Overview

AsianOption implements valuation of Asian options under transient and permanent market impact, as described in Tiwari and Majumdar (2025). The package provides three complementary pricing approaches:

1. Kemna-Vorst benchmark — frictionless Black-Scholes-type pricing for geometric and arithmetic Asian options.
2. Exogenous diffusion — passive trading regime where the impact state evolves as an exogenous Ornstein-Uhlenbeck process. Closed-form for geometric Asians; Monte Carlo for arithmetic Asians.
3. Endogenous utility-indifference (Bellman scheme) — a dealer with constant absolute risk aversion hedges the option in a market with price impact, running a self-financing cash account. Solving the dealer's problem with and without the option gives reservation bid and ask quotes.

Installation

# Install from CRAN
install.packages("AsianOption")
# Development version from GitHub
# install.packages("devtools")
devtools::install_github("plato-12/AsianOption")

Quick Start

Kemna-Vorst Benchmark (Frictionless)

library(AsianOption)
# Geometric Asian call (closed-form)
price_kemna_vorst_geometric(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2, Time = 1
)
# Arithmetic Asian call (Monte Carlo)
price_kemna_vorst_arithmetic(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2, Time = 1
)

Exogenous Diffusion (with Impact)

# Geometric Asian call — closed-form (Theorem 3.2)
price_geometric_asian_diffusion(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2, T = 1,
  lambda_T = 0.05, I0 = 0, kappa = 1, eta = 0.5, rho = 0
)
# Arithmetic Asian call — Monte Carlo
price_arithmetic_asian_diffusion(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2, T_mat = 1,
  lambda_T = 0.05, I0 = 0, kappa = 1, eta = 0.5, rho = 0
)

Endogenous Utility-Indifference (Dealer Hedging under Impact)

# Geometric Asian — reservation bid/ask for a CARA dealer
res <- price_geometric_asian_indiff(
  S0 = 100, K = 100, T = 1, N = 25,
  sigma = 0.2, r_cont = 0.05,
  gamma = 0.05,                                # dealer risk aversion
  lambda_bar_T = 0.05, lambda_bar_P = 0.025,   # execution impact
  k_A = 0.05, k_B = 0.05, psi_cost = 1,        # temporary execution cost
  kappa_J = 1, Q_bar = 2, nu_bar = 4
)
summary(res)          # quotes plus the numerical diagnostics
# Arithmetic Asian — same interface
price_arithmetic_asian_indiff(
  S0 = 100, K = 100, T = 1, N = 25, sigma = 0.2, r_cont = 0.05
)

The execution price is S + lambda_bar_P * Q + lambda_bar_T * J, where Q is the dealer's inventory and J its transient impact state. This is a change of meaning from the legacy *_hjb() functions, where lambda_bar_* appeared in the drift of S; the drift loading is now lambda_I. See NEWS.md.

Two practical notes. Leave n_logS = NULL so the engine aligns the log-price grid with one shock — an unaligned grid inflates the effective volatility. And check inst/scripts/indiff_convergence.R before quoting a spread, which is more grid-sensitive than the price level.

Main Functions

• price_kemna_vorst_geometric(): Kemna-Vorst geometric Asian (frictionless)
• price_kemna_vorst_arithmetic(): Kemna-Vorst arithmetic Asian (frictionless)
• price_geometric_asian_diffusion(): Exogenous diffusion geometric Asian (closed-form)
• price_arithmetic_asian_diffusion(): Exogenous diffusion arithmetic Asian (Monte Carlo)
• price_geometric_asian_indiff(): Utility-indifference geometric Asian bid/ask
• price_arithmetic_asian_indiff(): Utility-indifference arithmetic Asian bid/ask

Legacy (pre-revision) interface

price_geometric_asian_hjb() and price_arithmetic_asian_hjb() implement the earlier cost-minimisation formulation. They are deprecated — kept unchanged so the arXiv v2 numbers remain reproducible, to be made internal in 0.4.0 and removed in 0.5.0. New work should use the *_indiff() functions, which are self-financing, give the bid and ask an explicit economic meaning, and recover the frictionless benchmark as impact goes to zero.

Citation

If you use this package in your research, please cite:

Tiwari, P., & Majumdar, S. (2025). Asian option valuation under price impact. arXiv preprint. https://doi.org/10.48550/arXiv.2512.07154

License

GPL (>= 3)