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derivative analytics with python.pdf
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The book is divided into three parts. The first part is concerned with market-based valuation
as a process and empirical findings about market realities. The second part covers a number
of topics for the theoretical valuation of options and derivatives. It also develops tools much
needed during a market-based valuation. The third part finally covers the major aspects related
to a market-based valuation and also hedging strategies in such a context.
Part I “The Market” comprises two chapters:
Chapter 2: this chapter contains a discussion of topics related to market-based valuation,
like risks affecting the value of equity index options
Chapter 3: this chapter documents empirical and anecdotal facts about stocks, stock
indices and in particular volatility (e.g. stochasticity, clustering, smiles) as well as about
interest rates
Part II “Theoretical Valuation” comprises four chapters:
Chapter 4: this chapter covers arbitrage pricing theory and risk-neutral valuation in
discrete time (in some detail) and continuous time (on a higher level) according to the
Harrison-Kreps-Pliska paradigm (cf. Harrison and Kreps (1979) and Harrison and Pliska
(1981))
Chapter 5: the topic of this chapter is the complete market models of Black-Scholes-
Merton (BSM, cf. Black and Scholes (1973), Merton (1973)) and Cox-Ross-Rubinstein
(CRR, cf. Cox et al. (1979)) that are generally considered benchmarks for option valuation
Chapter 6: Fourier-based approaches allow us to derive semi-analytical valuation formulas
for European options in market models more complex and realistic than the BSM/CRR
models; this chapter introduces the two popular methods of Carr-Madan (cf. Carr and
Madan (1999)) and Lewis (cf. Lewis (2001))
Chapter 7: the valuation of American options is more involved than with European
options; this chapter analyzes the respective problem and introduces algorithms for American
option valution via binomial trees and MonteCarlo simulation; at the center stands the
Least-Squares Monte Carlo algorithm of Longstaff-Schwartz (cf. Longstaff and Schwartz
(2001))
Finally, Part III “Market-Based Valuation” has seven chapters:
Chapter 8: before going into details, this chapter illustrates the whole process of a marketbased
valuation effort in the simple, but nevertheless still useful, setting of Merton’s
jump-diffusion model (cf. Merton (1976))
Chapter 9: this chapter introduces the general market model used henceforth, which
is from Bakshi-Cao-Chen (cf. Bakshi et al. (1997)) and which accounts for stochastic
volatility, jumps and stochastic short rates
Chapter 10: Monte Carlo simulation is generally the method of choice for the valuation
of exotic/complex index options and derivatives; this chapter therefore discusses in some
detail the discretization and simulation of the stochastic volatility model by Heston
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