Add analytical solutions, fast mean and variance calculations

.github/workflows/FormatCheck.yml

@@ -14,6 +14,9 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v6
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: '1'
       - uses: fredrikekre/runic-action@v1
         with:
           version: '1'

docs/pages.jl

@@ -1,3 +1,3 @@
 # Put in a separate page so it can be used by SciMLDocs.jl
 
-pages = ["Home" => "index.md", "diffeqfinancial.md"]
+pages = ["Home" => "index.md", "Analytical Solutions" => "analytics.md", "API Reference" => "diffeqfinancial.md"]

docs/src/analytics.md

@@ -0,0 +1,62 @@
+# Analytical Solutions
+
+DiffEqFinancial.jl provides analytical (closed-form) solutions for the mean,
+variance, and standard deviation of the supported financial stochastic processes.
+These functions provide exact results without requiring Monte Carlo simulation,
+offering significant performance and accuracy benefits.
+
+## Geometric Brownian Motion
+
+The GBM process: ``dX = \mu X \, dt + \sigma X \, dW_t``
+
+```@docs
+gbm_mean
+gbm_variance
+gbm_std
+```
+
+## Ornstein-Uhlenbeck Process
+
+The OU process: ``dX = a(r - X) \, dt + \sigma \, dW_t``
+
+```@docs
+ou_mean
+ou_variance
+ou_std
+ou_stationary_mean
+ou_stationary_variance
+```
+
+## Cox-Ingersoll-Ross (CIR) Process
+
+The CIR process: ``dr = \kappa(\theta - r) \, dt + \sigma \sqrt{r} \, dW_t``
+
+```@docs
+cir_mean
+cir_variance
+cir_std
+cir_stationary_mean
+cir_stationary_variance
+```
+
+## Black-Scholes Log-Price
+
+The log-price process: ``d \ln S = (r - \sigma^2/2) \, dt + \sigma \, dW_t``
+
+```@docs
+bs_log_mean
+bs_log_variance
+bs_log_std
+```
+
+## Heston Model
+
+The Heston stochastic volatility model:
+``dS = \mu S \, dt + \sqrt{v} S \, dW_1``,
+``dv = \kappa(\Theta - v) \, dt + \sigma \sqrt{v} \, dW_2``
+
+```@docs
+heston_mean
+heston_variance_mean
+heston_variance_variance
+```

src/DiffEqFinancial.jl

@@ -8,6 +8,7 @@ using Markdown: @doc_str
 import RandomNumbers: Xorshifts
 
 include("problems.jl")
+include("analytics.jl")
 
 export HestonProblem, BlackScholesProblem, GeneralizedBlackScholesProblem,
     ExtendedOrnsteinUhlenbeckProblem, OrnsteinUhlenbeckProblem,
@@ -16,4 +17,11 @@ export HestonProblem, BlackScholesProblem, GeneralizedBlackScholesProblem,
     CIRProblem,
     CIRNoise
 
+# Analytical solutions and moment functions
+export gbm_mean, gbm_variance, gbm_std,
+    ou_mean, ou_variance, ou_std, ou_stationary_mean, ou_stationary_variance,
+    cir_mean, cir_variance, cir_std, cir_stationary_mean, cir_stationary_variance,
+    bs_log_mean, bs_log_variance, bs_log_std,
+    heston_mean, heston_variance_mean, heston_variance_variance
+
 end # module