirements. |
| Keywords: | Inflation-linked bonds, investor clientele, securities holdings, sovereign bonds, TIPS |
| JEL: | F21 G11 G15 G22 G23 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:cnb:wpaper:2026/08 |
| By: | Ying-Hui Shao; Yan-Hong Yang; Yun Zhang |
| Abstract: | Connectedness measures quantify aggregate risk spillovers but obscure the local interaction patterns that generate systemic risk. We develop a motif-based framework that first extracts multiscale backbones from quantile connectedness networks and then identifies directed triadic motifs whose frequencies exceed randomization baselines. To distinguish how assets' sectoral identities shape local spillover structures, we introduce colored motifs under sector partitions of increasing granularity. Using orbit positions that capture each node's structural role within directed triadic motifs, we construct portfolio strategies that exploit an asset's place in the spillover architecture. Applying the framework to 39 commodity and equity futures across lower, median, and upper conditional quantiles, we find that motif-based portfolios outperform minimum correlation and minimum connectedness benchmarks on risk-adjusted returns. We further show that in tail networks, assets with greater orbit-position diversity tend to act as net spillover transmitters rather than receivers, establishing positional diversity as a tail-specific marker of systemic influence. These findings demonstrate that local triadic topology carries portfolio-relevant information that aggregate connectedness measures miss. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25406 |
| By: | Ying Liao; Ankush Agarwal; Florian Bourgey |
| Abstract: | We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility expansions with computable correction terms. The resulting formulas enable fast and accurate calibration without requiring numerical root-finding. We illustrate the performance of the proposed expansions in both standard and rough Bergomi-type models, as well as in mixed specifications, and demonstrate their accuracy through numerical experiments. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25123 |
| By: | Girish Bahal; Damian Lenzo; Jia-Wei Loh |
| Abstract: | Idiosyncratic volatility in the stock returns of large firms can drive aggregate volatility and real activity. Using daily stock price data for firms in 21 countries over 1999 to 2020, we isolate firm-specific volatility shocks and exploit the fat-tailed distribution of market capitalization to construct a granular instrument for country-level volatility (uncertainty). A one standard deviation increase in aggregate volatility reduces real GDP by 1%, raises unemployment by 1.2 percentage points, and lowers investment by 7% over three years. We validate 389 firm episodes using contemporaneous news coverage and show that narratively verified shocks generate even larger macroeconomic effects. |
| Keywords: | uncertainty shocks, granular instrumental variables, firm-level volatility, aggregate uncertainty, investment |
| JEL: | E32 E44 G10 E22 C26 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-28 |
| By: | Merve Kutuk (CPB Netherlands Bureau); Sweder van Wijnbergen (University of Amsterdam) |
| Abstract: | This paper examines the role of currency crash risk in explaining the persistent profitability of carry trades. Focusing on the US Dollar–Turkish Lira market, we construct three forward-looking measures of crash risk: risk reversals, crash probabilities from option-implied distributions, and jump risk from a jump-diffusion model. Using survey-based exchange rate expectations, we separate ex ante carry premia from ex post surprises. Our results show that higher crash risk significantly increases expected returns, indicating that investors demand compensation for bearing such risk rather than arbitraging away mispricing. Shapley decomposition attributes over 20\% of the explained variance in expected carry returns to crash risk, while balance sheet constraints and global risk aversion further reinforce premia. A comparison of hedged and unhedged strategies reveals that 46–77\% of carry returns reflect compensation for crash exposure. |
| Keywords: | Exchangerates, currencycrashrisk, mispricing, dollarexchangerate, bankcur- rency mismatches |
| JEL: | F13 G01 G10 G12 G15 |
| Date: | 2025–10–10 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250058 |
| By: | Tomasz J. Kozubowski; Andrey Sarantsev; James A. Spiker |
| Abstract: | We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00196 |
| By: | Mr. Andre O Santos |
| Abstract: | This paper describes the 2023 euro area consultation top-down stress test that focused on the resilience of 91 systemically important banks’ capital buffers as of end-2022 to macro baseline and adverse scenarios over the period 2023-25. As a result, the paper is an illustration of a top-down stress test framework with an application to euro are banks. The 2023 euro area consultation top-down stress test included unbiased dynamic panel data estimators based on Lancaster (2002) for projecting profitability components and information on Pillar 3 disclosures (exposure-at-default, probability of default, loss-given-default, expected losses). The paper also expands the 2023 euro area consultation top-down stress test by considering risk-weight functions with Skew-Normal and Transmuted-Normal probability distributions for the idiosyncratic and systemic risk factors. The results of the stress test with both distributions indicate that most euro area banks were resilient under the 2023 euro area consultation baseline and adverse scenarios as of July 2023 (publication of the Staff report). |
| Keywords: | Bank capital; Bank profitability; Capital adequacy requirements; Corporate risk; ECB analysis; ECB-Banking Supervision; Europe; Nonperforming loans; Stress test; Working capital; Transmuted- Normal distribution |
| Date: | 2026–05–01 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2026/089 |
| By: | Alan Chernoff; Julapa Jagtiani; Nathaniel Yoshida |
