CustomDerivative

CustomDerivative is an R package for transparent derivative pricing and risk analytics. It combines analytical Black-Scholes pricing with extensible Monte Carlo engines for terminal and path-dependent payoffs.

Capabilities

Black-Scholes-Merton pricing for European calls and puts
continuous dividend yields
user-defined vectorized terminal payoff functions
antithetic variates and control variates
Monte Carlo standard errors and confidence intervals
geometric Brownian motion path simulation
Asian and discretely monitored barrier payoff helpers
generic finite-difference delta, gamma, vega, rho, and theta
input validation and reproducible simulation
cross-platform R CMD check through GitHub Actions

Installation

install.packages("pak")
pak::pak("AIM-IT4/CustomDerivative")

For the development branch:

pak::pak("AIM-IT4/CustomDerivative@agent/advanced-derivatives-engine")

Analytical European option

library(CustomDerivative)

black_scholes_price(
  spot = 100,
  strike = 100,
  maturity = 1,
  rate = 0.05,
  volatility = 0.20,
  type = "call"
)

Custom European payoff with Monte Carlo

The package prices a payoff (g(S_T)) as

[ V_0 = e^{-rT}{}[g(S_T)], ]

under risk-neutral geometric Brownian motion.

result <- price_european_mc(
  payoff = call_payoff(100),
  spot = 100,
  maturity = 1,
  rate = 0.05,
  volatility = 0.20,
  n_simulations = 100000,
  seed = 42
)

result
result$diagnostics$variance_reduction_ratio

A custom digital payoff can be supplied directly:

digital <- function(terminal_price) {
  100 * as.numeric(terminal_price > 110)
}

price_european_mc(
  payoff = digital,
  spot = 100,
  maturity = 1,
  rate = 0.05,
  volatility = 0.20,
  seed = 42
)

Path-dependent derivative

asian <- price_path_dependent_mc(
  payoff = asian_call_payoff(strike = 100),
  spot = 100,
  maturity = 1,
  rate = 0.05,
  volatility = 0.20,
  n_steps = 252,
  n_simulations = 20000,
  seed = 42
)

asian

Greeks

call_pricer <- function(spot, maturity, rate, volatility) {
  black_scholes_price(
    spot = spot,
    strike = 100,
    maturity = maturity,
    rate = rate,
    volatility = volatility,
    type = "call"
  )
}

finite_difference_greeks(
  pricer = call_pricer,
  spot = 100,
  maturity = 1,
  rate = 0.05,
  volatility = 0.20
)

Model scope

The current simulation model assumes a single tradable underlying following risk-neutral geometric Brownian motion with constant volatility, interest rate, and dividend yield. Path-dependent claims are monitored on a discrete grid. The package does not yet implement early exercise, stochastic volatility, jump diffusion, or multi-asset correlation models.

Development

install.packages(c("devtools", "testthat"))
devtools::document()
devtools::test()
devtools::check()