compute option-implied values

This study addresses the challenge of simultaneously achieving precise local shape control and strict static no-arbitrage compliance in implied volatility curve modeling. To this end, it proposes a parsimonious and interpretable parametric approach grounded in the risk-neutral distribution. By introducing parameters that exhibit stable cross-maturity patterns, the method directly governs local curvature characteristics—such as convexity and concavity—while inherently satisfying no-arbitrage constraints. The resulting model flexibly accommodates diverse curvature patterns and supports both term structure interpolation and dynamic modeling. Empirical validation on a two-year dataset of S&P 500 options, encompassing over 250,000 calibrated volatility curves, demonstrates the stability, generalizability, and high fidelity of the proposed parameterization in capturing complex market dynamics.

本文提出一种神经校准方法，通过变形基准格构建无套利、完整的二叉树定价模型，用于期权定价和复制交易策略。

Traditional calibration methods, while achieving high accuracy in fitting the volatility surface, often yield implied variance term structures that substantially deviate from market observations. This paper proposes a joint calibration framework for Bates-type jump–stochastic volatility models that simultaneously fits both option prices and the market-observed variance term structure. The core innovation lies in constructing a weighted objective function incorporating a penalty term for variance structure misfit, with hyperparameters enabling explicit control over the trade-off between these two calibration targets. Empirical evaluation on S&P 500 option data from 1996 to 2023, complemented by simulation studies, demonstrates that the method significantly improves the accuracy of variance term structure replication while preserving volatility surface fit quality. These results confirm the framework’s effectiveness, robustness, and practical applicability in derivative pricing and risk management.

This study addresses the challenge of robustly extracting risk-neutral densities from near-expiry options, which is hindered by low premiums, wide bid–ask spreads, and asynchronous quotes that undermine conventional approaches. To overcome these issues, the authors propose a model-free two-stage framework: first, the ARIES strategy eliminates static arbitrage opportunities under market depth constraints; second, the SEDEx method recovers the density by incorporating smoothness and maximum entropy principles while respecting bid–ask bounds. Notably, this approach explicitly treats the bid–ask spread as a fundamental market constraint and uniquely integrates executable arbitrage filtering with entropy regularization, substantially enhancing stability in processing short-dated option data. Empirical validation on both synthetic Heston-generated data and real-world SPX options demonstrates the method’s ability to reconstruct stable and accurate implied volatility smiles.

This study proposes a unified model integrating the Heston stochastic volatility, Bates jump-diffusion, and Cox-Ingersoll-Ross (CIR) stochastic interest rate frameworks to jointly address mid- to short-term equity option pricing and interest rate risk assessment. The model calibrates volatility and jump parameters using Lewis’s Fourier inversion and the Carr-Madan FFT method, while the CIR component is calibrated to Euribor data to generate economically plausible forward rate paths. Empirical results indicate that jump effects are negligible within 60 days, with stochastic volatility dominating short-term pricing dynamics, whereas stochastic interest rates exert a significant influence on valuations beyond one year. The model exhibits stable parameter estimates and produces forward rate trajectories consistent with economic intuition, thereby confirming the robustness of the standard Heston/Bates framework for mid- to short-term option pricing.

Existing methods struggle to construct risk-neutral marginal distributions from arbitrage-free option prices that simultaneously satisfy no butterfly arbitrage, no calendar spread arbitrage, exact market price recovery, efficient sampling, and full support. This work proposes an explicit construction method that exactly fits observed option prices within the range of quoted strikes via piecewise probability mass allocation, while extrapolating beyond this range using closed-form power-law tails that satisfy necessary boundary conditions. The approach uniquely achieves, within a unified framework, strict absence of static arbitrage, exact calibration to market prices, analytical expressions for both density and quantile functions, and efficient Monte Carlo sampling. Experiments on synthetic SSVI surfaces and S&P 500 market data demonstrate its computational efficiency, robustness, and practical utility, effectively bridging the gap between option pricing models and downstream applications.

This work addresses the long-standing challenge of explicitly solving for implied volatility in the Black–Scholes model by introducing the first closed-form analytical formula that requires neither iteration, approximation, nor series expansion. The approach reinterprets the option price as the survival probability of an inverse Gaussian distribution and leverages its quantile function to analytically invert the Black–Scholes framework, yielding an explicit expression for implied volatility that depends solely on observable market variables. Numerical experiments demonstrate that the method achieves machine precision and offers a computational speedup of approximately 3.4× compared to the current state-of-the-art benchmark.

This study addresses the absence of efficient and accurate analytical approximations for VIX option implied volatility, which has traditionally necessitated time-consuming numerical root-finding in model calibration. Building upon forward variance models—including the standard, rough Bergomi, and hybrid specifications—the authors derive, for the first time, closed-form asymptotic expansions of implied volatility with explicit correction terms by leveraging weak approximation and asymptotic expansion techniques. This approach entirely circumvents numerical root-finding and demonstrates high accuracy and exceptional computational efficiency across multiple model settings. Consequently, it substantially enhances both the speed and numerical stability of VIX option calibration.

This study addresses the monotonicity of normalized implied volatility coordinates within a finite quoted option chain under no-arbitrage conditions and derives model-independent variance identities. Relying solely on static no-arbitrage assumptions—including discrete strike comparisons, convexity, monotonicity, and call-put parity—the authors provide the first purely discrete proof of monotonicity for normalized coordinates in both the Black–Scholes and Bachelier frameworks, without requiring continuous quotes or differentiability. The main contributions are twofold: (1) a rigorous discrete verification of monotonicity in these two canonical implied volatility models, and (2) the introduction of a normal variance identity that serves as the natural counterpart to Fukasawa’s log-normal result, thereby establishing a model-independent theoretical foundation for volatility derivatives.

This paper addresses the numerical pricing of arithmetic Asian options and European/American options on stocks with discrete cash dividends. We propose a novel drift-free PDE modeling framework grounded in tradables—market-observable, self-financing assets—thereby eliminating reliance on drift specifications under arbitrary measures. Our method directly fits finite-difference schemes to analytic solutions of the drift-free pricing PDE and constructs a market-consistent hybrid finite-difference scheme amenable to end-to-end calibration against market quotes. Key technical contributions include tradables-based modeling, drift-free PDE discretization, adaptive hybrid finite differencing, and efficient numerical fitting. Experiments demonstrate pricing errors of 0.1% (10 ms) for arithmetic Asian options and 0.001% (1 s) for European/American options—substantially outperforming state-of-the-art methods—while naturally accommodating discrete cash dividends and enforcing strict market consistency.