arXiv subjects

Charlie Che

Publications and source records attributed to Charlie Che.

10 recordsLinked to original sources

arXiv2026

Global Multi-Maturity SPX-VIX Calibration Beyond Markovian Stitching

We develop a global framework for joint S&P 500 (SPX)-VIX smile calibration across multiple maturities without the conditional-independence restriction induced by Markovian stitching. Exact local and global feasibility are equivalent: every globally feasible law has a block-preserving SPX-Markovization that leaves each monthly $(S_i,V_i,S_{i+1})$ law unchanged. Nevertheless, stitched laws can form a strict subset of globally feasible path laws because Markovization discards dependence on earlier history beyond the current SPX level. Adjacent smiles therefore cannot identify this dependence, and laws with identical monthly calibrations can price multi-period claims differently. Under the standard Markov reference, relative entropy selects the stitched minimum-information completion; non-Markov dependence requires cross-period information, an appropriate objective, or a history-dependent prior. For finite discretizations, we introduce an augmented-Bregman mirror-descent scheme. It preserves the fit to observable quote moments while controlling martingale and dispersion residuals. In a controlled infeasible affine system, this split keeps prescribed marginals about $25$ times tighter than cyclic row projection by exposing the discrepancy in the conditional rows. An exact finite-state example verifies block preservation and exhibits material cross-period price changes after Markovization. On smoothed SPX and VIX surfaces, numerical calculations illustrate a finite-budget penalty path: the worst fitted-smile error remains below $0.70$ volatility points across the reported sweep while the bulk conditional diagnostics improve substantially.

q-fin.CP↗

arXiv2026

Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics

We develop a geometric theory of arbitrage-free implied variance surface dynamics. Smile dynamics are formulated as transport flows on the admissible class of static-arbitrage-free surfaces: spot movements generate transport vector fields, and the transport velocity field v(k) unifies all classical stickiness regimes. The skew-stickiness ratio (SSR) is the zeroth-order transport coefficient; higher-order coefficients govern ATM skew, curvature, and higher smile derivatives. A local jet transport corollary extends the theory to arbitrary log-moneyness and identifies v(k) nonparametrically from market data. Under explicit regularity conditions, the flow preserves butterfly and calendar arbitrage-freeness locally. Sticky-strike, sticky-delta, SSR, local volatility, and rough volatility all arise as special cases within this framework. Empirically, we apply a sequential forward-substitution estimator to five years of SPX implied-volatility data across seven tenors from one month to two years. Three findings emerge. First, SPX exhibits super-skew behavior: the SSR coefficient declines monotonically from 1.44 at one month toward 1.01 at two years. Second, self-similar transport is rejected at all tenors; the skew-transport coefficient changes sign between the six- and nine-month tenors. Third, the velocity profile varies significantly with moneyness at intermediate tenors and evolves from U-shaped at short maturities to monotonically decreasing at long maturities. Out-of-sample, the full three-parameter model outperforms SSR on curvature dynamics by 17-21% at medium tenors.

q-fin.CP↗

arXiv2026

Faster Algorithms for Multimarginal Optimal Transport

We study algorithms for approximating the multimarginal optimal transport (MOT) distance, a generalization of the classic optimal transport distance, between $m$ discrete probability distributions each supported on at most $n$ points. We give a classical algorithm that computes a coupling between these marginals whose expected transportation cost is within an additive $\varepsilon > 0$ of the MOT distance in time $O(m^2 n^m \varepsilon^{-1}\mathrm{polylog}(m,n,\varepsilon^{-1}))$. This is, to our knowledge, the first bound for general MOT problems with simultaneous linear dependence on the dimension $n^m$ and on the accuracy parameter $\varepsilon^{-1}$, improving the prior state of the art. On the quantum side, we give two algorithms that achieve speedups in dimension, though with worse accuracy dependence than classical approaches. First, we construct a quantum projected subgradient method for estimating the MOT distance within an additive $\varepsilon >0$ with runtime $O( m^3 n^{\frac{m}{2}+1} \varepsilon^{-2} \mathrm{polylog}(m,n,\varepsilon^{-1}))$. This algorithm works with the linear programming dual of the MOT problem, and does not return a coupling. We also give a quantum multimarginal Sinkhorn algorithm for entropy-regularized MOT. This algorithm returns an implicit description of an approximately optimal coupling with runtime $O(m^8n^{\frac{m+1}{2}} \varepsilon^{-5} \mathrm{polylog}(m,n,\varepsilon^{-1})))$ after the usual reduction from entropic MOT to unregularized MOT. We also record query lower bounds: for any precision $\varepsilon<1/2$, randomized classical algorithms require $\Omega(n^m/(1+\varepsilon n))$ queries and quantum algorithms require $\Omega(\sqrt{n^m/(1+\varepsilon n)})$ queries.

