Extensible Derivative Pricing and Risk Analytics

Tools for pricing and analysing financial derivatives under the classical lognormal diffusion model and geometric Brownian motion assumptions. The package provides analytical European option prices, Monte Carlo pricing with antithetic and control variates, confidence intervals, finite-difference Greeks, and path simulation for path-dependent payoffs. The simulation interfaces accept user-defined payoff functions, enabling transparent construction of custom contracts while reporting numerical uncertainty.

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}\mathbb{E}^{\mathbb{Q}}[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()

License

MIT. Copyright Amit Kumar Jha.