55 papers
Bridging Stochastic Control and Deep Hedging: Structural Priors for No-Transaction Band Networks
This paper studies the problem of hedging and pricing a European call option under proportional transaction costs, from two complementary perspectives. We first derive the optimal hedging strategy under CARA utility, following the stochastic control framework of Davis et al. (1993), characterising the no-transaction band via the Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJBQVI) and the Whalley-Wilmott asymptotic approximation. We then adopt a deep hedging approach, proposing two architectures that build on the No-Transaction Band Network of Imaki et al. (2023): NTBN-Delta, which makes delta-centring explicit, and WW-NTBN, which incorporates the Whalley-Wilmott formula as a structural prior on the bandwidth and replaces the hard clamp with a differentiable soft clamp. Numerical experiments show that WW-NTBN converges faster, matches the stochastic control no-transaction bands more closely, and generalises well across transaction cost regimes. We further apply both frameworks to the bull call spread, documenting the breakdown of price linearity under transaction costs.
2603.29994Mar 2026
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Option Pricing on Automated Market Maker Tokens
We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiting case of infinite liquidity. We obtain closed-form European option prices and introduce liquidity-adjusted Greeks. The CEV structure generates a leverage effect -- volatility rises as price falls -- whose normalized implied volatility skew depends only on the pool's weighting parameter, not on pool depth: Black-Scholes underprices 20%-out-of-the-money puts by roughly 6% in implied volatility terms at every pool depth, while the absolute pricing discrepancy vanishes as pools deepen. Empirically, after controlling for pool depth and flow volatility, realized return variance across 90 Bittensor subnets exhibits a strongly negative price elasticity, decisively rejecting geometric Brownian motion and consistent with the CEV prediction. A complementary delta-hedged backtest across 82 subnets confirms near-identical hedging errors at the money, consistent with the prediction that pricing differences are concentrated in the wings.
2603.29763Mar 2026
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Rough volatility dynamics in commodity markets
In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the theoretical analysis of this general model, we focus on the rBergomi and rHeston models and their calibration to market data of vanilla futures options on WTI Crude Oil. Finally, numerical results illustrate the performance of the proposed rough volatility models for commodities pricing.
2603.26514Mar 2026
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STN-GPR: A Singularity Tensor Network Framework for Efficient Option Pricing
We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.
2603.26318Mar 2026
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2603.14760At-the-money short-time call-price asymptotics for new classes of exponential Lévy models
We develop at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a class of asset-price models whose log returns follow a Lévy process. Under mild assumptions placing the driving Lévy process in the small-time domain of attraction of an $α$-stable law with $α\in (1,2)$, we give first-order at-the-money call-price and implied volatility asymptotics. A key observation is that both the stable domain of attraction and the finiteness of the centering constant $\barμ$ are preserved under the share measure transformation, so that all of the distributional input needed for the call-price expansion can be read off from the regular variation of the Lévy measure near the origin. When the Lévy process has no Brownian component, new rates of convergence of the form $t^{1/α} \ell(t)$ where $\ell$ is a slowly varying function are obtained. We provide an example of an exponential Lévy model exhibiting this behavior, with $\ell$ not asymptotically constant, yielding a convergence rate of $(t / \log(1/t))^{1/α}$. In the case of a Lévyprocess with Brownian component, we show that the jump contribution is always lower order, so that the leading $\sqrt{t}$ behavior of the at-the-money call price is universal and driven entirely by the Gaussian part of the characteristic triplet.
2603.14760Mar 2026
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One Rising Ship Sinks Other Ships: Cross-Chain Negative Spillovers in Crypto Markets
We document the first systematic evidence of negative spillover effects in crypto asset returns across blockchains. Using on-chain data from Ethereum, Solana, Binance Smart Chain, Arbitrum, and Avalanche (2022-2025), we show that surges on one chain often coincide with declines on others, in contrast to the positive co-movements typical of equity markets. These spillovers intensify during attention shocks, proxied by chain activity and extreme return events, and persist after controlling for global equity returns, interest rates, and Bitcoin. Nonlinear factor models reveal that attention-driven capital reallocation, rather than common information, underlies these dynamics. Our findings introduce a new form of cross-market linkage, attention-induced substitution, that shapes risk transmission in crypto markets. The results carry implications for portfolio diversification, systemic risk measurement, and regulation of token launches that may trigger cross-chain capital flight.