quant-ph↗

arXiv2026

Arbitrage-Free Multi-Maturity Risk-Neutral Marginals

Many quantitative finance methods and applications are formulated in terms of option-implied risk-neutral marginals rather than directly in terms of option prices. Representative examples include martingale optimal transport, Bass local-volatility calibration, scenario analysis, and option-implied tail-risk measurement. The desired risk-neutral marginals should define a genuine probability law on the entire support, reproduce the input arbitrage-free option prices exactly, be free of butterfly and calendar arbitrage, and admit efficient evaluation of the density, distribution function, and quantiles, as well as Monte Carlo sampling. Existing methods typically optimize only a subset of these properties, depending on their intended purpose. This leaves a gap between upstream arbitrage-free option prices and the readily usable risk-neutral marginals required by downstream applications. We propose an explicit construction of risk-neutral marginals from discrete arbitrage-free option prices. On the observed strike range, probability mass is assigned interval by interval to exactly reproduce the input option prices. Outside the observed range, closed-form power-law tails complete the distribution by satisfying price and slope boundary conditions and allocating the remaining probability mass. Butterfly- and calendar-arbitrage-freeness are guaranteed by construction. The construction is feasible by design and computationally efficient. The resulting marginal laws admit closed-form densities, distribution functions, quantiles, and efficient Monte Carlo sampling. Numerical experiments on synthetic SSVI data and S\&P~500 market data demonstrate that the proposed construction efficiently and robustly produces marginals satisfying all of these properties in practice.

q-fin.CP↗

arXiv2026

SPX-VIX Risk Computations Via Perturbed Optimal Transport

We propose a model independent framework for generating SPX and VIX risk scenarios based on a joint optimal transport calibration of their market smiles. Starting from the entropic martingale optimal transport formulation of Guyon, we introduce a perturbation methodology that computes sensitivities of the calibrated coupling using a Fisher information linearization. This allows risk to be generated without performing a full recalibration after market shocks. We further introduce a dimension reduction method based on perturbed optimal transport that produces fast and stable risk estimates while preserving the structural properties of the calibrated model. The approach is combined with Skew Stickiness Ratio(SSR) dynamics to translate SPX shocks into perturbations of forward variance and VIX distributions. Numerical experiments show that the proposed method produces accurate risk estimates relative to full recalibration while being computationally much faster. A backtesting study also demonstrates improved hedging performance compared with stochastic local volatility models.

q-fin.CP↗

arXiv2026

Dual Attainment in Multi-Period Multi-Asset Martingale Optimal Transport and Its Computation

We establish dual attainment for the multimarginal, multi-asset martingale optimal transport (MOT) problem, a fundamental question in the mathematical theory of model-independent pricing and hedging in quantitative finance. Our main result proves the existence of dual optimizers under mild regularity and irreducibility conditions, extending previous duality and attainment results from the classical and two-marginal settings to arbitrary numbers of assets and time periods. This theoretical advance provides a rigorous foundation for robust pricing and hedging of complex, path-dependent financial derivatives. To support our analysis, we present numerical experiments that demonstrate the practical solvability of large-scale discrete MOT problems using the state-of-the-art primal-dual linear programming (PDLP) algorithm. In particular, we solve multi-dimensional (or vectorial) MOT instances arising from the robust pricing of worst-of autocallable options, confirming the accuracy and feasibility of our theoretical results. Our work advances the mathematical understanding of MOT and highlights its relevance for robust financial engineering in high-dimensional and model-uncertain environments.

