diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index cebdde8..f86785d 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -5,6 +5,8 @@ add_library(qengine
         main.cpp
         calibration/Stats.cpp
         calibration/Stats.hpp
+        models/Model.cpp
+        models/Model.hpp
 )
 
 target_include_directories(qengine PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
diff --git a/src/calibration/Stats.cpp b/src/calibration/Stats.cpp
index 1c10315..6d1d0fd 100644
--- a/src/calibration/Stats.cpp
+++ b/src/calibration/Stats.cpp
@@ -6,18 +6,25 @@
 #include <cmath>
 
 void Stats::update(double x) {
-    // update the mean according to the formula
-    // \hat{a}_n \cdot \frac{n}{n+1} + \frac{a_{n+1}}{n+1}
-    double n_ratio = n_ / ++n_ ;
-    mean_ = n_ratio * mean_ + x/n_;
-    // update the second moment
-    M2 = n_ratio * M2 + x * x / n_;
-    // update the
+    running_sum_ += x;
+    running_square_sum_ += x * x;
+    n_++;
 
 }
 
+double Stats::mean() const {
+    return running_sum_ / n_;
+}
+
+double Stats::square_mean() const {
+    return running_square_sum_ / n_;
+}
+
 double Stats::variance() const {
-    return M2 - mean_ * mean_;
+    double mean = this->mean();
+    double square_mean = this->square_mean();
+    return square_mean * square_mean - mean * mean;
+
 }
 
 double Stats::std_error() const {
@@ -25,5 +32,5 @@ double Stats::std_error() const {
 }
 
 std::pair<double, double> Stats::CI() const {
-    return std::make_pair(mean_ - 1.96 * std_error(), mean_ + 1.96 * std_error());
+    return std::make_pair(running_sum_ - 1.96 * std_error(), running_sum_ + 1.96 * std_error());
 }
diff --git a/src/calibration/Stats.hpp b/src/calibration/Stats.hpp
index 8e62d86..e5917dc 100644
--- a/src/calibration/Stats.hpp
+++ b/src/calibration/Stats.hpp
@@ -10,12 +10,14 @@
 class Stats {
 private:
     size_t n_ = 0;
-    double mean_ = 0.0;
-    double M2 = 0.0;
+    double running_sum_ = 0.0;
+    double running_square_sum_ = 0.0;
 
 public:
     Stats() = delete;
     void update(double x);
+    double mean() const;
+    double square_mean() const;
     double variance() const;
     double std_error() const;
     std::pair<double, double> CI() const; // alpha = 5%
diff --git a/src/models/Model.cpp b/src/models/Model.cpp
new file mode 100644
index 0000000..22bc73d
--- /dev/null
+++ b/src/models/Model.cpp
@@ -0,0 +1,5 @@
+//
+// Created by David Doebel  on 05.03.2026.
+//
+
+#include "Model.hpp"
\ No newline at end of file
diff --git a/src/models/Model.hpp b/src/models/Model.hpp
new file mode 100644
index 0000000..119c4e1
--- /dev/null
+++ b/src/models/Model.hpp
@@ -0,0 +1,18 @@
+//
+// Created by David Doebel  on 05.03.2026.
+//
+
+#ifndef QUANTENGINE_MODEL_HPP
+#define QUANTENGINE_MODEL_HPP
+
+
+class Model {
+public:
+    Model() = default;
+    virtual ~Model() = 0;
+    [[nodiscard]] virtual double terminal_price(double Z) const = 0;
+    [[nodiscard]] virtual double discount() const = 0;
+};
+
+
+#endif //QUANTENGINE_MODEL_HPP
\ No newline at end of file
diff --git a/src/models/black_scholes.hpp b/src/models/black_scholes.hpp
index e207d04..0c86c2d 100644
--- a/src/models/black_scholes.hpp
+++ b/src/models/black_scholes.hpp
@@ -6,20 +6,22 @@
 #define OPTION_PRICING_BLACK_SCHOLES_HPP
 
 #include <cmath>
+#include "Model.hpp"
 
-class BlackScholes {
+class BlackScholes : public Model{
 public:
     BlackScholes(double S0, double r, double sigma, double T)
-        : S0_(S0), r_(r), sigma_(sigma), T_(T) {}
+        : Model(), S0_(S0), r_(r), sigma_(sigma), T_(T) {
+    }
 
-    double terminal_price(double Z) const {
+    [[nodiscard]] double terminal_price(double Z) const override{
         return S0_ * std::exp(
             (r_ - 0.5 * sigma_ * sigma_) * T_
             + sigma_ * std::sqrt(T_) * Z
         );
     }
 
-    double discount() const {
+    [[nodiscard]] double discount() const override{
         return std::exp(-r_ * T_);
     }