| Abstract: | This study examines the impact of the stablecoin Tether (USDT) on systemic liquidity across the Ethereum and Bitcoin markets, utilizing an event study approach that integrates on-chain wallet data, pricing, and financial metrics. By analyzing cryptocurrency market responses to key protocol and market-moving events, augmented by nonlinear volatility models, we identify distinct, chain-specific flight-to-safety behaviors. Our results show that USDT acts as a primary liquidity lifeline for Ethereum holders during stress, particularly among retail investors, whereas its role for Bitcoin holders is more muted and stabilizing. Notably, we find stronger flight-to-safety evidence in Wrapped Bitcoin (Ethereum-based) than in native Bitcoin, highlighting that USDT’s function is network dependent. These findings imply that effective regulatory frameworks must be differentiated, accounting for chain-specific liquidity, investor composition, and risk dynamics, as a uniform approach would likely be systematically miscalibrated. |
| Keywords: | Cryptocurrency; Stablecoins; Bitcoin; Ethereum; Tether; Flight to safety; BTC; ETH; USDT |
| JEL: | G14 G23 G28 G41 |
| Date: | 2026–05–07 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedpwp:103156 |
| By: | Thomas Conlon; John Cotter; Iason Kynigakis |
| Abstract: | We demonstrate that machine learning methods provide a powerful framework for modelling conditional asymmetric risk. Using a large cross-section of US stocks and a comprehensive set of firm characteristics, we show that allowing for nonlinearities significantly increases the out-of-sample performance across a wide range of asymmetric beta measures and forecasting horizons. Trading frictions, followed by characteristics related to intangibles, momentum and growth, emerge as the most important drivers of future risk dynamics. Reconstructing CAPM beta from forecasts of asymmetric beta components indicates that a more granular decomposition of systematic risk yields a more accurate representation of market beta. We also find that incorporating conditional beta forecasts into discounted cash flow models that account for the term structure of betas enhances equity valuation accuracy. Finally, we show that the statistical outperformance of conditional betas translates into economically significant benefits for market-neutral portfolio investors. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22933 |
| By: | Valentin Tissot-Daguette |
| Abstract: | We introduce the Local Occupied Volatility (LOV) model that sits between Dupire's local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the flexibility to capture stylized facts of volatility or fit additional instruments. This is achieved by tuning the occupation sensitivity function that quantifies the effect of path-dependent shocks on volatility. We validate the model through the joint American-European calibration of options chain on non-dividend paying stocks. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.26151 |
| By: | Erdinc Akyildirim; Gonul Colak; Giray Gozgor; Thang Ho |
| Abstract: | This paper constructs a novel firm-level measure of geopolitical risk using textual analysis of 130, 061 earnings conference call transcripts and examines its impact on firms' reliance on bank-based financing. Using a panel of 4, 692 listed firms across 38 countries over 2005–2024, we find that higher firm-level geopolitical risk is associated with a significant increase in the bank debt ratio. Instrument-level analysis shows that this effect is driven by greater reliance on term loans, while revolving credit facilities exhibit no systematic response. The relationship holds across United States and non-United States firms, as well as across developed and emerging economies, with stronger effects in emerging markets and in institutional environments that facilitate contracting and enforcement. A comprehensive set of robustness tests confirms that the results are not driven by industry composition, regional concentration, crisis periods, or omitted institutional factors. Difference-in-differences evidence around the Russia–Ukraine war provides additional support, showing that firms with higher pre-war geopolitical risk increase their reliance on bank debt after 2022. Overall, the findings identify geopolitical risk as a time-varying determinant of corporate financing decisions. |
| Keywords: | geopolitical risk, bank debt, term loans, capital structure, institutional environment, difference-in-differences |
| JEL: | G32 G21 F34 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12624 |
| By: | Lorenzo Mazzucchelli; Marco Zanotti; Luca Vincenzo Ballestra; Andrea Guizzardi |
| Abstract: | This study examines the disposition effect in both long and short exposure positions in FTSE MIB tracking ETFs using a unique dataset of almost 9 million individual transactions. Building on the integrated framing approach, we extend the analysis to explicitly incorporate leverage and long short exposures, allowing us to assess how portfolio context and systematic risk exposure jointly are associated to investors realization behavior. Methodologically, we generalize Odean canonical Count and Total measures to wide and integrated framing, introduce a novel Value metric that captures the return thresholds required to realize gains versus losses, and implement these measures in dispositionEffect, an open-source R package for large-scale intraday data. We show that short positions exhibit a weaker disposition effect than long positions under narrow framing, but that this asymmetry reverses in positively performing portfolios under integrated framing. Systematic risk further amplifies these behavioral asymmetries across positions. Overall, our findings demonstrate that the disposition effect is not solely asset-specific, but is critically shaped by the interaction between portfolio context, position type, and systematic risk exposure. More broadly, the results are consistent with the joint predictions of Prospect Theory and Regret Theory, highlighting the central role of framing in investor decision-making. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00016 |
| By: | Ya-Juan Wang; Yi-Shuai Niu; Artan Sheshmani; Shing-Tung Yau |
