6

12

 

World Scientific Publishing Company (Visit publisher website)

2006

English

 

 

 

Intermediate

 

 

quantitative analysis, market risk, investment management, stochastic processes, stochastic calculus, derivatives (general), modeling derivatives, options, strike price, exercise time, call option, put option, European option, American option, short vs. long position, put-call parity, binomial tree, Black-scholes partial differential equation, in the money, out of the money

 

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

 

6.1 Properties of Options
6.2 Pricing an Option Using a Binary Model
6.3 Black-Scholes Partial Differential Equation
6.4 Boundary and Initial Conditions
6.5 Exercises

 

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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.