add Symbolics, coverage

src/financial_symbolics.jl

@@ -6,47 +6,30 @@ end
 
 @register_symbolic blimpv(S0, K, T, Price, FlagIsCall::Bool, xtol::Float64, n_iter_max::Int64)
 
-function blvega_impl_registered(S0, K, T, σ)
-    return blvega_impl(S0, K, T, σ)
-end
-
-function Symbolics.derivative(::typeof(blvega_impl_registered), ::NTuple{4, Any}, ::Any)
-    return 0
-end
 function finalize_derivative_fwd(S0, K, T, σ, der_fwd)
-    vega = blvega_impl_registered(S0, K, T, σ)
+    vega = blvega_impl(S0, K, T, σ)
     return der_fwd / vega
 end
-# function finalize_derivative_fwd(vega, price_diff, target_var, original_var)
-#     der_fwd = Symbolics.derivative(price_diff, target_var)
-#     der_fwd = substitute(der_fwd, Dict(target_var => original_var))
-#     return der_fwd / vega
-# end
-function bldelta(S0, K, T, σ, FlagIsCall)
-    sigma_sqrtT = σ * sqrt(T)
-    S0_K = S0 / K
-    d1 = log(S0_K) / sigma_sqrtT + sigma_sqrtT / FinancialToolbox.two_internal
-    iscall = ifelse(FlagIsCall, FinancialToolbox.one_internal, FinancialToolbox.minus_one_internal)
-    Δ = normcdf(iscall * d1) * iscall
-    return Δ
-end
+
 #TODO: implement derivatives
 function Symbolics.derivative(::typeof(blimpv), args::NTuple{7, Any}, ::Val{1})
     S0, K, T, price_d, FlagIsCall, xtol, n_iter_max = args
     σ = blimpv(S0, K, T, price_d, FlagIsCall, xtol, n_iter_max)
     @variables new_S0
+    D_S0 = Differential(new_S0)
     price_diff = -blprice_impl(new_S0, K, T, σ, FlagIsCall)
-    der_fwd = Symbolics.derivative(price_diff, new_S0)
+    der_fwd = expand_derivatives(D_S0(price_diff))
     der_fwd = substitute(der_fwd, Dict(new_S0 => S0))
-    #der_fwd = bldelta(S0, K, r, T, σ, d, FlagIsCall)
+    # der_fwd = -bldelta(S0, K, T, σ, FlagIsCall)
     return finalize_derivative_fwd(S0, K, T, σ, der_fwd)
 end
 function Symbolics.derivative(::typeof(blimpv), args::NTuple{7, Any}, ::Val{2})
     S0, K, T, price_d, FlagIsCall, xtol, n_iter_max = args
     σ = blimpv(S0, K, T, price_d, FlagIsCall, xtol, n_iter_max)
     @variables new_K
+    D_K = Differential(new_K)
     price_diff = -blprice_impl(S0, new_K, T, σ, FlagIsCall)
-    der_fwd = Symbolics.derivative(price_diff, new_K)
+    der_fwd = expand_derivatives(D_K(price_diff))
     der_fwd = substitute(der_fwd, Dict(new_K => K))
     #der_fwd = bldelta(S0, K, r, T, σ, d, FlagIsCall)
     return finalize_derivative_fwd(S0, K, T, σ, der_fwd)
@@ -55,18 +38,20 @@ function Symbolics.derivative(::typeof(blimpv), args::NTuple{7, Any}, ::Val{3})
     S0, K, T, price_d, FlagIsCall, xtol, n_iter_max = args
     σ = blimpv(S0, K, T, price_d, FlagIsCall, xtol, n_iter_max)
     @variables new_T
+    D_T = Differential(new_T)
     price_diff = -blprice_impl(S0, K, new_T, σ, FlagIsCall)
-    der_fwd = Symbolics.derivative(price_diff, new_T)
+    der_fwd = expand_derivatives(D_T(price_diff))
     der_fwd = substitute(der_fwd, Dict(new_T => T))
     #der_fwd = bldelta(S0, K, r, T, σ, d, FlagIsCall)
     return finalize_derivative_fwd(S0, K, T, σ, der_fwd)
 end
 function Symbolics.derivative(::typeof(blimpv), args::NTuple{7, Any}, ::Val{4})
     S0, K, T, price_d, FlagIsCall, xtol, n_iter_max = args
     σ = blimpv(S0, K, T, price_d, FlagIsCall, xtol, n_iter_max)
-    vega = blvega_impl_registered(S0, K, T, σ)
+    vega = blvega_impl(S0, K, T, σ)
     return inv(vega)
 end
+
 function Symbolics.derivative(::typeof(blimpv), ::NTuple{7, Any}, ::Any)
     return 0
 end

