trinomial

module jetblack_options.trees.trinomial

Summary

Option valuations using a trinomial tree.

function jetblack_options.trees.trinomial.greeks

Summary

A trinomial tree options pricer returning the price and some greeks.

jetblack_options.trees.trinomial.greeks(

is_european: bool,

is_call: bool,

S: float,

K: float,

T: float,

r: float,

b: float,

v: float,

n: int

) -> Tuple[float, float, float, float]

Parameters

is_european: bool

True for European, false for American.

is_call: bool

True for a call, false for a put.

S: float

The current asset price.

K: float

The option strike price

T: float

The time to maturity of the option in years.

r: float

The risk free rate.

b: float

The cost of carry of the asset.

v: float

The volatility of the asset.

n: int

The number of the steps in the tree.

Returns

Tuple[float, float, float, float]: The price, delta, gamma, theta.

---

function jetblack_options.trees.trinomial.ivol

Summary

Calculate the volatility of an option that is implied by the price.

jetblack_options.trees.trinomial.ivol(

is_european: bool,

is_call: bool,

S: float,

K: float,

T: float,

r: float,

b: float,

p: float,

n: int,

*,

max_iterations: int, Optional,

epsilon: float, Optional

) -> float

Parameters

is_european: bool

True for European, false for American.

is_call: bool

True for a call, false for a put.

S: float

The current asset price.

K: float

The option strike price

T: float

The time to expiry of the option in years.

r: float

The risk free rate.

b: float

The cost of carry of the asset.

p: float

The option price.

n: int

The number of the steps in the tree.

max_iterations: int, Optional

The maximum number of iterations before a price is returned. Defaults to 20.

epsilon: float, Optional (optional)

The largest acceptable error. Defaults to 1e-8.

Returns

float: The implied volatility.

---

function jetblack_options.trees.trinomial.make_numeric_greeks

Summary

Make a class to generate greeks numerically using finite difference methods.

jetblack_options.trees.trinomial.make_numeric_greeks(

is_european: bool,

is_call: bool,

n: int

) -> NumericGreeks

Parameters

is_european: bool

True for European, false for American.

is_call: bool

True for a call, false for a put.

n: int

The number of the steps in the tree.

Returns

NumericGreeks: A class which can generate Greeks using finite difference methods.

---

function jetblack_options.trees.trinomial.price

Summary

Calculate the price of an option using a trinomial tree.

jetblack_options.trees.trinomial.price(

is_european: bool,

is_call: bool,

S: float,

K: float,

T: float,

r: float,

b: float,

v: float,

n: int

) -> Tuple[float, float, float, float]

Parameters

is_european: bool

True for European, false for American.

is_call: bool

True for a call, false for a put.

S: float

The current asset price.

K: float

The option strike price

T: float

The time to maturity of the option in years.

r: float

The risk free rate.

b: float

The cost of carry of the asset.

v: float

The volatility of the asset.

n: int

The number of the steps in the tree.

Returns

Tuple[float, float, float, float]: The price, delta, gamma, theta.

---