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ajd.sim.bk

Simulation of Affine Jump Diffusions Using Broadie-Kaya Method

https://github.com/xmlongan/ajd.sim.bk

Science Score: 44.0%

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Keywords

affine-jump-diffusion exact-simulation heston-model heston-stochastic-volatility jump-diffusion
Last synced: 6 months ago · JSON representation ·

Repository

Simulation of Affine Jump Diffusions Using Broadie-Kaya Method

Basic Info
  • Host: GitHub
  • Owner: xmlongan
  • License: other
  • Language: R
  • Default Branch: main
  • Homepage:
  • Size: 96.7 KB
Statistics
  • Stars: 0
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Topics
affine-jump-diffusion exact-simulation heston-model heston-stochastic-volatility jump-diffusion
Created over 1 year ago · Last pushed about 1 year ago
Metadata Files
Readme License Citation

README.Rmd 

---
output: github_document
---




```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# ajd.sim.bk




The goal of `ajd.sim.bk` is to **sim**ulate exactly the Heston 
Stochastic Volatility (SV) model and its **A**ffine **J**ump **D**iffusion (AJD) 
extensions using the **B**roadie-**K**aya algorithm (Broadie and Kaya, 2006),
hence the name `ajd.sim.bk`. The extended models include

- SVJ: SV model with jumps in the price process.

- SVCJ: SV model with contemporaneous jumps both in the price and variance
  processes.

*Reference*:

Broadie, M., & Kaya, Ö. (2006). Exact simulation of stochastic volatility and
other affine jump diffusion processes. *Operations Research*, 54(2), 217-231.

## Installation

You can install the development version of `ajd.sim.bk` like so:

``` r
# library(devtools)
install_github("xmlongan/ajd.sim.bk")
```

## Simulate return samples of the Heston SV model

This is a basic example which shows you how to simulate some return 
(not the price) samples of the Heston SV model and plot a histogram of these
simulated returns:

```{r example}
library(ajd.sim.bk)
v0 = 0.010201; k = 6.21; theta = 0.019; sigma = 0.61; rho = -0.7
r = 0.0319; tau = 1
Y = ajd.sim.bk::ryield_hest(1000, v0, tau, r, k, theta, sigma, rho)
hist(Y, main="Heston SV model")
```

If you want to simulate samples from the other two SV models, use:

- `ryield_svj()` for SVJ model,

- `ryield_svcj()` for SVCJ model.

## Pricing the European call option Using Monte Carlo simulation

If your are interested in pricing the European call option using Monte Carlo
simulation for the Heston SV, SVJ and SVCJ models. Please refer to functions
`?price_hest`, `?price_svj` and `?price_svcj`.

Owner

  • Name: Yanfeng
  • Login: xmlongan
  • Kind: user
  • Location: Shanghai

Ph.D. in Management Science, Fudan U.

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Wu"
  given-names: "Yan-Feng"
  orcid: "https://orcid.org/0000-0002-7105-1070"
title: "Simulation of Affine Jump Diffusions Using Broadie-Kaya Method"
version: 1.0.0
doi:
date-released: 2024-08-19
url: "https://github.com/xmlongan/ajd.sim.bk"

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Dependencies

DESCRIPTION cran
  • Bessel * imports
  • knitr * suggests
  • rmarkdown * suggests
  • testthat >= 3.0.0 suggests