garman_kohlhagen

module jetblack_options.european.garman_kohlhagen

Summary

Garman and Kohlhagen (1983) Currency options.

Description

The value of a call option.

c = S_{0} e^{- r_{f} T} 𝒩 (d_{1}) - K e^{- r_{d} T} 𝒩 (d_{2})

The value of a put option.

p = K e^{- r_{d} T} 𝒩 (- d_{2}) - S_{0} e^{- r_{f} T} 𝒩 (- d_{1})

where:

d_{1} = \frac{\ln (S_{0} / K) + (r_{d} - r_{f} + σ^{2} / 2) T}{σ \sqrt{T}}

and

d_{2} = d_{1} - σ \sqrt{T}

$S_{0}$ is the current spot rate
$K$ is the strike price
$𝒩 (x)$ is the cumulative normal distribution function
$r_{d}$ is domestic risk free [[simple interest]] rate
$r_{f}$ is foreign risk free simple interest rate
$T$ is the time to maturity (calculated according to the appropriate day count convention)
$σ$ is the volatility of the FX rate.

function jetblack_options.european.garman_kohlhagen.ivol

Summary

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

jetblack_options.european.garman_kohlhagen.ivol(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

rf: float,

p: float,

*,

max_iterations: int, Optional,

epsilon: float, Optional

) -> float

Parameters

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 of the base currency.

rf: float

The risk free rate of the quote currency.

p: float

The option price.

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.european.garman_kohlhagen.make_numeric_greeks

Summary

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

jetblack_options.european.garman_kohlhagen.make_numeric_greeks(

is_call: bool

) -> NumericGreeks

Parameters

is_call: bool

If true the options is a call; otherwise it is a put.

Returns

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

function jetblack_options.european.garman_kohlhagen.price

Summary

Garman and Kohlhagen (1983) Currency options.

jetblack_options.european.garman_kohlhagen.price(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

rf: float,

v: float

) -> float

Parameters

is_call: bool

True for a call, false for a put.

S: float

The asset price.

K: float

The strike price.

T: float

The time to expiry in years.

r: float

The risk free rate of the base currency.

rf: float

The risk free rate of the quote currency.

v: float

The asset volatility.

Returns

float: description