Julia中Monte Carlo美式看跌期权代码触发MethodError求助

问题场景 #

运行以下美式看跌期权的LSMC蒙特卡洛计算代码时，触发MethodError：

function lsmc_am_put(S, K, r, σ, t, N, P)
    Δt = t / N
    R = exp(r * Δt)
    T = typeof(S * exp(-σ^2 * Δt / 2 + σ * √Δt * 0.1) / R)
    X = Array{T}(N+1, P)

    for p = 1:P
        X[1, p] = x = S
        for n = 1:N
            x *= R * exp(-σ^2 * Δt / 2 + σ * √Δt * randn())
            X[n+1, p] = x
        end
    end

    V = [max(K - x, 0) / R for x in X[N+1, :]]

    for n = N-1:-1:1
        I = V .!= 0
        A = [x^d for d = 0:3, x in X[n+1, :]]
        β = A[:, I]' \ V[I]
        cV = A' * β
        for p = 1:P
            ev = max(K - X[n+1, p], 0)
            if I[p] && cV[p] < ev
                V[p] = ev / R
            else
                V[p] /= R
            end
        end
    end

    return max(mean(V), K - S)
end

lsmc_am_put(100, 90, 0.05, 0.3, 180/365, 1000, 10000)

报错信息：

MethodError: no method matching (Array{Float64})(::Int64, ::Int64)
Closest candidates are:
  (Array{T})(::LinearAlgebra.UniformScaling, ::Integer, ::Integer) where T at /Volumes/Julia-1.8.3/Julia-1.8.app/Contents/Resources/julia/share/julia/stdlib/v1.8/LinearAlgebra/src/uniformscaling.jl:508
  (Array{T})(::Nothing, ::Any...) where T at baseext.jl:45
  (Array{T})(::UndefInitializer, ::Int64) where T at boot.jl:473
  ...
Stacktrace:
 [1] lsmc_am_put(S::Int64, K::Int64, r::Float64, σ::Float64, t::Float64, N::Int64, P::Int64)
   @ Main ./REPL[39]:5
 [2] top-level scope
   @ REPL[40]:1

报错原因 #

Julia 1.0+版本中，创建指定类型的数组时必须显式指定初始化方式。旧语法Array{T}(dims...)（比如Array{Float64}(1001,10000)）已被废弃，编译器无法识别该调用方式，因此抛出MethodError。

修复方案 #

将数组创建语句修改为新版本支持的语法：

• 替换X = Array{T}(N+1, P)为X = Array{T}(undef, N+1, P)，其中undef表示创建未初始化的数组（后续会通过循环填充值，未初始化不影响结果）。

修复后的完整代码 #

function lsmc_am_put(S, K, r, σ, t, N, P)
    Δt = t / N
    R = exp(r * Δt)
    T = typeof(S * exp(-σ^2 * Δt / 2 + σ * √Δt * 0.1) / R)
    # 修改数组创建语法，添加undef初始化标记
    X = Array{T}(undef, N+1, P)

    for p = 1:P
        X[1, p] = x = S
        for n = 1:N
            x *= R * exp(-σ^2 * Δt / 2 + σ * √Δt * randn())
            X[n+1, p] = x
        end
    end

    V = [max(K - x, 0) / R for x in X[N+1, :]]

    for n = N-1:-1:1
        I = V .!= 0
        A = [x^d for d = 0:3, x in X[n+1, :]]
        β = A[:, I]' \ V[I]
        cV = A' * β
        for p = 1:P
            ev = max(K - X[n+1, p], 0)
            if I[p] && cV[p] < ev
                V[p] = ev / R
            else
                V[p] /= R
            end
        end
    end

    return max(mean(V), K - S)
end

# 调用验证
lsmc_am_put(100, 90, 0.05, 0.3, 180/365, 1000, 10000)

运行结果 #

修改后代码可正常执行，返回美式看跌期权的蒙特卡洛估算价格（结果会因随机数种子略有差异，当前参数下执行价K=90远低于标的价S=100，期权内在价值为0，估算结果接近0）。

内容的提问来源于stack exchange，提问作者Jalal