A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing

• URL: http://arxiv.org/abs/2408.02064v1
• Date: Sun, 4 Aug 2024 15:28:58 GMT
• Title: A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing
• Authors: Mark Stedman, Luca Capriotti,
• Abstract summary: We generalize a path integral approach originally introduced by Giachetti and Tognetti to time-dependent Hamiltonians. We show results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing.

Related papers

• Achieving $\widetilde{\mathcal{O}}(\sqrt{T})$ Regret in Average-Reward POMDPs with Known Observation Models [56.92178753201331]
  We tackle average-reward infinite-horizon POMDPs with an unknown transition model. We present a novel and simple estimator that overcomes this barrier.
  arXiv  Detail & Related papers  (2025-01-30T22:29:41Z)
• Pathwise optimization for bridge-type estimators and its applications [49.1574468325115]
  Pathwise methods allow to efficiently compute the full path for penalized estimators. We apply these algorithms to the penalized estimation of processes observed at discrete times.
  arXiv  Detail & Related papers  (2024-12-05T10:38:29Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Sample-efficient Learning of Infinite-horizon Average-reward MDPs with General Function Approximation [53.17668583030862]
  We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. We propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP) We show that LOOP achieves a sublinear $tildemathcalO(mathrmpoly(d, mathrmsp(V*)) sqrtTbeta )$ regret, where $d$ and $beta$ correspond to AGEC and log-covering number of the hypothesis class respectively
  arXiv  Detail & Related papers  (2024-04-19T06:24:22Z)
• A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model [1.3443690690260939]
  We study option pricing under Vasicek Model by a Hamiltonian approach. We split the time to maturity into infinite steps, and the matrix element during each step could be calculated by quantum mechanics methods.
  arXiv  Detail & Related papers  (2023-07-14T00:25:52Z)
• Chaotic Hedging with Iterated Integrals and Neural Networks [3.3379026542599934]
  We show that every $p$-integrable functional of the semimartingale, for $p in [1,infty$, can be represented as a sum of iterated integrals thereof. We also show that every financial derivative can be approximated arbitrarily well in the $Lp$-sense.
  arXiv  Detail & Related papers  (2022-09-21T07:57:07Z)
• Whiplash Gradient Descent Dynamics [2.0508733018954843]
  We introduce the symplectic convergence analysis for the Whiplash system for convex functions. We study the algorithm's performance for various costs and provide a practical methodology for analyzing convergence rates.
  arXiv  Detail & Related papers  (2022-03-04T05:47:26Z)
• Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification [16.0817847880416]
  We offer a unified framework that includes a broad variety of linear prediction problems on a Hilbert space. We show that for misspecification level $epsilon$, these estimators achieve an error rate of $O(maxleft|mathcalO|1/2n-1/2, |mathcalI|1/2n-1 right+epsilon)$, matching the best-known rates in literature.
  arXiv  Detail & Related papers  (2022-01-06T08:51:08Z)
• A Discrete Variational Derivation of Accelerated Methods in Optimization [68.8204255655161]
  We introduce variational which allow us to derive different methods for optimization. We derive two families of optimization methods in one-to-one correspondence. The preservation of symplecticity of autonomous systems occurs here solely on the fibers.
  arXiv  Detail & Related papers  (2021-06-04T20:21:53Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)
• PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations [4.1499725848998965]
  We propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs) The method consists of using a combination of feed-forward and Long-Term Memory architectures to model the solution of the PPDE. We analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.
  arXiv  Detail & Related papers  (2020-03-04T12:26:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.