Try to run any date picker, having set constant :
testedDatePicker.setValue(LocalDate.MAX);
testedDatePicker.setValue(LocalDate.MIN);

and try to open popup.

Exception:
java.time.DateTimeException: Invalid value for Year (valid values -999999999 - 999999999): 1000000000
at java.time.temporal.ValueRange.checkValidIntValue(ValueRange.java:327)
at java.time.temporal.ChronoField.checkValidIntValue(ChronoField.java:723)
at java.time.YearMonth.plusMonths(YearMonth.java:801)
at com.sun.javafx.scene.control.skin.DatePickerContent.updateDayCells(DatePickerContent.java:459)
at com.sun.javafx.scene.control.skin.DatePickerContent.updateValues(DatePickerContent.java:387)
at com.sun.javafx.scene.control.skin.DatePickerContent.refresh(DatePickerContent.java:380)
at com.sun.javafx.scene.control.skin.DatePickerContent.<init>(DatePickerContent.java:207)
at com.sun.javafx.scene.control.skin.DatePickerSkin.getPopupContent(DatePickerSkin.java:139)
at com.sun.javafx.scene.control.skin.ComboBoxPopupControl.show(ComboBoxPopupControl.java:72)
at com.sun.javafx.scene.control.skin.DatePickerSkin.show(DatePickerSkin.java:152)
at com.sun.javafx.scene.control.skin.ComboBoxBaseSkin.handleControlPropertyChanged(ComboBoxBaseSkin.java:116)
at com.sun.javafx.scene.control.skin.DatePickerSkin.handleControlPropertyChanged(DatePickerSkin.java:157)
at com.sun.javafx.scene.control.skin.BehaviorSkinBase$2.call(BehaviorSkinBase.java:179)
at com.sun.javafx.scene.control.skin.BehaviorSkinBase$2.call(BehaviorSkinBase.java:177)
at com.sun.javafx.scene.control.MultiplePropertyChangeListenerHandler$1.changed(MultiplePropertyChangeListenerHandler.java:55)
at javafx.beans.value.WeakChangeListener.changed(WeakChangeListener.java:87)
at com.sun.javafx.binding.ExpressionHelper$Generic.fireValueChangedEvent(ExpressionHelper.java:347)
at com.sun.javafx.binding.ExpressionHelper.fireValueChangedEvent(ExpressionHelper.java:80)
at javafx.beans.property.ReadOnlyBooleanWrapper$ReadOnlyPropertyImpl.fireValueChangedEvent(ReadOnlyBooleanWrapper.java:177)
at javafx.beans.property.ReadOnlyBooleanWrapper$ReadOnlyPropertyImpl.access$100(ReadOnlyBooleanWrapper.java:147)
at javafx.beans.property.ReadOnlyBooleanWrapper.fireValueChangedEvent(ReadOnlyBooleanWrapper.java:143)
at javafx.beans.property.BooleanPropertyBase.markInvalid(BooleanPropertyBase.java:108)
at javafx.beans.property.BooleanPropertyBase.set(BooleanPropertyBase.java:141)
at javafx.scene.control.ComboBoxBase.setShowing(ComboBoxBase.java:183)
at javafx.scene.control.ComboBoxBase.show(ComboBoxBase.java:386)
at com.sun.javafx.scene.control.behavior.ComboBoxBaseBehavior.show(ComboBoxBaseBehavior.java:247)
at com.sun.javafx.scene.control.behavior.ComboBoxBaseBehavior.mouseReleased(ComboBoxBaseBehavior.java:205)
at com.sun.javafx.scene.control.behavior.DatePickerBehavior.mouseReleased(DatePickerBehavior.java:149)
at com.sun.javafx.scene.control.skin.DatePickerSkin$1.handle(DatePickerSkin.java:68)
at com.sun.javafx.scene.control.skin.DatePickerSkin$1.handle(DatePickerSkin.java:66)
at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:86)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:238)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:191)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:59)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:58)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:74)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:54)
at javafx.event.Event.fireEvent(Event.java:202)
at javafx.scene.Scene$MouseHandler.process(Scene.java:3633)
at javafx.scene.Scene$MouseHandler.process(Scene.java:3464)
at javafx.scene.Scene$MouseHandler.access$1900(Scene.java:3416)
at javafx.scene.Scene.impl_processMouseEvent(Scene.java:1692)
at javafx.scene.Scene$ScenePeerListener.mouseEvent(Scene.java:2484)
at com.sun.javafx.tk.quantum.GlassViewEventHandler$MouseEventNotification.run(GlassViewEventHandler.java:312)
at com.sun.javafx.tk.quantum.GlassViewEventHandler$MouseEventNotification.run(GlassViewEventHandler.java:237)
at java.security.AccessController.doPrivileged(Native Method)
at com.sun.javafx.tk.quantum.GlassViewEventHandler.handleMouseEvent(GlassViewEventHandler.java:354)
at com.sun.glass.ui.View.handleMouseEvent(View.java:514)
at com.sun.glass.ui.View.notifyMouse(View.java:877)
at com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
at com.sun.glass.ui.win.WinApplication.access$300(WinApplication.java:39)
at com.sun.glass.ui.win.WinApplication$3$1.run(WinApplication.java:101)
at java.lang.Thread.run(Thread.java:724)