Elementary Financial Math Contents

2025/04/10　 updated

Based on my modest experience, I believe beginners tend to grasp fundamental concepts more effectively by quickly learning key points through simple calculation examples. Later, when they have more time, thoroughly reading specialized books to learn sophisticated theories may reduce the chances of stumbling or giving up midway in their learning journey. To offer some reference, although it may not be ideal, I've summarized key points primarily using simple calculation examples for this quick-learning method. In these calculations, I utilize not only spreadsheet software like Excel but also free statistical software such as R and free mathematical software like Maxima. All of these tools are valuable in practical business scenarios. Even those who are not skilled in mathematics can attempt fairly complex calculations using these tools.

The pages on this website are written in Japanese. Please use translation applications to convert the text into your preferred language. I believe that the program code for the statistical software R and the mathematical software Maxima, as well as the Excel worksheets, can be easily verified. Please test and verify them yourself.

This website has been carefully examined; however, omissions or errors may still exist for various reasons. Before using this information, please consult relevant experts or professionals and carefully evaluate its content.

Options

Black Scholes model with MAXIMA　

deriving Black Scholes option's Delta   

Greek letters)option greeks with MAXIMA

option greeks in R

monte carlo simulation of skewed distribution  of OTM option's returns in R

option pricing and volatility estimating with Excel

geometric brownian motion using R 

Interval estimate of mean (application for financial analysis using Excel and R)

normal distribution plot in MAXIMA

lognormal distribution and　confidence interval of stock price 

Portfolio Analysis

portfolio analysis using Excel matrix function(3 assets)

CAPM and SML derivation using Excel

_{efficient frontier with short selling will be examined using Excel}