test/testSymbolics.jl

@@ -24,11 +24,10 @@ using HyperDualNumbers
 #S0
 der_vol_S0 = Symbolics.derivative(vol_s, S0_s, simplify = true);
 der_vol_S02 = Symbolics.derivative(der_vol_S0, S0_s, simplify = true);
-vol_h_S0 = blsimpv(hyper(S0, 1.0, 1.0, 0.0), K, r, T, price, d)
+@show vol_h_S0 = blsimpv(hyper(S0, 1.0, 1.0, 0.0), K, r, T, price, d)
 delta = substitute(der_vol_S0, dict_vals)
-gamma = substitute(der_vol_S02, dict_vals)
+@show gamma = substitute(der_vol_S02, dict_vals)
 @test abs(delta - vol_h_S0.epsilon1) < toll
-@test abs(gamma - vol_h_S0.epsilon12) < toll
 
 #K
 der_vol_K = Symbolics.derivative(vol_s, K_s, simplify = true);
@@ -37,20 +36,35 @@ vol_h_K = blsimpv(S0, hyper(K, 1.0, 1.0, 0.0), r, T, price, d)
 delta_k = substitute(der_vol_K, dict_vals)
 gamma_k = substitute(der_vol_K2, dict_vals)
 @test abs(delta_k - vol_h_K.epsilon1) < toll
-@test abs(gamma_k - vol_h_K.epsilon12) < toll
 #r
 der_vol_r = Symbolics.derivative(vol_s, r_s, simplify = true);
 der_vol_r2 = Symbolics.derivative(der_vol_r, r_s, simplify = true);
 vol_h_r = blsimpv(S0, K, hyper(r, 1.0, 1.0, 0.0), T, price, d)
 delta_r = substitute(der_vol_r, dict_vals)
 gamma_r = substitute(der_vol_r2, dict_vals)
 @test abs(delta_r - vol_h_r.epsilon1) < toll
-@test abs(gamma_r - vol_h_r.epsilon12) < toll
 #T
 der_vol_T = Symbolics.derivative(vol_s, T_s, simplify = true);
 der_vol_T2 = Symbolics.derivative(der_vol_T, T_s, simplify = true);
 vol_h_T = blsimpv(S0, K, r, hyper(T, 1.0, 1.0, 0.0), price, d)
 delta_T = substitute(der_vol_T, dict_vals)
 gamma_T = substitute(der_vol_T2, dict_vals)
 @test abs(delta_T - vol_h_T.epsilon1) < toll
+
+#Mixed derivative r,T
+der_vol_T = Symbolics.derivative(vol_s, T_s, simplify = true);
+der_vol_T_r_s = Symbolics.derivative(der_vol_T, r_s, simplify = true);
+vol_h_T = blsimpv(S0, K, hyper(r, 0.0, 1.0, 0.0), hyper(T, 1.0, 0.0, 0.0), price, d)
+delta_T = substitute(der_vol_T, dict_vals)
+gamma_T = substitute(der_vol_T_r_s, dict_vals)
+@test abs(delta_T - vol_h_T.epsilon1) < toll
+
+println("Test First Order Passed")
+
+@test abs(gamma - vol_h_S0.epsilon12) < toll
+@test abs(gamma_k - vol_h_K.epsilon12) < toll
+@test abs(gamma_r - vol_h_r.epsilon12) < toll
+@test abs(gamma_T - vol_h_T.epsilon12) < toll
 @test abs(gamma_T - vol_h_T.epsilon12) < toll
+
+println("Test Second Order Passed")