Convert variable to type only known at run-time?

foreach (var filter in filters)
{
    var filterType = typeof(Filters);
    var method = filterType.GetMethod(filter, BindingFlags.IgnoreCase | BindingFlags.Public | BindingFlags.Static);
    if (method != null)
    {
        var parameters = method.GetParameters();
        Type paramType = parameters[0].ParameterType;
        value = (string)method.Invoke(null, new[] { value });
    }
}

How can I cast value to paramType? value is a string, paramType will probably just be a basic type like int, string, or maybe float. I'm cool with it throwing an exception if no conversion is possible.

The types you are using all implement IConvertible. As such you can use ChangeType.

 value = Convert.ChangeType(method.Invoke(null, new[] { value }), paramType);

You could go dynamic; for example:

using System;

namespace TypeCaster
{
    class Program
    {
        internal static void Main(string[] args)
        {
            Parent p = new Parent() { name = "I am the parent", type = "TypeCaster.ChildA" };
            dynamic a = Convert.ChangeType(new ChildA(p.name), Type.GetType(p.type));
            Console.WriteLine(a.Name);

            p.type = "TypeCaster.ChildB";
            dynamic b = Convert.ChangeType(new ChildB(p.name), Type.GetType(p.type));
            Console.WriteLine(b.Name);
        }
    }

    internal class Parent
    {
        internal string type { get; set; }
        internal string name { get; set; }

        internal Parent() { }
    }

    internal class ChildA : Parent
    {
        internal ChildA(string name)
        {
            base.name = name + " in A";
        }

        public string Name
        {
            get { return base.name; }
        }
    }

    internal class ChildB : Parent
    {
        internal ChildB(string name)
        {
            base.name = name + " in B";
        }

        public string Name
        {
            get { return base.name; }
        }
    }
}