diff --git a/DESCRIPTION b/DESCRIPTION
index 9f9ea6c..d84bca0 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: greeks
 Title: Sensitivities of Prices of Financial Options and Implied Volatilities
-Version: 1.3.3
+Version: 1.3.4
 Authors@R: 
     person(given = "Anselm",
            family = "Hudde",
diff --git a/src/Binomial_American_Greeks.cpp b/src/Binomial_American_Greeks.cpp
index 7bb66df..83f6c59 100644
--- a/src/Binomial_American_Greeks.cpp
+++ b/src/Binomial_American_Greeks.cpp
@@ -7,12 +7,12 @@ using std::string;
 using std::max;
 
 
-double american_call(double x, double price, double exercise_price) {
-  return max(x, price - exercise_price);
+double american_call(double price, double exercise_price) {
+  return max(0.0, price - exercise_price);
 }
 
-double american_put(double x, double price, double exercise_price) {
-  return max(x, exercise_price - price);
+double american_put(double price, double exercise_price) {
+  return max(0.0, exercise_price - price);
 }
 
 // [[Rcpp::export]]
@@ -26,7 +26,7 @@ NumericVector Binomial_American_Greeks_cpp(double initial_price = 100,
                                            const int steps = 1000) {
 
   // payoff_function
-  double (*payoff_function)(double x, double price, double exercise_price);
+  double (*payoff_function)(double price, double exercise_price);
 
   // iterators
   int i;
@@ -42,7 +42,7 @@ NumericVector Binomial_American_Greeks_cpp(double initial_price = 100,
   const double down = exp(-volatility * sqrt(dt));
   const double p = (exp((r-dividend_yield)*dt) - down)/(up-down);
   const double q = (1 - p);
-  const double exp_min_r_dt = exp(-r*dt);
+  const double exp_min_r_steps_dt = exp(-r*steps*dt);
 
   // generate the price vector
   NumericVector price(2*steps+1);
@@ -62,17 +62,20 @@ NumericVector Binomial_American_Greeks_cpp(double initial_price = 100,
   }
 
   for(i = 0; i <= steps; i++) {
-    american_value(i) = payoff_function(0.0, price(2*steps - 2*i), exercise_price);
+    european_value(i) =
+      exp_min_r_steps_dt * payoff_function(price(2*steps - 2*i), exercise_price);
   }
 
-  european_value = clone(american_value);
+  american_value = clone(european_value);
 
   for(j = steps-1; j >= 0; j--) {
     for(i = 0; i <= j; i++) {
-      american_value(i) = payoff_function(
-        exp_min_r_dt * (p*american_value(i) + q*american_value(i+1)),
-        price(2*steps - 2*i + j - steps), exercise_price);
       european_value(i) = p * european_value(i) + q * european_value(i+1);
+      american_value(i) = p * american_value(i) + q * american_value(i+1);
+      american_value(i) = max(
+        exp(-(r-dividend_yield)*j*dt) *
+          payoff_function(price(2*steps - 2*i + j - steps), exercise_price),
+          american_value(i));
     }
   }