Converting a parsed string from csv to datetime property via reflection

I have created a modelbinder using reflection to set property values from a csv file. I am using Convert.ChangeType which has worked for most cases but now a date value needs to be parsed to my DateTime property. The format in the csv is YYYYMMDD. The code I have so far:

foreach (var property in matchedModel)
{
    Type propType = Nullable.GetUnderlyingType(property.Value.PropertyType) ?? 
                                               property.Value.PropertyType;

    var value = string.IsNullOrEmpty(data.Value[property.Key]) ? null : 
                Convert.ChangeType(data.Value[property.Key], propType);

    property.Value.SetValue(instance, value, null);
}

The property variable is the relevant property that needs to be set. Since I had some nullable properties I had to use the Nullable.GetUnderlyingType.

The problem is with the value not being converted to a proper DateTime as explained above. The easy solution would be to have something like:

if(property is datetime) do value conversion

However this would be too hardcoded and I want something more generic/dynamic. What would be the best way to approach this?