Initial selection on dropdowns with objects using KnockoutJS

Question

I have a model that looks something like this (not actual code so don't mind the possible mistyping).

model = function(option, items) {
    self = this;
    self.options = options;
    self.items = ko.mapping.fromJS(items);
}

The options coantains list of objects that one can select from in a dropdown. The items also contains a list of object where each object has a identical object like one in the options-list.

I then foreach over the items list and display an dropdown box on each row. I here need the object in the current items from the items list to be the selected option. When I however don't set an optionValue but only try to match on whole object it doesn't work ... My observable then however works fine and all the subscribing fields for the whole object get updated with the new selection. I however got the initial selection to work with optionValue and Id like below.

<select data-bind="options: $parent.options, optionsValue:'Id', optionsText: 'Name', value: item.Id"></select> 

My problem now is that only the element bound to the Id gets updated? I need to have all the properties of the current item updated even if it's only the Id that changes now when I change something in the dropdown.

How should I do this?