Type: Package
Title: Adaptive Multilevel Splitting for Option Simulation and Pricing
Version: 0.1.0
Description: Simulation and pricing routines for rare-event options using Adaptive Multilevel Splitting and standard Monte Carlo under Black-Scholes and Heston models. Core routines are implemented in C++ via Rcpp and RcppArmadillo with lightweight R wrappers.
License: MIT + file LICENSE
URL: https://github.com/RiccardoGozzo/amsSim, https://arxiv.org/html/2510.23461v1
BugReports: https://github.com/RiccardoGozzo/amsSim/issues
Encoding: UTF-8
Language: en-US
Depends: R (≥ 4.1)
Imports: Rcpp (≥ 1.0.0)
LinkingTo: Rcpp, RcppArmadillo
SystemRequirements: C++17
ByteCompile: true
NeedsCompilation: yes
RoxygenNote: 7.3.3
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
Packaged: 2025-10-28 11:45:15 UTC; riccardogozzo
Author: Riccardo Gozzo [aut, cre]
Maintainer: Riccardo Gozzo <gozzoriccardo0@gmail.com>
Repository: CRAN
Date/Publication: 2025-10-31 18:20:23 UTC

amsSim: Adaptive Multilevel Splitting e Monte Carlo

Description

Simulation and pricing routines for rare-event options using Adaptive Multilevel Splitting and standard Monte Carlo under Black-Scholes and Heston models. Core routines are implemented in C++ via Rcpp and RcppArmadillo with lightweight R wrappers.

Author(s)

Maintainer: Riccardo Gozzo gozzoriccardo0@gmail.com

See Also

Useful links:

AMS Adaptive Multilevel Splitting estimator for rare-event option payoffs.

Description

Pipeline per iteration:

Usage

AMS(
  model,
  type,
  funz,
  n,
  t,
  p,
  r,
  sigma,
  S0,
  rho = NULL,
  rim = 0L,
  v0 = 0.04,
  Lmax = 0,
  strike = 1,
  K = 1L
)

Arguments

model

1 = Black–Scholes; 2,3,4 = Heston variants (as in simulate_AMS).

type

Payoff type passed to payoff() and function_AMS_Cpp (1..6).

funz

1 = BS digital proxy in continuation; 2 = raw feature (signed).

n

Population size (> K).

t

Maturity in years (>0).

p

Total time steps (>0).

r

Risk–free rate.

sigma

BS volatility (used by continuation; >0 if funz == 1).

S0

Initial spot.

rho

Correlation for Heston models (required for model >= 2, in [-1,1]).

rim

Left-trim for simulation (keep last p - rim steps; 0 <= rim < p).

v0

Initial variance for Heston models (>=0).

Lmax

Stopping level: iterate while L < L_{\max}.

strike

Strike K used by continuation and final payoff.

K

Number of resampled offspring per iteration (1..n-1).

Value

List with price and std.

Examples


  out <- AMS(model = 2, type = 3, funz = 1, n = 500, t = 1, p = 252, r = 0.03,
             sigma = 0.2, rho = -0.5, S0 = 1, rim = 0, Lmax = 0.5, strike = 1.3, K = 200)
  str(out)

simulate_AMS Monte Carlo simulation of price paths under: 1 = Black–Scholes (exact solution) 2 = Heston (Euler discretisation) 3 = Heston (Milstein discretisation) 4 = Heston (Quadratic–Exponential scheme, Andersen 2008)

Description

simulate_AMS Monte Carlo simulation of price paths under: 1 = Black–Scholes (exact solution) 2 = Heston (Euler discretisation) 3 = Heston (Milstein discretisation) 4 = Heston (Quadratic–Exponential scheme, Andersen 2008)

Usage

simulate_AMS(model, n, t, p, r, sigma, S0, rho = NULL, rim = 0L, v0 = 0.04)

Arguments

model

Integer in \{1,2,3,4\} selecting the model.

n

Number of simulated paths (>0).

t

Maturity in years (>0).

p

Total time steps (>0).

r

Risk–free rate.

sigma

Black–Scholes volatility (>=0, used only when model == 1).

S0

Initial spot price (>0).

rho

Correlation between asset and variance Brownian motions (required for Heston models, finite in [-1,1]).

rim

Left–trim: discard the first rim time steps (0 <= rim < p). Returned matrices keep p - rim + 1 columns including the initial time.

v0

Initial variance for Heston models (>=0).

Value

List: for model 1 returns S (n \times (p-rim+1)); for Heston models returns S and V.

Examples


  b <- simulate_AMS(1, n = 50, t = 1, p = 10, r = 0.01, sigma = 0.2, S0 = 100, rho = NULL)
  str(b)