American Option

torchquantlib.core.asset_pricing.option.american_option.american_option(option_type: str, spot: Tensor, strike: Tensor, expiry: Tensor, volatility: Tensor, rate: Tensor, steps: int) → Tensor[source]

Price an American option using the binomial tree model.

This function implements the Cox-Ross-Rubinstein binomial tree model to price American call or put options, which can be exercised at any time up to expiration.

Parameters:

  • option_type (str) – Type of option - either ‘call’ or ‘put’.

  • spot (Tensor) – Current price of the underlying asset.

  • strike (Tensor) – Strike price of the option.

  • expiry (Tensor) – Time to expiration in years.

  • volatility (Tensor) – Volatility of the underlying asset.

  • rate (Tensor) – Risk-free interest rate (annualized).

  • steps (int) – Number of time steps in the binomial tree.

Returns:

The price of the American option.

Return type:

Tensor

Note

This implementation uses a backward induction approach to account for the possibility of early exercise at each node of the tree.

Overview

The American Option module provides functionality for pricing and analyzing American-style options using various numerical methods. American options can be exercised at any time up to the expiration date, making them more complex to value than European options.

Key Features

  • Pricing of American call and put options

  • Support for various underlying assets (e.g., stocks, indices)

  • Implementation of multiple pricing methods (e.g., binomial tree, finite difference)

  • Greeks calculation for risk management

Classes

AmericanOption

Functions

Examples

Here’s a basic example of how to use the AmericanOption class:

from torchquantlib.core.asset_pricing.option.american_option import AmericanOption

# Create an American call option
option = AmericanOption(
    underlying=100,
    strike=95,
    expiry=1.0,
    rf_rate=0.05,
    volatility=0.2,
    option_type='call'
)

# Price the option using the binomial tree method
price = option.price(method='binomial', steps=1000)
print(f"American call option price: {price:.4f}")

# Calculate option Greeks
delta = option.delta()
gamma = option.gamma()
theta = option.theta()
vega = option.vega()
rho = option.rho()

print(f"Delta: {delta:.4f}")
print(f"Gamma: {gamma:.4f}")
print(f"Theta: {theta:.4f}")
print(f"Vega: {vega:.4f}")
print(f"Rho: {rho:.4f}")