Revisiting History - "Pricing the upside derivative"

Our finance professor, Kent Womack, was just describing the model for pricing derivatives and it is almost exactly what I suggested the best method for pricing options would be based on my intuition in January (and was the topic of my Peter Godsoe Scholarship Award in Financial Engineering). He even asked the same questions I was looking into when I was studying for the CFA exam regarding the profit profiles for different put options and call options and why you would enter into different positions.

In his slide, he even mentions the idea of the distribution of stock prices influencing the expected outcome. I think the only difference in our models is that he used a distribution called Geometric Brownian Motion. It's similar to my normal distribution assumption, however, it accounts for an upward drift (which I didn't account for). However, I wonder if it can be approximated with a shifted normal distribution (mean greater than zero).

Also, to actually determine his option price prof. Womack used simulations whereas my model was based more on mathematical calculations. I'm sure both methods to determine the price are acceptable as it's more the model for describing the final underlying price that is more important.

Another improvement from his model is the inclusion of the time value of money as he discounts the future gains back to the present value.