Package {JumpDiffSim}

JDFitResult: MLE Estimation Output Class

Description

JDFitResult: MLE Estimation Output Class

Usage

## S4 method for signature 'JDFitResult'
show(object)

## S4 method for signature 'JDFitResult'
confint(object, parm, level = 0.95, ...)

Arguments

Methods (by generic)

• confint(JDFitResult): Wald-type 95\

Slots

estimates

Named numeric. Parameter estimates.

se

Named numeric. Standard errors.

loglik

Numeric. Log-likelihood at optimum.

converged

Logical. Did optimisation converge?

model_type

Character. Model name.

JDSimResult: Simulation Output Class

Description

JDSimResult: Simulation Output Class

Slots

paths

Matrix. Simulated price paths (n x steps+1).

times

Numeric vector. Time grid.

params

List. Model parameters used in simulation.

model_type

Character. Model name.

JumpDiffModel: Virtual Base Class for Jump-Diffusion Models

Description

Abstract base class. Do not instantiate directly. Concrete subclasses: MertonModel.

Slots

mu

Numeric. Drift parameter (annualised).

sigma

Positive numeric. Diffusion volatility.

lambda

Non-negative numeric. Jump intensity (jumps per year).

Create a MertonModel Object

Description

Create a MertonModel Object

Usage

MertonModel(mu = 0.05, sigma = 0.2, lambda = 1, mu_j = -0.1, sigma_j = 0.15)

Arguments

Value

A validated MertonModel object.

Examples

m <- MertonModel(mu = 0.05, sigma = 0.20, lambda = 1,
                 mu_j = -0.10, sigma_j = 0.15)
show(m)

MertonModel: Merton (1976) Jump-Diffusion Model

Description

Extends JumpDiffModel with log-normal jump parameters.

Usage

## S4 method for signature 'MertonModel'
show(object)

Arguments

Slots

mu_j

Numeric. Mean log-jump size.

sigma_j

Positive numeric. Std dev of log-jump sizes.

References

Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144.

Diagnostic Plots for a JDSimResult Object

Description

Creates three diagnostic plots for a JDSimResult object: a simulated path fan chart, a histogram of log-returns with a normal density overlay, and the autocorrelation function of squared log-returns.

Usage

diagnosticPlots(object)

Arguments

Value

A named list of three ggplot objects:

• fan_chart: simulated path quantile fan chart.

• density: histogram of log-returns with a normal overlay.

• acf_sq: autocorrelation of squared log-returns with 95\

Examples

m    <- MertonModel()
sim  <- simulateMerton(m, n = 50, T_ = 1, steps = 100)
plts <- diagnosticPlots(sim)
print(plts$fan_chart)
print(plts$density)
print(plts$acf_sq)

Fit Model to Log-Returns via MLE

Description

Fit Model to Log-Returns via MLE

Usage

fit(object, log_returns, ...)

Arguments

Value

A JDFitResult object.

Fit Merton Jump-Diffusion Model via MLE

Description

Maximises the log-likelihood of the Merton (1976) model using L-BFGS-B optimisation. Returns a JDFitResult object containing parameter estimates, standard errors, and convergence info.

Usage

fitMerton(
  log_returns,
  start = c(mu = 0.05, sigma = 0.2, lambda = 1, mu_j = -0.1, sigma_j = 0.15),
  dt = 1/252,
  N_max = 50L,
  verbose = FALSE
)

Arguments

Value

A JDFitResult object.

Examples

ret <- jdSampleData("merton", n = 500, seed = 42)
fit <- fitMerton(ret, verbose = TRUE)
print(fit)
confint(fit)

Generate Synthetic Log-Returns from a Jump-Diffusion Model

Description

Convenience function for generating reproducible synthetic log-returns for use in examples, tests, and vignettes. All package examples and tests use this function to avoid any dependency on live market data.

