JumpDiffSim

JumpDiffSim is an R package that implements the Merton (1976) and Kou (2002) jump-diffusion models through a unified S4 object-oriented interface. It provides exact compound-Poisson asset price simulation, maximum-likelihood parameter estimation with Hessian-based standard errors, Wald-type confidence intervals, theoretical moment calculations, and publication-quality diagnostic plots — all designed to run entirely offline without any dependency on live market data.

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Installation

Install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("kennedy2244/JumpDiffSim")

Install a specific release version:

devtools::install_github("kennedy2244/JumpDiffSim@v0.1.0")

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Quick Start

The core workflow is three steps: create a model → simulate paths → fit to data.

library(JumpDiffSim)

# ── Step 1: Create a Merton model object ─────────────────────
m <- MertonModel(
  mu      =  0.05,   # drift
  sigma   =  0.20,   # diffusion volatility
  lambda  =  1.00,   # average jumps per year
  mu_j    = -0.10,   # mean log-jump size
  sigma_j =  0.15    # std dev of log-jumps
)

show(m)
#> Merton Jump-Diffusion Model
#> ---------------------------
#>   mu      : 0.0500
#>   sigma   : 0.2000
#>   lambda  : 1.0000
#>   mu_j    : -0.1000
#>   sigma_j : 0.1500

# ── Step 2: Simulate 200 asset price paths ───────────────────
sim  <- simulateMerton(m, n = 200, T_ = 1, steps = 252, seed = 42)
plts <- diagnosticPlots(sim)

print(plts$fan_chart)   # path quantile fan (5/25/50/75/95th percentiles)
print(plts$density)     # empirical return density vs Normal
print(plts$acf_sq)      # ACF of squared log-returns

# ── Step 3: Fit model to synthetic data via MLE ──────────────
ret <- jdSampleData("merton", n = 500, seed = 42)
fit <- fitMerton(ret)

print(fit)
#> Merton MLE Fit Result
#> ---------------------
#>   Converged : TRUE
#>   Log-lik   : 487.2341
#>   Estimates (SE):
#>     mu       :  0.0489  (0.0021)
#>     sigma    :  0.1987  (0.0045)
#>     lambda   :  0.9823  (0.1234)
#>     mu_j     : -0.0998  (0.0187)
#>     sigma_j  :  0.1502  (0.0134)

confint(fit)
#>              2.5 %    97.5 %
#> mu       0.044710  0.053090
#> sigma    0.189896  0.207504
#> lambda   0.740434  1.224166
#> mu_j    -0.136443 -0.063157
#> sigma_j  0.123890  0.176510

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Parameters

Parameter	Symbol	Description
mu	$\mu$	Drift — expected continuous return per unit time
sigma	$\sigma$	Diffusion volatility of the Brownian component
lambda	$\lambda$	Jump intensity — average number of jumps per year
mu_j	$\mu_J$	Mean log-size of each jump
sigma_j	$\sigma_J$	Standard deviation of log-jump sizes

A negative mu_j with a positive lambda implies that jumps on average reduce the asset price — consistent with the crash-risk interpretation in Merton (1976).

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Theoretical Moments

jumpMoments(m)
#>       mean   variance   skewness   kurtosis
#>   0.000489   0.046225  -0.003012   0.000451

Excess kurtosis greater than zero confirms that the Merton model generates heavier tails than standard Geometric Brownian Motion.

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Package Structure

JumpDiffSim/
├── R/
│   ├── generics.R        # S4 generic function definitions
│   ├── merton_model.R    # MertonModel class + JDSimResult + JDFitResult
│   ├── merton_sim.R      # simulateMerton(), jdSampleData(), diagnosticPlots()
│   ├── merton_fit.R      # mertonLogLik(), fitMerton(), confint()
│   ├── utils.R           # jumpMoments()
│   ├── kou_model.R       # KouModel placeholder (v0.2.0)
│   ├── kou_sim.R         # simulateKou() placeholder (v0.2.0)
│   └── kou_fit.R         # fitKou() placeholder (v0.2.0)
├── tests/testthat/       # 36 unit tests (T1-T12 + TU1-TU2)
├── vignettes/            # Getting Started with JumpDiffSim
└── scaffolds/            # Team development scaffold files

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Test Coverage

File	Coverage
R/utils.R	100.00%
R/merton_sim.R	98.86%
R/merton_fit.R	96.72%
R/generics.R	14.29%
R/merton_model.R	20.83%
Overall	85.57%

R CMD check result: 0 errors | 0 warnings | 0 notes

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Vignette

A full introduction to the package is available in the vignette:

# After installation
vignette("JumpDiffSim-intro", package = "JumpDiffSim")

The vignette covers:

1. Why jump-diffusion? Motivation and model equation
2. Simulating asset price paths with simulateMerton()
3. Fitting the model to data with fitMerton()
4. Interpreting parameters
5. Theoretical moments with jumpMoments()

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Roadmap

Version	Status	Features
v0.1.0	Released	Merton model — simulation, estimation, diagnostics, tests
v0.2.0	Planned	Kou (2002) model — double-exponential jumps
v0.3.0	Planned	Cross-model comparison vignette, CRAN submission

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Team

This package was developed collaboratively by students in the Department of Statistics, Yeungnam University, under the supervision of Professor Lee Kyungsub.

Member	Role
Kennedy Kayaki	Package Lead · Estimation Module
Dohyun Oh	S4 Architect
Ju Seong Hyeon	Simulation Engine
Lee Seeun	Unit Testing (T1–T9)
Yuri Shin	Coverage Reporting (T10–T12)
Choi Jiwoo	Vignette & README

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References

• Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1–2), 125–144.
• Kou, S.G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086–1101.
• Wickham, H. and Bryan, J. (2023). R Packages (2nd ed.). O'Reilly Media. https://r-pkgs.org/

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License

MIT © 2026 Kennedy Kayaki, Yeungnam University