diff --git a/pfhedge/instruments/primary/brownian.py b/pfhedge/instruments/primary/brownian.py
index ffde5e8f..dd500da2 100644
--- a/pfhedge/instruments/primary/brownian.py
+++ b/pfhedge/instruments/primary/brownian.py
@@ -137,7 +137,7 @@ def simulate(
 
         spot = generate_geometric_brownian(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             sigma=self.sigma,
             mu=self.mu,
diff --git a/pfhedge/instruments/primary/cir.py b/pfhedge/instruments/primary/cir.py
index 51560c78..2b2be8f6 100644
--- a/pfhedge/instruments/primary/cir.py
+++ b/pfhedge/instruments/primary/cir.py
@@ -106,7 +106,7 @@ def simulate(
 
         spot = generate_cir(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             kappa=self.kappa,
             theta=self.theta,
diff --git a/pfhedge/instruments/primary/heston.py b/pfhedge/instruments/primary/heston.py
index 56c77a92..f74b7258 100644
--- a/pfhedge/instruments/primary/heston.py
+++ b/pfhedge/instruments/primary/heston.py
@@ -129,7 +129,7 @@ def simulate(
 
         output = generate_heston(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             kappa=self.kappa,
             theta=self.theta,
diff --git a/pfhedge/instruments/primary/kou_jump.py b/pfhedge/instruments/primary/kou_jump.py
index 786bf605..f811e3c8 100644
--- a/pfhedge/instruments/primary/kou_jump.py
+++ b/pfhedge/instruments/primary/kou_jump.py
@@ -159,7 +159,7 @@ def simulate(
 
         spot = generate_kou_jump(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             sigma=self.sigma,
             mu=self.mu,
diff --git a/pfhedge/instruments/primary/local_volatility.py b/pfhedge/instruments/primary/local_volatility.py
index 4dfeebc7..25ed77de 100644
--- a/pfhedge/instruments/primary/local_volatility.py
+++ b/pfhedge/instruments/primary/local_volatility.py
@@ -123,7 +123,7 @@ def simulate(
 
         output = generate_local_volatility_process(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             sigma_fn=self.sigma_fn,
             init_state=init_state,
             dt=self.dt,
diff --git a/pfhedge/instruments/primary/merton_jump.py b/pfhedge/instruments/primary/merton_jump.py
index 3384c2ce..0dcdc685 100644
--- a/pfhedge/instruments/primary/merton_jump.py
+++ b/pfhedge/instruments/primary/merton_jump.py
@@ -150,7 +150,7 @@ def simulate(
 
         output = generate_merton_jump(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             sigma=self.sigma,
             mu=self.mu,
diff --git a/pfhedge/instruments/primary/rough_bergomi.py b/pfhedge/instruments/primary/rough_bergomi.py
index 631f76c7..ed54be88 100644
--- a/pfhedge/instruments/primary/rough_bergomi.py
+++ b/pfhedge/instruments/primary/rough_bergomi.py
@@ -129,7 +129,7 @@ def simulate(
 
         output = generate_rough_bergomi(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             alpha=self.alpha,
             rho=self.rho,
diff --git a/pfhedge/instruments/primary/vasicek.py b/pfhedge/instruments/primary/vasicek.py
index 4416f457..9bb2a15b 100644
--- a/pfhedge/instruments/primary/vasicek.py
+++ b/pfhedge/instruments/primary/vasicek.py
@@ -88,7 +88,7 @@ def simulate(
 
         spot = generate_vasicek(
             n_paths=n_paths,
-            n_steps=ceil(time_horizon / self.dt + 1),
+            n_steps=ceil(round(time_horizon / self.dt, 8) + 1),
             init_state=init_state,
             kappa=self.kappa,
             theta=self.theta,