AsianOption-package: AsianOption: Asian Option Pricing with Price Impact

In AsianOption: Asian Option Pricing with Price Impact

AsianOption: Asian Option Pricing with Price Impact

Description

Implements binomial tree pricing for geometric and arithmetic Asian options incorporating market price impact from hedging activities. Uses the Cox-Ross-Rubinstein (CRR) model with the replicating portfolio method.

Main Functions

• price_geometric_asian: Exact pricing for geometric Asian calls

• arithmetic_asian_bounds: Bounds for arithmetic Asian calls

• compute_p_adj: Compute adjusted risk-neutral probability

• compute_adjusted_factors: Compute modified up/down factors

• check_no_arbitrage: Validate no-arbitrage condition

Price Impact Mechanism

When market makers hedge options, their trading volume causes price movements following the Kyle (1985) linear impact model. This modifies the binomial tree dynamics through adjusted up/down factors and risk-neutral probability.

Mathematical Framework

The package uses the replicating portfolio approach where the option value equals the cost of constructing a portfolio that replicates its payoff, leading to risk-neutral pricing.

For geometric Asian options, the geometric average of stock prices is used. For arithmetic Asian options, rigorous upper and lower bounds are computed using Jensen's inequality. A tighter path-specific bound is available via exact path enumeration.

No-Arbitrage Condition

For valid pricing, the model requires that the adjusted down factor is less than the risk-free rate, which is less than the adjusted up factor. This ensures a valid risk-neutral probability. All pricing functions validate this condition automatically.

For detailed mathematical formulations, see the package vignettes and the reference paper.

Computational Complexity

The implementation enumerates all 2^n possible price paths:

• n \leq 15: Fast (< 1 second)

• n = 20: ~1 million paths (~10 seconds)

• n > 20: Warning issued automatically

Author(s)

Maintainer: Priyanshu Tiwari [e-mail] (ORCID)

Other contributors:

• Sourav Majumdar [e-mail] [contributor]

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

Useful links:

• https://github.com/plato-12/AsianOption

• Report bugs at https://github.com/plato-12/AsianOption/issues

Examples

# Price geometric Asian option with price impact
price_geometric_asian(
  S0 = 100, K = 100, r = 1.05,
  u = 1.2, d = 0.8,
  lambda = 0.1, v_u = 1, v_d = 1,
  n = 3
)

# Compute bounds for arithmetic Asian option
bounds <- arithmetic_asian_bounds(
  S0 = 100, K = 100, r = 1.05,
  u = 1.2, d = 0.8,
  lambda = 0.1, v_u = 1, v_d = 1,
  n = 3
)
print(bounds)

# Check no-arbitrage condition
check_no_arbitrage(r = 1.05, u = 1.2, d = 0.8,
                   lambda = 0.1, v_u = 1, v_d = 1)

# Compute adjusted factors
factors <- compute_adjusted_factors(u = 1.2, d = 0.8,
                                    lambda = 0.1, v_u = 1, v_d = 1)
print(factors)

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