A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model

• URL: http://arxiv.org/abs/2307.07103v2
• Date: Thu, 4 Jan 2024 01:54:31 GMT
• Title: A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model
• Authors: Qi Chen Hong-tao Wang and Chao Guo
• Abstract summary: Hamiltonian approach in quantum theory provides a new thinking for option pricing with interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics. For double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well.
• Score: 1.1965844936801802
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hamiltonian approach in quantum theory provides a new thinking for option pricing with stochastic interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using Hamiltonian approach, the expressions of pricing kernels and option prices under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown.

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)
• A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing [0.0]
  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.
  arXiv  Detail & Related papers  (2024-08-04T15:28:58Z)
• A time-stepping deep gradient flow method for option pricing in (rough) diffusion models [0.0]
  We develop a novel deep learning approach for pricing European options in diffusion models. The proposed scheme respects the behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices.
  arXiv  Detail & Related papers  (2024-03-01T18:46:26Z)
• Time series generation for option pricing on quantum computers using tensor network [0.0]
  Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. We propose a novel approach using Matrix Product State (MPS) as a generative model for time series generation. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers.
  arXiv  Detail & Related papers  (2024-02-27T02:29:24Z)
• Pricing with Contextual Elasticity and Heteroscedastic Valuation [23.96777734246062]
  We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer's expected demand by incorporating feature-based price elasticity. Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.
  arXiv  Detail & Related papers  (2023-12-26T11:07:37Z)
• Towards Efficient Time Stepping for Numerical Shape Correspondence [55.2480439325792]
  Methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature. We consider here several time stepping schemes. The goal of this investigation is to assess, if one may identify a useful property of methods for time integration for the shape analysis context.
  arXiv  Detail & Related papers  (2023-12-21T13:40:03Z)
• Path Integral Method for Pricing Proportional Step Double-Barrier Option with Time Dependent Parameters [7.891031556378682]
  Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional double-barrier step (PDBS) options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well.
  arXiv  Detail & Related papers  (2023-02-15T12:53:34Z)
• Autoregressive Bandits [58.46584210388307]
  We propose a novel online learning setting, Autoregressive Bandits, in which the observed reward is governed by an autoregressive process of order $k$. We show that, under mild assumptions on the reward process, the optimal policy can be conveniently computed. We then devise a new optimistic regret minimization algorithm, namely, AutoRegressive Upper Confidence Bound (AR-UCB), that suffers sublinear regret of order $widetildemathcalO left( frac(k+1)3/2sqrtnT (1-G
  arXiv  Detail & Related papers  (2022-12-12T21:37:36Z)
• Quantum computational finance: martingale asset pricing for incomplete markets [69.73491758935712]
  We show that a variety of quantum techniques can be applied to the pricing problem in finance. We discuss three different methods that are distinct from previous works.
  arXiv  Detail & Related papers  (2022-09-19T09:22:01Z)
• Generative Principal Component Analysis [47.03792476688768]
  We study the problem of principal component analysis with generative modeling assumptions. Key assumption is that the underlying signal lies near the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order $sqrtfracklog Lm$, where $m$ is the number of samples.
  arXiv  Detail & Related papers  (2022-03-18T01:48:16Z)
• Navigating to the Best Policy in Markov Decision Processes [68.8204255655161]
  We investigate the active pure exploration problem in Markov Decision Processes. Agent sequentially selects actions and, from the resulting system trajectory, aims at the best as fast as possible.
  arXiv  Detail & Related papers  (2021-06-05T09:16:28Z)

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.