2602.23762Feb 2026
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Finite Element Solution of the Two-Dimensional Bates Model for Option Pricing Under Stochastic Volatility and Jumps
We propose a fourth--order compact finite--difference (HOC--FD) scheme for the transformed Bates partial integro--differential equation (PIDE). The method employs an implicit--explicit (IMEX) Crank--Nicolson framework for local terms and Simpson quadrature for the jump integral. Benchmarks against second--order finite differences (FD) and quadratic finite elements (FEM, p=2) confirm near--fourth--order spatial accuracy for HOC--FD, near--second--order for FEM, and second--order temporal convergence for all time integrators. Efficiency tests show that HOC--FD achieves similar accuracy at up to two orders of magnitude lower runtime than FEM, establishing it as a practical baseline for option pricing under stochastic volatility jump--diffusion models.
2602.19092Feb 2026
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Music as an Asset Class
In the streaming era, music revenues distributed to rights holders have become more transparent. However, it is not yet clear how to quantify the risk and return characteristics of music royalty assets, as is done with equities. In this paper, we fit three discounted cashflow models to transactions on the Royalty Exchange platform. We use our best model to backtest the one year and five year performance of music royalty assets, after transaction costs. We find that Life of Rights (LOR) music assets had risk and return characteristics comparable to stocks in the S\&P500, when held over 5 years. Since the performance of stocks and music assets are likely to be uncorrelated, this result may help investors assess this asset class within the context of a more traditional stock and bond portfolio.
2602.05007Feb 2026
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Fair Pricing in Long-Term Insurance: A Unified Framework
Extant literature on fair pricing methods for actuarial contexts has primarily focused on the regression setting. While such approaches are well-suited to short-term products, it is unclear how they generalize to long-term products, whose pricing essentially relies on estimating transition rates in multi-state models. To address this gap, we propose a unified framework that recasts the estimation of any given multi-state transition model as a set of Poisson regression problems. This reformulation enables the direct application of existing fair pricing methods, which together constitute our proposed methodology. As an illustration, we apply the framework to a fair pricing exercise for a stylized long-term care insurance product using data from the University of Michigan Health and Retirement Study (HRS), focusing on a post-processing approach. We further explain how the framework readily accommodates pre-processing and in-processing fairness methods.
2602.04791Feb 2026
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Keeping Up with the Correlations: Stochastic Spot/Volatility Correlation and Exotic Pricing
We consider a novel use case for the Double Heston model (Christoffersen et al,, 2009), where the two Heston sub-variances have different spot/volatility correlations but the same volatility of volatility and mean reversion speed. This parameterization generalizes the traditional Heston stochastic volatility model (Heston, 1993) to include stochastic spot/volatility correlation. It is an affine model, allowing European options to be priced efficiently by numerically integrating over a closed-form characteristic function. This model incorporates a key dynamic relevant for pricing barrier derivatives in the foreign exchange markets: a positive correlation between moves in implied volatility skew and moves in the spot price. We analyze that correlation and its impact on both barrier option pricing and volatility swap pricing. Those price impacts are comparable to or larger than the bid/ask spreads for these products. Adding stochastic spot/volatility correlation increases the prices of out-of-the-money knockout options and one touch options, assuming that the model is calibrated to market vanilla option prices. It also increases the fair strike of volatility swaps compared to the Heston model.
