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Pricing of perpetual American put option with sub-mixed fractional Brownian motion

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Published/Copyright: October 23, 2019
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 22 Issue 4

Abstract

The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process. First of all, the sub-mixed fractional Black-Scholes partial differential equation is established by using the delta hedging method and the principle of no arbitrage. Then, by solving the free boundary problem, we get the pricing formula of the perpetual American put option.

MSC 2010: 60H10; 90A06
Key Words and Phrases: option pricing; sub-mixed fractional Brownian motion; perpetual American option; pricing models

Acknowledgements

The authors would like to thank the anonymous referees for valuable suggestions for the improvement of this paper. All remaining errors are the responsibility of the authors.

  1. Funding: The first author is supported by pre-research project of Suzhou Vocational University (SVU2018YY01) and Blue project of Suzhou Vocational University.

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Received: 2018-04-24
Revised: 2019-08-02
Published Online: 2019-10-23
Published in Print: 2019-08-27

© 2019 Diogenes Co., Sofia

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  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 22–4–2019)
  4. Research Paper
  5. Fractional equations via convergence of forms
  6. About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
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  8. The vertical slice transform on the unit sphere
  9. Research Paper
  10. Well-posedness of time-fractional advection-diffusion-reaction equations
  11. Existence of solutions for nonlinear fractional order p-Laplacian differential equations via critical point theory
  12. Exact asymptotic formulas for the heat kernels of space and time-fractional equations
  13. Estimates of damped fractional wave equations
  14. A modified time-fractional diffusion equation and its finite difference method: Regularity and error analysis
  15. On the fractional diffusion-advection-reaction equation in ℝ
  16. Controllability of nonlinear stochastic fractional higher order dynamical systems
  17. Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2
  18. Analysis of fractional order error models in adaptive systems: Mixed order cases
  19. Fractional calculus of variations: a novel way to look at it
  20. Pricing of perpetual American put option with sub-mixed fractional Brownian motion
https://doi.org/10.1515/fca-2019-0060
Keywords for this article
option pricing; sub-mixed fractional Brownian motion; perpetual American option; pricing models

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 22–4–2019)
  4. Research Paper
  5. Fractional equations via convergence of forms
  6. About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
  7. Survey Paper
  8. The vertical slice transform on the unit sphere
  9. Research Paper
  10. Well-posedness of time-fractional advection-diffusion-reaction equations
  11. Existence of solutions for nonlinear fractional order p-Laplacian differential equations via critical point theory
  12. Exact asymptotic formulas for the heat kernels of space and time-fractional equations
  13. Estimates of damped fractional wave equations
  14. A modified time-fractional diffusion equation and its finite difference method: Regularity and error analysis
  15. On the fractional diffusion-advection-reaction equation in ℝ
  16. Controllability of nonlinear stochastic fractional higher order dynamical systems
  17. Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2
  18. Analysis of fractional order error models in adaptive systems: Mixed order cases
  19. Fractional calculus of variations: a novel way to look at it
  20. Pricing of perpetual American put option with sub-mixed fractional Brownian motion
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