***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 function of (among other things) the value of the security underlying the option. In this chapter we explore derivatives from the mathematician’s perspective. In the Chapter 9 we will use these derivates in the manner of a quantitative analyst. Members of the quantitative financial profession refer to the subject matter of this chapter as the “Greeks” since a Greek letter is used to name each derivative (except for the one which we will meet in due time).
8.6 Relationships between Delta, Theta and Gamma
This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three or four semester sequence of calculus courses. It introduces the theory of interest, random variables and probability, stochastic processes, arbitrage, option pricing, hedging, and portfolio optimization. The student progresses from knowing only elementary calculus to understanding the derivation and solution of the Black–Scholes partial differential equation and its solutions. This is one of the few books on the subject of financial mathematics which is accessible to undergraduates having only a thorough grounding in elementary calculus. It explains the subject matter without “hand waving” arguments and includes numerous examples. Every chapter concludes with a set of exercises which test the chapter’s concepts and fill in details of derivations.