black_scholes_73

module jetblack_options.european.black_scholes_73

Summary

Black-Scholes 1973.

Description

The original Black-Scholes option formula for an option on a non-dividend paying stock option.

$$d_1=\frac{1}{\sigma \sqrt{T-t}}[\ln \left(\frac{S_t}{K}\right)+(r+\frac{{\sigma }^2}{2})(T-t)]$$ $$d_2=d_1-\sigma \sqrt{T-t}$$

function jetblack_options.european.black_scholes_73.charm

jetblack_options.european.black_scholes_73.charm(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

is_call: bool

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.delta

jetblack_options.european.black_scholes_73.delta(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

is_call: bool

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.gamma

Summary

Calculates option gamma

jetblack_options.european.black_scholes_73.gamma(

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.ivol

Summary

Calculate the volatility of a Black-Scholes 73 option that is implied by

Description

the price.

jetblack_options.european.black_scholes_73.ivol(

is_call: bool,

S: float,

K: float,

T: float,

r: 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 maturity of the option in years.

r: float

The risk free rate.

p: float

The option price.

max_iterations: int, Optional

The maximum number of iterations before a price is returned. Defaults to 35.

epsilon: float, Optional (optional)

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

Returns

float: The implied volatility.

---

function jetblack_options.european.black_scholes_73.make_numeric_greeks

Summary

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

jetblack_options.european.black_scholes_73.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.black_scholes_73.price

Summary

Black-Scholes for a non-dividend paying stock.

Description

C(St,t)=N(d1)St−N(d2)Ke−r(T−t)

jetblack_options.european.black_scholes_73.price(

is_call: bool,

S: float,

K: float,

T: float,

r: 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.

v: float

The asset volatility.

Returns

float: The price of the option.

---

function jetblack_options.european.black_scholes_73.rho

jetblack_options.european.black_scholes_73.rho(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

is_call: bool

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.theta

Summary

Calculates option theta

jetblack_options.european.black_scholes_73.theta(

is_call: bool,

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

is_call: bool

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.vanna

jetblack_options.european.black_scholes_73.vanna(

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.vega

jetblack_options.european.black_scholes_73.vega(

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

S: float

K: float

T: float

r: float

v: float

Returns

float:

---

function jetblack_options.european.black_scholes_73.vomma

jetblack_options.european.black_scholes_73.vomma(

S: float,

K: float,

T: float,

r: float,

v: float

) -> float

Parameters

S: float

K: float

T: float

r: float

v: float

Returns

float:

---