1 / 27

Efficient Lattice for Derivative Pricing with Jump-Diffusion: Convergence and Accuracy

This paper explores an efficient lattice model for pricing derivatives under a jump-diffusion process. It compares different lattice structures for pricing options on stock assets, highlighting convergence issues related to nonlinearity errors. The study addresses the problem posed by distributions with heavier tails and higher peaks in jump-diffusion processes and evaluates the accuracy of various lattice models such as Amin's and Hilliard and Schwartz's. The text discusses the modeling and definitions needed for risk-neutralized jump-diffusion processes and presents a detailed analysis of the lattice construction complexity. Numerical results are provided to demonstrate the effectiveness of the proposed lattice in pricing derivatives with improved convergence and accuracy.

miller
Download Presentation

Efficient Lattice for Derivative Pricing with Jump-Diffusion: Convergence and Accuracy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An Efficient and Accurate Lattice for Pricing Derivatives under a Jump-Diffusion Process

  2. 1. Introduction • In a lattice, the prices of the derivatives converge when the number of time steps increase. • Nonlinearity error from nonlinearity option value causes the pricing results to converge slowly or oscillate significantly.

  3. Underlying assets : Stock • Derivatives : Option • CRR Lattice Lognormal diffusion process • Amin’s Lattice • HS Lattice Jump diffusion process • Paper’s Lattice

  4. CRR Lattice Lognormal Diffusion Process Su with Sd with =1- d < u ud = 1

  5. Problem !? • Distribution has heavier tails & higher peak  ---------------------------------------------------------------- Jump diffusion process !!! ↙ ↘ Diffusion component Jump component ↓ ↓ lognormal diffusion process lognormal jump (Poisson)

  6. Amin’s Lattice less accurate !? Volatility (lognormal jump > diffusion component)

  7. Hilliard and Schwartz’s (HS) Lattice Diffusion nodes Jump nodes Rate of

  8. Paper’s Lattice Trinomial structure lower the node Rate of

  9. 2. Modeling and Definitions The risk-neutralized version of the underlying asset’s jump diffusion process

  10. Financial knowledge (Pricing options) • { • {

  11. 3. Preliminaries • (a) CRR Lattice jump diffusion process (λ=0)

  12. (b) HS Lattice

  13. Continuous-time distribution of the jump component → obtain 2m+1 probabilities from solving 2m+1 equations

  14. Pricing option

  15. Complexity Analysis

  16. Problem !? 1. time complexity 2. oscillation

  17. 4. Lattice Construction • Trinomial Structure

  18. → Cramer’s rule

  19. fitting the derivatives specification

  20. Jump nodes

  21. Complexity analysis

  22. 5. Numerical Results

More Related