***Excerpt from book*** One of the first types of investments that people learn about is some variation on the savings account. In exchange for the temporary use of an investor’s money, a bank or other financial institution agrees to pay interest, a percentage of the amount invested, to the investor. ... click here for more details.

***Excerpt from book*** Since the number and interactions of forces driving the values of investments are so large and complex, development of a deterministic mathematical model of a market is likely to be impossible. In this book a probabilistic or stochastic model of a market will be developed instead. ... click here for more details.

***Excerpt from book*** Whereas in Chapter 2 random variables could take on only a finite number of values taken from a set with gaps between the values, in the present chapter, continuous random variables will be described. A continuous random variable can take on an infinite number of different values from ... click here for more details.

***Excerpt from book*** The concept known as arbitrage is subtle and can seem counter-intuitive. In its basic form arbitrage exists whenever two financial instruments are mis-priced relative to one another. Due to the mis-pricing, it becomes possible to make a financial gain. The assumption that financial markets are ... click here for more details.

***Excerpt from book*** In this chapter we will introduce and explain some of the concepts surrounding the probabilistic models used to capture the behavior of stock, security, option and index prices. Topics covered here could be expanded into an entire book of their own. For our purposes we will ... click here for more details.

This chapter introduces the fundamental concepts and terminology of options. The relationships between options and the underlying securities are intuitively explained and how these relationship must be maintained to eliminate arbitrage is used to then motivate and setup the Black-Scholes PDE

***Excerpt from book*** In Chapter 6 the Black-Scholes partial differential equation was derived and summarized in Eq. (6.14). Every European style option satisfies this PDE. The differences in the options are due to different boundary and final conditions. In the present chapter we will solve the Black-Scholes equation ... click here for more details.

***Excerpt from book*** To mathematics the word derivative means an instantaneous rate of change in a quantity. To a quantitative analyst a derivative is a financial entity whose value is derived from the value of some underlying asset. Hence a European call option is a derivative who value is a ... click here for more details.

***Excerpt from book*** Hedging is the practice of making a portfolio of investments less sensitive to changes in the market variables such as the prices of securities and interest rates. In Chapter 8 the partial derivatives of the values of European put and call options were calculated. In this ... click here for more details.

***Excerpt from book*** There are several notions of the idea of optimizing a portfolio of securities, options, bonds, cash, etc. In this chapter we will explore optimality in the sense of maximizing the rate of return, minimizing the variance in the rate of return and minimizing risk to the investor. ... click here for more details.