price_european: Price European Option with Price Impact

In AsianOption: Asian Option Pricing with Price Impact

Price European Option with Price Impact

Description

Computes the exact price of a European option (call or put) using the Cox-Ross-Rubinstein (CRR) binomial model with price impact from hedging activities.

Usage

price_european(
  S0,
  K,
  r,
  u,
  d,
  lambda,
  v_u,
  v_d,
  n,
  option_type = "call",
  validate = TRUE
)

Arguments

S0	Initial stock price (must be positive)
K	Strike price (must be positive)
r	Gross risk-free rate per period (e.g., 1.05 for 5% rate)
u	Base up factor in CRR model (must be > d)
d	Base down factor in CRR model (must be positive)
lambda	Price impact coefficient (non-negative)
v_u	Hedging volume on up move (non-negative)
v_d	Hedging volume on down move (non-negative)
n	Number of time steps (positive integer)
option_type	Character; either "call" (default) or "put"
validate	Logical; if TRUE, performs input validation

Details

Computes exact prices for European options (call or put) using the binomial model with price impact. Price impact from hedging activities modifies the stock dynamics through adjusted up/down factors and risk-neutral probability.

Unlike path-dependent Asian options, European options only depend on the terminal stock price, allowing for efficient O(n) computation instead of O(2^n). See the package vignettes and reference paper for detailed mathematical formulations.

Value

European option price (numeric)

References

Tiwari, P., & Majumdar, S. (2025). Asian option valuation under price impact. arXiv preprint. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2512.07154")}

See Also

price_geometric_asian, compute_p_adj

Examples

# Call option with no price impact
price_european(
  S0 = 100, K = 100, r = 1.05, u = 1.2, d = 0.8,
  lambda = 0, v_u = 0, v_d = 0, n = 10, option_type = "call"
)

# Put option with price impact
price_european(
  S0 = 100, K = 100, r = 1.05, u = 1.2, d = 0.8,
  lambda = 0.1, v_u = 1, v_d = 1, n = 10, option_type = "put"
)

# Verify put-call parity
call <- price_european(100, 100, 1.05, 1.2, 0.8, 0.1, 1, 1, 10, "call")
put <- price_european(100, 100, 1.05, 1.2, 0.8, 0.1, 1, 1, 10, "put")

AsianOption documentation built on Dec. 23, 2025, 1:08 a.m.