55 lines
1.3 KiB
Julia
55 lines
1.3 KiB
Julia
###
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# Black-Scholes model functionality for Julia.
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#
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# Designed to be a reference implementation of the Black-Scholes option
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# pricing formula, supporting the original formula and greeks calculation
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###
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using Distributions
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Φ = x -> cdf(Normal(0, 1), x)
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type BlackScholes
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S0::Float64
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K::Float64
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σ::Float64
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r::Float64
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q::Float64
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t::Float64
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T::Float64
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end
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"""
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Calculate the value of \$d_1\$ in the Black-Scholes Formula
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"""
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function d1(S, K, σ, r, q, T, t=0)
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return (log(S./K) + (r - q + σ.^2/2).*(T-t)) ./ (σ.*sqrt(T-t))
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end
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function d2(d1_val, σ, T, t=0)
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return d1_val - σ .* sqrt(T-t)
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end
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function blackscholes_call(S, K, σ, r, q, T, t=0)
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d1_val = d1(S, K, σ, r, q, T, t)
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d2_val = d2(d1_val, σ, T, t)
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return Φ(d1_val) .* S - Φ(d2_val) .* K .* exp(-(r-q) .* (T - t))
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end
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function blackscholes_call(model::BlackScholes)
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return blackscholes_call(model.S0, model.K, model.σ, model.r, model.q,
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model.T, model.t)
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end
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function blackscholes_put(S, K, σ, r, q, T, t=0)
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d1_val = d1(S, K, σ, r, q, T, t)
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d2_val = d2(d1_val, σ, T, t)
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return Φ(-d2_val).*K.*exp(-(r-q).*(T-t)) - Φ(-d1_val).*S
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end
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function blackscholes_put(model::BlackScholes)
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return blackscholes_put(model.S0, model.K, model.σ, model.r, model.q,
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model.T, model.t)
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end
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