2602.01376Feb 2026
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Optimal strategy and deep hedging for share repurchase programs
In recent decades, companies have frequently adopted share repurchase programs to return capital to shareholders or for other strategic purposes, instructing investment banks to rapidly buy back shares on their behalf. When the executing institution is allowed to hedge its exposure, it encounters several challenges due to the intrinsic features of the product. Moreover, contractual clauses or market regulations on trading activity may make it infeasible to rely on Greeks. In this work, we address the hedging of these products by developing a machine-learning framework that determines the optimal execution of the buyback while explicitly accounting for the bank's actual trading capabilities. This unified treatment of execution and hedging yields substantial performance improvements, resulting in an optimized policy that provides a feasible and realistic hedging approach. The pricing of these programs can be framed in terms of the discount that banks offer to the client on the price at which the shares are delivered. Since, in our framework, risk measures serve as objective functions, we exploit the concept of indifference pricing to compute this discount, thereby capturing the actual execution performance.
2601.18686Jan 2026
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VIX and European options with jumps in the short-maturity regime
We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The leading-order asymptotics are obtained in closed-form. We apply our results to three examples: the Eraker model, a Kou-type model, and a folded normal model. Numerical illustrations are provided for these three examples that show the accuracy of predictions based on the asymptotic results.
2601.17248Jan 2026
View2601.07664Crypto Pricing with Hidden Factors
We estimate risk premia in the cross-section of cryptocurrency returns using the Giglio-Xiu (2021) three-pass approach, allowing for omitted latent factors alongside observed stock-market and crypto-market factors. Using weekly data on a broad universe of large cryptocurrencies, we find that crypto expected returns load on both crypto-specific factors and selected equity-industry factors associated with technology and profitability, consistent with increased integration between crypto and traditional markets. In addition, we study non-tradable state variables capturing investor sentiment (Fear and Greed), speculative rotation (Altcoin Season Index), and security shocks (hacked value scaled by market capitalization), which are new to the literature. Relative to conventional Fama-MacBeth estimates, the latent-factor approach yields materially different premia for key factors, highlighting the importance of controlling for unobserved risks in crypto asset pricing.
2601.07664Jan 2026
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Reinforcement Learning for Option Hedging: Static Implied-Volatility Fit versus Shortfall-Aware Performance
We extend the Q-learner in Black-Scholes (QLBS) framework by incorporating risk aversion and trading costs, and propose a novel Replication Learning of Option Pricing (RLOP) approach. Both methods are fully compatible with standard reinforcement learning algorithms and operate under market frictions. Using SPY and XOP option data, we evaluate performance along static and dynamic dimensions. Adaptive-QLBS achieves higher static pricing accuracy in implied volatility space, while RLOP delivers superior dynamic hedging performance by reducing shortfall probability. These results highlight the importance of evaluating option pricing models beyond static fit, emphasizing realized hedging outcomes.
2601.01709Jan 2026
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Machine learning models for predicting catastrophe bond coupons using climate data
In recent years, the growing frequency and severity of natural disasters have increased the need for effective tools to manage catastrophe risk. Catastrophe (CAT) bonds allow the transfer of part of this risk to investors, offering an alternative to traditional reinsurance. This paper examines the role of climate variability in CAT bond pricing and evaluates the predictive performance of various machine learning models in forecasting CAT bond coupons. We combine features typically used in the literature with a new set of climate indicators, including Oceanic Ni{ñ}o Index, Arctic Oscillation, North Atlantic Oscillation, Outgoing Longwave Radiation, Pacific-North American pattern, Pacific Decadal Oscillation, Southern Oscillation Index, and sea surface temperatures. We compare the performance of linear regression with several machine learning algorithms, such as random forest, gradient boosting, extremely randomized trees, and extreme gradient boosting. Our results show that including climate-related variables improves predictive accuracy across all models, with extremely randomized trees achieving the lowest root mean squared error (RMSE). These findings suggest that large-scale climate variability has a measurable influence on CAT bond pricing and that machine learning methods can effectively capture these complex relationships.