Usage

jdSampleData(
  model = "merton",
  n = 500,
  mu = 0.05,
  sigma = 0.2,
  lambda = 1,
  mu_j = -0.1,
  sigma_j = 0.15,
  dt = 1/252,
  seed = 42L
)

Arguments

Value

Numeric vector of n log-returns.

Examples

ret <- jdSampleData("merton", n = 200, seed = 42)
head(ret)
hist(ret, breaks = 40, main = "Synthetic Merton Returns")

Theoretical Moments of the Log-Return Distribution

Description

Theoretical Moments of the Log-Return Distribution

Usage

jumpMoments(object)

Arguments

Value

Named numeric vector: mean, variance, skewness, kurtosis.

Theoretical Moments of the Merton Jump-Diffusion Log-Return

Description

Returns the theoretical mean, variance, skewness, and excess kurtosis of the log-return distribution under the Merton (1976) model.

Usage

## S4 method for signature 'MertonModel'
jumpMoments(object)

Arguments

Value

Named numeric vector with elements mean, variance, skewness, kurtosis.

Examples

m <- MertonModel(mu = 0.05, sigma = 0.20, lambda = 1,
                 mu_j = -0.10, sigma_j = 0.15)
jumpMoments(m)

Compute Negative Log-Likelihood

Description

Compute Negative Log-Likelihood

Usage

loglik(object, log_returns, ...)

Arguments

Value

Scalar negative log-likelihood value.

Negative Log-Likelihood for the Merton Jump-Diffusion Model

Description

Evaluates the negative log-likelihood of observing log_returns under the Merton (1976) model. The density is approximated by a Gaussian mixture truncated at N_max = 50 terms.

Usage

mertonLogLik(params, log_returns, dt = 1/252, N_max = 50L)

Arguments

Value

Scalar. Negative log-likelihood. Returns Inf for invalid parameter values.

Examples

ret <- jdSampleData("merton", n = 200, seed = 42)
p   <- c(mu = 0.05, sigma = 0.2, lambda = 1, mu_j = -0.1, sigma_j = 0.15)
mertonLogLik(p, ret)

Price a European Option under the Merton Jump-Diffusion Model

Description

Computes the European call or put price under the Merton (1976) jump-diffusion model using the analytic series expansion. The price is expressed as a Poisson-weighted sum of Black-Scholes prices with jump-adjusted drift and volatility.

The formula is:

C = \sum_{n=0}^{N} \frac{e^{-\lambda' T}(\lambda' T)^n}{n!} \cdot BS(S, K, r_n, \sigma_n, T)

where \lambda' = \lambda(1 + \bar\mu_J), r_n = r - \lambda\bar\mu_J + n\log(1+\bar\mu_J)/T, and \sigma_n^2 = \sigma^2 + n\sigma_J^2/T.

Usage

priceEuropean(
  fit,
  S = 100,
  K = 100,
  r = 0.05,
  T_ = 1,
  type = "call",
  N_max = 50L
)

Arguments

Value

A named list with elements:

References

Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144.

Examples

ret <- jdSampleData("merton", n = 500, seed = 42)
fit <- fitMerton(ret)
price <- priceEuropean(fit, S = 100, K = 100,
                       r = 0.05, T_ = 1, type = "call")
print(price)

Simulate Asset Price Paths

Description

Simulate Asset Price Paths

Usage

simulate(object, n, T_, steps, seed = NULL, ...)

Arguments

Value

A JDSimResult object.

Simulate Merton Jump-Diffusion Asset Paths

Description

Generates n exact compound-Poisson asset price paths under the Merton (1976) jump-diffusion model. Simulation is exact in the sense that jump arrivals are drawn directly from the Poisson process rather than approximated via Euler discretisation.

Usage

simulateMerton(object, n = 100, T_ = 1, steps = 252, S0 = 1, seed = NULL, ...)

Arguments

Value

A JDSimResult object.

Examples

m   <- MertonModel()
sim <- simulateMerton(m, n = 10, T_ = 1, steps = 252, seed = 42)
dim(sim@paths)   # should be 200 x 253