| Abstract: | Unrestricted mean-variance-skewness-kurtosis portfolio optimization can capture asymmetry and tail risk, but sample-moment formulations become computationally impractical when the asset universe is large: they produce dense nonconvex quartic objectives with prohibitive coskewness and cokurtosis tensors and anisotropic, ill-conditioned level sets. We develop a structure-exploiting algorithm based on Yau's affine-normal descent that follows affine-normal directions of the current level set while working directly with the return matrix. The method avoids explicit higher-order tensors and exploits the quartic structure for exact sample oracles, derivative evaluation, and exact line search. We also provide theory for the reduced simplex formulation, including regularity and convexity conditions that separate data-map geometry from investor preference coefficients. Computational results show a clear implementation split: a direct configuration is effective on the standard small benchmark, whereas a preconditioned conjugate-gradient configuration with stall recovery becomes the preferred large-scale implementation by the upper end of the hundreds and remains competitive as the asset universe moves into the thousands. On a 5-minute A-share panel with 5, 440 stocks, the method makes direct full-universe comparisons with exact mean-variance portfolios feasible and shows on the baseline split that the incremental value of higher moments is strongest at moderate return targets. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25378 |
| By: | Laura Baselga-Pascual; Lidia Loban; Emma-Riikka Myllymäki (Audencia Business School) |
| Abstract: | This study investigates the relationship between credit risk and bank exposure to sovereign debt. Using an international dataset of commercial banks from 2002 to 2022, we apply various regressions and panel data models to address potential endogeneity issues. Our results reveal that banks with higher levels of impaired loans tend to hold more sovereign debt. Furthermore, we observe that this relationship is stronger in countries with high sovereign credit ratings. This suggests that banks, when confronted with elevated credit risk from impaired loans, may seek safety in sovereign debt as a seemingly secure investment. |
| Keywords: | Financial institutions, Bank risk, Sovereign debt nexus, Credit risk |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05585256 |
| By: | Raeid Saqur |
| Abstract: | We present fast-vollib, an open-source Python library that provides high-performance European option pricing, implied volatility (IV) computation, and Greeks under the Black-76, Black-Scholes, and Black-Scholes-Merton models. The library is designed as a drop-in alternative to the de-facto-standard py_vollib and py_vollib_vectorized packages, with pluggable PyTorch and JAX execution backends, a CUDA fused-kernel Triton contribution for batched IV workloads, and a compatibility-first public API. In addition to a vectorized Halley-method IV solver, fast-vollib ships an experimental, fully-vectorized implementation of J\"ackel's "Let's Be Rational" (LBR) algorithm with NumPy/Numba, torch.compile, JAX, and Triton single-pass GPU kernels for batched option chains. This note announces the library and describes its public API surface, with source, documentation, and packaging artifacts available at: GitHub (https://github.com/raeidsaqur/fast-vollib), Docs (https://raeidsaqur.github.io/fast-vollib/), PyPI (https://pypi.org/project/fast-vollib/). |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27210 |
| By: | Adil Reghai; Lama Tarsissi; G\'erard Biau; Alex Lipton |
| Abstract: | This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic differential equations of the SABR model. Unlike approaches that fully replace analytical formulas with black-box models, the proposed framework preserves the analytical backbone of the model. The hybridization operates along two complementary dimensions. First, geometry-aware variables reflecting intrinsic properties of the SABR dynamics are used as structured inputs to the network. Second, the neural network is trained to learn the residual error relative to Hagan's closed-form approximation rather than implied volatility directly. The resulting model acts as a structured residual correction to the analytical formula, retaining interpretability while capturing higher-order effects that are not included in the asymptotic expansion. Numerical experiments conducted over realistic parameter domains, as well as stressed environments, show that the method improves accuracy and robustness compared with both analytical approximations and standard neural-network approaches. Because the correction remains lightweight and structurally consistent with the underlying model, the framework is well suited for real-time pricing and calibration in practical trading environments. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.06604 |
| By: | Eduardo Abi Jaber; Cl\'ement Rey; Dimitri Sotnikov |
| Abstract: | Malliavin calculus is a powerful and general framework for the analysis of square-integrable random variables, but it often suffers from a lack of tractability and explicit representations. To address this limitation, we focus on a subclass of random variables given by finite linear combinations of time-extended Brownian motion signatures. The class remains rich due to the universal approximation properties of signatures. Leveraging the algebraic structure of signatures, we first derive explicit formulas for the Malliavin derivative of signatures of continuous It\^o processes. As a consequence, we obtain closed-form expressions for the Clark--Ocone representation, the Ornstein--Uhlenbeck semigroup and its generator, as well as the integration-by-parts formula within the class of Brownian signature variables. These results provide purely algebraic formulations of the classical operators of Malliavin calculus. As an application, we compute Greeks for general path-dependent options under signature volatility models, and numerically compare different choices of Malliavin weights. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22528 |