Bermudan Option

Bermudan Option Pricing Module This module provides functionality for pricing Bermudan options using a binomial tree model.

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

Price a Bermudan option using a binomial tree model.

This function implements a binomial tree approach to price Bermudan options, which are options that can be exercised on specific dates before 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.

  • exercise_dates (Tensor) – Tensor of indices representing the steps at which the option can be exercised.

Returns:

The price of the Bermudan option.

Return type:

Tensor

Note

This implementation combines features of European and American options. It allows for early exercise, but only on specified dates.

Overview

The Bermudan Option module provides functionality for pricing Bermudan-style options using a binomial tree model. Bermudan options are a type of exotic option that can be exercised on specific dates before expiration, combining features of both American and European options.

Key Features

  • Pricing of Bermudan call and put options

  • Implementation using a binomial tree model

  • Support for multiple exercise dates

Functions

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

Price a Bermudan option using a binomial tree model.

This function implements a binomial tree approach to price Bermudan options, which are options that can be exercised on specific dates before 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.

  • exercise_dates (Tensor) – Tensor of indices representing the steps at which the option can be exercised.

Returns:

The price of the Bermudan option.

Return type:

Tensor

Note

This implementation combines features of European and American options. It allows for early exercise, but only on specified dates.

Price a Bermudan option using a binomial tree model.

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

  • exercise_dates (Tensor) – Tensor of indices representing the steps at which the option can be exercised

Returns:

The price of the Bermudan option

Return type:

Tensor

Examples

Here’s a basic example of how to use the bermudan_option function:

import torch
from torchquantlib.core.asset_pricing.option.bermudan_option import bermudan_option

# Set option parameters
option_type = 'call'
spot = torch.tensor(100.0)
strike = torch.tensor(95.0)
expiry = torch.tensor(1.0)
volatility = torch.tensor(0.2)
rate = torch.tensor(0.05)
steps = 100
exercise_dates = torch.tensor([25, 50, 75])  # Exercise allowed at 1/4, 1/2, and 3/4 of the option's life

# Price the Bermudan option
price = bermudan_option(option_type, spot, strike, expiry, volatility, rate, steps, exercise_dates)
print(f"Bermudan {option_type} option price: {price:.4f}")