Teaching Measure Transformation in Option Pricing with a Loaded Die

We argue that students can be introduced to the counter-intuitive concept of probability measure transformation by applying it to gambling games with a die. The effect of loading a die on the odds of a simple game is readily understood by students and transformed probabilities can easily be calculated. More complex transformations can be obtained with the solver of a spreadsheet program. They can be expressed in measure transformation functions that give an intuitive understanding of the Radon-Nikodym derivative used in risk neutral valuation. The connection with option pricing is made by placing a die game in a simple but general pricing framework. The die loading analogy may be of use to instructors teaching risk neutral valuation or probability measure transformation.