q-fin.MF↗

arXiv2026

Quantum Speedups for Derivative Pricing Beyond Black-Scholes

This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides the state-of-the-art provable, asymptotic performance: polynomial in problem dimension and quadratic in inverse-precision. While quantum algorithms are known to offer quadratic speedups over classical Monte Carlo methods, end-to-end speedups have been proven only in the simplified setting over the Black-Scholes geometric Brownian motion (GBM) model. This paper extends existing frameworks to demonstrate novel quadratic speedups for more practical models, such as the Cox-Ingersoll-Ross (CIR) model and a variant of Heston's stochastic volatility model, utilizing a characteristic of the underlying SDEs which we term fast-forwardability. Additionally, for general models that do not possess the fast-forwardable property, we introduce a quantum Milstein sampler, based on a novel quantum algorithm for sampling L\'evy areas, which enables quantum multi-level Monte Carlo to achieve quadratic speedups for multi-dimensional stochastic processes exhibiting certain correlation types. We also present an improved analysis of numerical integration for derivative pricing, leading to substantial reductions in the resource requirements for pricing GBM and CIR models. Furthermore, we investigate the potential for additional reductions using arithmetic-free quantum procedures. Finally, we critique quantum partial differential equation (PDE) solvers as a method for derivative pricing based on amplitude estimation, identifying theoretical barriers that obstruct achieving a quantum speedup through this approach. Our findings significantly advance the understanding of quantum algorithms in derivative pricing, addressing key challenges and open questions in the field.

quant-ph↗

arXiv2025

Volatility Calibration via Automatic Local Regression

Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices across all strikes and maturities with high accuracy. However, LV calibration is fundamentally ill-posed: finite market observables must determine a continuously-defined surface with infinite local volatility parameters. This ill-posed nature often causes spiky LV surfaces that are particularly problematic for finite-difference-based valuation, and induces high-frequency oscillations in solutions, thus leading to unstable Greeks. To address this challenge, we propose a pre-calibration smoothing method that can be integrated seamlessly into any LV calibration workflow. Our method pre-processes market observables using local regression that automatically minimizes asymptotic conditional mean squared error to generate denoised inputs for subsequent LV calibration. Numerical experiments demonstrate that the proposed pre-calibration smoothing yields significantly smoother LV surfaces and greatly improves Greek stability for exotic options with negligible additional computational cost, while preserving the LV model's ability to fit market observables with high fidelity.

q-fin.CP↗

arXiv2024

Robust and Fast Bass Local Volatility

The Bass Local Volatility Model, as studied in {henry2021bass}, stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional local volatility models. However, its performance highly depends on accurate construction of risk neutral densities and the corresponding marginal distributions and efficient numerical convolutions which are necessary when solving the associated fixed point problems. In this paper, we propose a new approach combining local quadratic estimation and lognormal mixture tails for the construction of risk neutral densities. We investigate computational efficiency of trapezoidal rule based schemes for numerical convolutions and show that they outperform commonly used Gauss-Hermite quadrature. We demonstrate the performance of the proposed method, both in standard option pricing models, as well as through a detailed market case study.

q-fin.CP↗

arXiv2024

Quantum option pricing via the Karhunen-Lo\`{e}ve expansion

We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$ and polynomial in $1/\epsilon$, where $\epsilon$ is the additive approximation error. Our algorithms are obtained respectively by using an $O(\log T)$-qubit semi-digital quantum encoding of the Brownian motion that allows for exponentiation of the stochastic process and by analyzing classical Monte Carlo algorithms inspired by the semi-digital encodings. The best quantum algorithm obtained using this approach has complexity $\widetilde{O}(1/\epsilon^{3})$ where the $\widetilde{O}$ suppresses factors poly-logarithmic in $T$ and $1/\epsilon$. The methods proposed in this work generalize to pricing options where the underlying asset price is modeled by a smooth function of a sub-Gaussian process and the payoff is dependent on the weighted time-average of the underlying asset price.

quant-ph↗