% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/merton_price.R
\name{priceEuropean}
\alias{priceEuropean}
\title{Price a European Option under the Merton Jump-Diffusion Model}
\usage{
priceEuropean(
  fit,
  S = 100,
  K = 100,
  r = 0.05,
  T_ = 1,
  type = "call",
  N_max = 50L
)
}
\arguments{
\item{fit}{A \linkS4class{JDFitResult} object from
\code{\link{fitMerton}}.}

\item{S}{Positive numeric. Current asset price.}

\item{K}{Positive numeric. Strike price.}

\item{r}{Numeric. Continuously compounded risk-free rate.}

\item{T_}{Positive numeric. Time to expiry in years.}

\item{type}{Character. Either \code{"call"} or \code{"put"}.}

\item{N_max}{Integer. Number of series terms (default 50).}
}
\value{
A named list with elements:
\item{price}{Merton jump-diffusion option price.}
\item{bs_price}{Black-Scholes benchmark price (no jumps).}
\item{jump_premium}{Difference between Merton and BS price.}
\item{params}{List of inputs and fitted parameters used.}
}
\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:
\deqn{C = \sum_{n=0}^{N} \frac{e^{-\lambda' T}(\lambda' T)^n}{n!}
  \cdot BS(S, K, r_n, \sigma_n, T)}
where \eqn{\lambda' = \lambda(1 + \bar\mu_J)},
\eqn{r_n = r - \lambda\bar\mu_J + n\log(1+\bar\mu_J)/T},
and \eqn{\sigma_n^2 = \sigma^2 + n\sigma_J^2/T}.
}
\examples{
\donttest{
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)
}

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