/BS.jl

Black-Scholes Option Pricing Formulae

Primary LanguageJuliaMIT LicenseMIT

BS.jl

License travis codecov

Black-Scholes Option Pricing Formulae.

Model Parameters

  • s : current underlying asset price.

  • k : strike price.

  • t : time to expiry.

  • r : continuously compounded risk-free rate.

  • σ : underlying price volatility, as defined in the underlying price dynamics.

Underlying Asset Price Dynamics

The Black-Scholes model assumes that s follows a Geometric Brownian Motion in the real world.

ds = μ * s * dt + σ * S * dz

The pricing uses the risk-neutral measure. In this case, μ equals the risk-free rate r.

Examples

import BS
using Test

s = 42
k = 40
r = 0.1
sigma = 0.2
t = 0.5

@test BS.price(BS.EuropeanCall(), s, k, t, r, sigma) ≈ 4.759422392871542
@test BS.price(BS.EuropeanPut(), s, k, t, r, sigma) ≈ 0.8085993729000975
@test BS.delta(BS.EuropeanCall(), s, k, t, r, sigma) ≈ 0.7791312909426691
@test BS.delta(BS.EuropeanPut(), s, k, t, r, sigma) ≈ -0.22086870905733091
@test BS.theta(BS.EuropeanCall(), s, k, t, r, sigma) ≈ -4.559092194592626
@test BS.theta(BS.EuropeanPut(), s, k, t, r, sigma) ≈ -0.7541744965897705
@test BS.gamma(BS.EuropeanCall(), s, k, t, r, sigma) ≈ 0.04996267040591185
@test BS.gamma(BS.EuropeanPut(), s, k, t, r, sigma) ≈ 0.04996267040591185
@test BS.vega(BS.EuropeanCall(), s, k, t, r, sigma) ≈ 8.813415059602853
@test BS.vega(BS.EuropeanPut(), s, k, t, r, sigma) ≈ 8.813415059602853
@test BS.rho(BS.EuropeanCall(), s, k, t, r, sigma) ≈ 13.982045913360281
@test BS.rho(BS.EuropeanPut(), s, k, t, r, sigma) ≈ -5.042542576653999
@test BS.impvol(BS.EuropeanCall(), 4.12, s, k, t, r) ≈ 0.1135753892186858
@test BS.impvol(BS.EuropeanPut(), 4.12, s, k, t, r) ≈ 0.5246966268060681

Development status

This repo is a sketch only and not intended for new developments. No PRs will be accepted. Feel free to copy the source code for your project.