# Welcome to Finance Press

Thanks for visiting. This site provides supplementary material for the “Option Valuation under Stochastic Volatility” books: material that you won’t find at Amazon or other selling sites.

For the latest book,
“Option Valuation under Stochastic Volatility II”, you can find:

In addition, you will find a blog by Alan L. Lewis, the author.

## A featured chart from the latest book

What is it? This chart shows early exercise boundaries for the American-style put under discrete dividend models. The models are associated to Black-Scholes (geometric Brownian motion, or GBM) stock price evolution. How to handle discrete dividends is, remarkably (even in this basic GBM case), still a contentious issue more than 40 years after Black and Scholes’ seminal publication.

Two general approaches are: (i) piecewise GBM, using various dividend policies $\mathcal{D}(S)$ , and (ii) escrowed dividends. The first two rows of the chart show the early exercise boundary in the $(t,S)$ plane under piecewise GBM and various $\mathcal{D}(S)$. The last row shows the same in the $(t,\tilde{S})$ plane under the escrowed dividend model, where $\tilde{S}$ is the risky part of the stock price. More details are found in Chapter 9 of the latest book.

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