Usage

Usage

To use jax_russell in a project

import jax_russell

For example, this computes the value of an example option given in The Complete Guide to Option Pricing Formulas:

from jax import numpy as jnp
import jax_russell as jr
haug_start_price = jnp.array([100.0])
haug_volatility = jnp.array([0.3])
haug_time_to_expiration = jnp.array([0.5])
haug_is_call = jnp.array([0.0])
haug_strike = jnp.array([95.0])
haug_risk_free_rate = jnp.array([0.08])
haug_cost_of_carry = jnp.array([0.08])
haug_inputs = (
    haug_start_price,
    haug_volatility,
    haug_time_to_expiration,
    haug_risk_free_rate,
    haug_is_call,
    haug_strike,
)
tree = jr.StockOptionCRRTree(5, "american")
print(tree(*haug_inputs))

Run this, and you should see Array([4.9192114], dtype=float32). Try calling tree.first_order(*haug_inputs) to see the example's first-order greeks:

>>> tree.first_order(*haug_inputs)
Array([[ -0.37834674,  26.823406  ,   5.7209864 , -14.537726  ]], dtype=float32)

These values correspond to the order of the inputs, i.e. respectfully delta, vega or kappa, theta and rho. Vega, rho report the change resulting from a full-unit change in volatility, interest rate; divide these by 100 and they'll report the value per 1% change. Likewise, the returned theta value is reported per year. Typically, theta is reported per trading day, so the value given by first_order() will require adjustment to match what you see in trading platforms.

In the example above, five is an impractically small number of steps. As of this writing (Sept. 2023), Interactive Brokers reports implied volatility using a 100-step tree. Because __call__(), first_order() and second_order() are just-in-time compiled, steps values of this magnitude can make for a long first call to these methods. Subsequent calls are speedy.