35 lines
854 B
Julia
35 lines
854 B
Julia
###
|
||
# Black-Scholes model functionality for Julia.
|
||
#
|
||
# Designed to be a reference implementation of the Black-Scholes option
|
||
# pricing formula, supporting the original formula and greeks calculation
|
||
###
|
||
using Distributions
|
||
|
||
Φ = x -> cdf(Normal(0, 1), x)
|
||
|
||
"""
|
||
Calculate the value of \$d_1\$ in the Black-Scholes Formula
|
||
"""
|
||
function d1(S, K, σ, r, T, t=0)
|
||
return (log(S./K) + (r + σ.^2/2).*(T-t)) ./ (σ.*sqrt(T-t))
|
||
end
|
||
|
||
function d2(d1_val, σ, T, t=0)
|
||
return d1_val - σ .* sqrt(T-t)
|
||
end
|
||
|
||
function blackscholes_call(S, K, σ, r, T, t=0)
|
||
d1_val = d1(S, K, σ, r, T, t)
|
||
d2_val = d2(d1_val, σ, T, t)
|
||
|
||
return Φ(d1_val) .* S - Φ(d2_val) .* K .* exp(-r .* (T - t))
|
||
end
|
||
|
||
function blackscholes_put(S, K, σ, r, T, t=0)
|
||
d1_val = d1(S, K, σ, r, T, t)
|
||
d2_val = d2(d1_val, σ, T, t)
|
||
|
||
return Φ(-d2_val).*K.*exp(-r.*(T-t)) - Φ(-d1_val).*S
|
||
end
|