2512.22660Dec 2025
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Almost-Exact Simulation Scheme for Heston-type Models: Bermudan and American Option Pricing
Recently, an Almost-Exact Simulation (AES) scheme was introduced for the Heston stochastic volatility model and tested for European option pricing. This paper extends this scheme for pricing Bermudan and American options under both Heston and double Heston models. The AES improves Monte Carlo simulation efficiency by using the non-central chi-square distribution for the variance process. We derive the AES scheme for the double Heston model and compare the performance of the AES schemes under both models with the Euler scheme. Our numerical experiments validate the effectiveness of the AES scheme in providing accurate option prices with reduced computational time, highlighting its robustness for both models. In particular, the AES achieves higher accuracy and computational efficiency when the number of simulation steps matches the exercise dates for Bermudan options.
2601.00815Dec 2025
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Interpretable Deep Learning for Stock Returns: A Consensus-Bottleneck Asset Pricing Model
We introduce the \textit{Consensus-Bottleneck Asset Pricing Model} (CB-APM), a partially interpretable neural network that replicates the reasoning processes of sell-side analysts by capturing how dispersed investor beliefs are compressed into asset prices through a consensus formation process. By modeling this ``bottleneck'' to summarize firm- and macro-level information, CB-APM not only predicts future risk premiums of U.S. equities but also links belief aggregation to expected returns in a structurally interpretable manner. The model improves long-horizon return forecasts and outperforms standard deep learning approaches in both predictive accuracy and explanatory power. Comprehensive portfolio analyses show that CB-APM's out-of-sample predictions translate into economically meaningful payoffs, with monotonic return differentials and stable long-short performance across regularization settings. Empirically, CB-APM leverages consensus as a regularizer to amplify long-horizon predictability and yields interpretable consensus-based components that clarify how information is priced in returns. Moreover, regression and GRS-based pricing diagnostics reveal that the learned consensus representations capture priced variation only partially spanned by traditional factor models, demonstrating that CB-APM uncovers belief-driven structure in expected returns beyond the canonical factor space. Overall, CB-APM provides an interpretable and empirically grounded framework for understanding belief-driven return dynamics.
2512.16251Dec 2025
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Amortizing Perpetual Options
In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. In this way, analytical expressions are possible for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.
2512.06505Dec 2025
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Generative Pricing of Basket Options via Signature-Conditioned Mixture Density Networks
We present a generative framework for pricing European-style basket options by learning the conditional terminal distribution of the log arithmetic-weighted basket return. A Mixture Density Network (MDN) maps time-varying market inputs encoded via truncated path signatures to the full terminal density in a single forward pass. Traditional approaches either impose restrictive assumptions or require costly re-simulation whenever inputs change, limiting real-time use. Trained on Monte Carlo (MC) under GBM with time-varying volatility or local volatility, the MDN acts as a reusable surrogate distribution: once trained, it prices new scenarios by integrating the learned density. Across maturities, correlations, and basket weights, the learned densities closely match MC (low KL) and produce small pricing errors, while enabling \emph{train-once, price-anywhere} reuse at inference-time latency.
2511.09061Nov 2025
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Semi-analytical pricing of American options with hybrid dividends via integral equations and the GIT method
This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously complex because discrete dividends create abrupt price drops and affect the optimal exercise timing, making traditional continuous-dividend models unsuitable. Our approach utilizes the Generalized Integral Transform (GIT) method introduced by the author and his co-authors in a number of papers, which transforms the pricing problem from a complex partial differential equation with a free boundary into an integral Volterra equation of the second or first kind. In this paper we illustrate this approach by considering a popular GBM model that accounts for discrete cash and proportional dividends using Dirac delta functions. By reframing the problem as an integral equation, we can sequentially solve for the option price and the early exercise boundary, effectively handling the discontinuities caused by the dividends. Our methodology provides a powerful alternative to standard numerical techniques like binomial trees or finite difference methods, which can struggle with the jump conditions of discrete dividends by losing accuracy or performance. Several examples demonstrate that the GIT method is highly accurate and computationally efficient, bypassing the need for extensive computational grids or complex backward induction steps.
2510.18159Oct 2025
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