--- a/ql/pricingengines/blackformula.cpp
+++ b/ql/pricingengines/blackformula.cpp
@@ -601,7 +601,7 @@
         auto sign = Integer(optionType);
 
         if (stdDev==0.0)
-            return (forward * sign < strike * sign ? 1.0 : 0.0);
+            return (forward * sign > strike * sign ? 1.0 : 0.0);
 
         forward = forward + displacement;
         strike = strike + displacement;
@@ -954,9 +954,10 @@
                         Real stdDev) {
         QL_REQUIRE(stdDev>=0.0,
                    "stdDev (" << stdDev << ") must be non-negative");
-        Real d = (forward - strike) * Integer(optionType), h = d / stdDev;
+        Real d = (forward - strike) * Integer(optionType);
         if (stdDev==0.0)
-            return std::max(d, 0.0);
+            return (d > 0.0 ? 1.0 : 0.0);
+        Real h = d / stdDev;
         CumulativeNormalDistribution phi;
         Real result = phi(h);
         return result;
--- a/test-suite/blackformula.cpp
+++ b/test-suite/blackformula.cpp
@@ -442,6 +442,47 @@
     assertBachelierBlackFormulaForwardDerivative(Option::Put, strikes, vol);
 }
 
+
+BOOST_AUTO_TEST_CASE(testAssetItmProbabilityAtZeroStdDev) {
+    BOOST_TEST_MESSAGE("Testing deterministic Black asset ITM probabilities...");
+    for (auto type : {Option::Call, Option::Put}) {
+        const Real sign = Integer(type);
+        for (Real forward : {80.0, 120.0}) {
+            for (Real shift : {0.0, 50.0}) {
+                const Real strike = 100.0;
+                const Real expected = sign * (forward - strike) > 0.0 ? 1.0 : 0.0;
+                auto payoff = ext::make_shared<PlainVanillaPayoff>(type, strike);
+                QL_CHECK_SMALL(blackFormulaAssetItmProbability(type, strike, forward, 0.0, shift) - expected, 1e-14);
+                QL_CHECK_SMALL(blackFormulaAssetItmProbability(payoff, forward, 0.0, shift) - expected, 1e-14);
+                const Real bump = 1e-4;
+                const Real slope = (blackFormula(type, strike, forward + bump, 0.0, 1.0, shift) -
+                                    blackFormula(type, strike, forward - bump, 0.0, 1.0, shift)) / (2.0 * bump);
+                QL_CHECK_SMALL(sign * blackFormulaAssetItmProbability(type, strike, forward, 0.0, shift) - slope, 1e-8);
+            }
+        }
+    }
+}
+
+BOOST_AUTO_TEST_CASE(testBachelierAssetItmProbabilityAtZeroStdDev) {
+    BOOST_TEST_MESSAGE("Testing deterministic Bachelier ITM probabilities...");
+    for (auto type : {Option::Call, Option::Put}) {
+        const Real sign = Integer(type);
+        for (Real scale : {0.001, 1.0, 1000.0}) {
+            for (Real forward : {80.0 * scale, 120.0 * scale}) {
+                const Real strike = 100.0 * scale;
+                const Real expected = sign * (forward - strike) > 0.0 ? 1.0 : 0.0;
+                auto payoff = ext::make_shared<PlainVanillaPayoff>(type, strike);
+                QL_CHECK_SMALL(bachelierBlackFormulaAssetItmProbability(type, strike, forward, 0.0) - expected, 1e-14);
+                QL_CHECK_SMALL(bachelierBlackFormulaAssetItmProbability(payoff, forward, 0.0) - expected, 1e-14);
+                const Real bump = 1e-4 * scale;
+                const Real slope = (bachelierBlackFormula(type, strike, forward + bump, 0.0) -
+                                    bachelierBlackFormula(type, strike, forward - bump, 0.0)) / (2.0 * bump);
+                QL_CHECK_SMALL(sign * bachelierBlackFormulaAssetItmProbability(type, strike, forward, 0.0) - slope, 1e-8);
+            }
+        }
+    }
+}
+
 BOOST_AUTO_TEST_SUITE_END()
 
 BOOST_AUTO_TEST_SUITE_END()