Stability in the Bansal Yaron (and BKY) Model



In [13]:

    
include("src/utilities.jl")
include("src/bansal_yaron_discretized.jl")









    



WARNING: replacing docs for 'EpsteinZin :: Union{}' in module 'Main'.
WARNING: replacing docs for 'EpsteinZin :: Tuple{Any,Any,Any}' in module 'Main'.
WARNING: replacing docs for 'EpsteinZinBY :: Tuple{}' in module 'Main'.
WARNING: replacing docs for 'EpsteinZinBKY :: Tuple{}' in module 'Main'.
WARNING: replacing docs for 'EpsteinZinSSY :: Tuple{}' in module 'Main'.
WARNING: replacing docs for 'StochasticVolatility :: Union{}' in module 'Main'.
WARNING: replacing docs for 'StochasticVolatilityBY :: Tuple{}' in module 'Main'.
WARNING: replacing docs for 'StochasticVolatilityBKY :: Tuple{}' in module 'Main'.
WARNING: replacing docs for 'multi_from_single :: Tuple{Any,Any}' in module 'Main'.
WARNING: replacing docs for 'discretize_sv :: Tuple{StochasticVolatility,Integer,Integer}' in module 'Main'.
WARNING: replacing docs for 'compute_fp_bansal_yaron :: Tuple{EpsteinZin,StochasticVolatility}' in module 'Main'.






    Out[13]:





compute_fp_bansal_yaron

Default parameter values:



In [14]:

    
ez_by = EpsteinZinBY()
sv_by = StochasticVolatilityBY()









    Out[14]:





StochasticVolatility{Float64}(0.979, 0.044, 0.987, 7.9092e-7, 2.3e-6)



In [15]:

    
K = compute_K_bansal_yaron(ez_by, sv_by);



In [16]:

    
compute_spec_rad(K)









    Out[16]:




1.0553238060529466

Spectral Radius Plot, Bansal--Yaron Parameters



In [17]:

    
using PyPlot
plt = PyPlot









    Out[17]:





PyPlot



In [18]:

    
J = 20 # grid size
R = Array{Float64}(J, J);



In [19]:

    
x_vals = linspace(1.25, 2.25, J)          # ψ
y_vals = linspace(0.0005, 0.01, J)        # μ









    Out[19]:





0.0005:0.0005:0.01



In [20]:

    
for (i, x) in enumerate(x_vals)
    for (j, y) in enumerate(y_vals)
        ez = EpsteinZinBY(ψ=x)
        @assert ez.θ < 0 "Detected non-negative theta value"
        K = compute_K_bansal_yaron(ez, sv_by, μ=y)
        R[i, j] = compute_spec_rad(K)
    end
end



In [21]:

    
fig, ax = plt.subplots(figsize=(10, 5.7))

#lvs = [0.0, 0.8, 1.0, 1.4, 1.8, 2.2, 4.4]
#cls = [cm.jet(i) for i in np.linspace(0.4, 1, len(lvs))]

cs1 = ax[:contourf](x_vals, 
                    y_vals, 
                    R',
                    alpha=0.6)
                    #levels=lvs,


ctr1 = ax[:contour](x_vals, 
                    y_vals, 
                    R', 
                    levels=[1.0])

plt.clabel(ctr1, inline=1, fontsize=13)
plt.colorbar(cs1, ax=ax)

ax[:set_title]("Spectral radius")
ax[:set_xlabel]("ψ", fontsize=16)
ax[:set_ylabel]("μ", fontsize=16)


ax[:annotate]("Bansal-Yaron", 
         xy=(1.5 + 0.024, 0.0015 - 0.0001),  
         xycoords="data",
         xytext=(5, 40),
         textcoords="offset points",
         fontsize=12,
         arrowprops=Dict("arrowstyle" => "->"))

ax[:plot]([1.5], [0.0015],  "ko", alpha=0.6)

plt.savefig("by.pdf")
plt.show()

Spectral Radius Plot with BKY Parameters



In [22]:

    
ez_bky = EpsteinZinBKY()
sv_bky = StochasticVolatilityBKY()









    Out[22]:





StochasticVolatility{Float64}(0.975, 0.038, 0.999, 5.184e-8, 2.8e-6)



In [23]:

    
for (i, x) in enumerate(x_vals)
    for (j, y) in enumerate(y_vals)
        ez = EpsteinZinBY(ψ=x)
        @assert ez.θ < 0 "Detected non-negative theta value"
        K = compute_K_bansal_yaron(ez, sv_bky, μ=y)
        R[i, j] = compute_spec_rad(K)
    end
end



In [24]:

    
fig, ax = plt.subplots(figsize=(10, 5.7))

#lvs = [0.0, 0.8, 1.0, 1.4, 1.8, 2.2, 4.4]
#cls = [cm.jet(i) for i in np.linspace(0.4, 1, len(lvs))]

cs1 = ax[:contourf](x_vals, 
                    y_vals, 
                    R',
                    alpha=0.6)
                    #levels=lvs,


ctr1 = ax[:contour](x_vals, 
                    y_vals, 
                    R', 
                    levels=[1.0])

plt.clabel(ctr1, inline=1, fontsize=13)
plt.colorbar(cs1, ax=ax)

ax[:set_title]("Spectral radius")
ax[:set_xlabel]("ψ", fontsize=16)
ax[:set_ylabel]("μ", fontsize=16)


ax[:annotate]("Bansal-Kiku-Yaron", 
         xy=(1.5 + 0.024, 0.0015 - 0.0001),  
         xycoords="data",
         xytext=(5, 40),
         textcoords="offset points",
         fontsize=12,
         arrowprops=Dict("arrowstyle" => "->"))

ax[:plot]([1.5], [0.0015],  "ko", alpha=0.6)

plt.savefig("bky.pdf")
plt.show()



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