Diffusion Model

This chapter begins Part 2 of the book and introduces actual asset price modeling using a real dataset. As you know, Stochastic Finance requires a hefty amount of knowledge in probability and simulation, so we spent five chapters in Part 1 solidifying our grasp of these fundamentals. Don’t think that we have read five chapters, but we are still about to start the crux of the subject – Stochastic Finance is never taught like that. Concepts for this subject highly overlap between the prerequisites and core topics. In some books, it is discussed completely from an applied probability perspective, and to maintain the consistency, we didn’t want to deviate ourselves from there. This chapter takes the reader from the basic theory of stochastic process learned earlier to specialization with financial concepts, estimation of diffusion model parameters, computing the forecasted path distribution, capturing uncertainties in asset price, risk-neutral pricing, etc. At the end of the chapter, you should be able to do a basic asset price modeling with SDE and Monte Carlo simulation and start forecasting the future quotes.