Notes on the Bibliography.

Here we point out references which complement and extend the material

in the text. There are several excellent books (many of which did not exist

when this book began) whose material intersects with that of several chap-

ters including the comprehensive book Glasserman (2004) and Jaeckel (2003).

Both of these texts deal speci¬cally with Monte Carlo methods in Finance.

There is a number of excellent more general Monte Carlo books as well, includ-

ing Gentle(2003), Fishman(1996) and the succinct but classic Hammersley and

Handscomb(1964) book, from which much of modern variance reduction has

grown and the pioneering paper of Hammersley(1960). More specialized books

on Monte Carlo are Robert and Cassella (1999) and Liu (2001). Boyle (1977)

is usually credited as the ¬rst use of simulation methodology in Finance. The

remainder of these notes are broken down by Chapter. There is discussion of

much of the ¬nance and econometrics material of this book in Campbell, Lo,

MacKinlay(1996), a book which takes a more statistical (hence somewhat more

critical) view of the standard models in Finance and econometrics.

Chapter 2. Background material on the types and uses of options can be

found in Boyle and Boyle (2001) and an excellent and popular discussion the

mathematical theory of Finance in Björk (1998). Bachelier(1900) deserves credit

as the founder of stochastic models in ¬nance. Fundamental papers on the valu-

ation of options include Black and Scholes (1973), Merton(1973), Cox and Ross

(1976a, 1976b), Cox, Ross and Rubinsten (1979), Hull and White(1987) and a

standard text on option pricing, Hull(1993). References for the material on En-

tropy in ¬nance are the theses of Samperi(1998), Gulko(1998) and Reesor(2002)

as well as papers by Gerber and Shiu(1994) and Avellaneda(1998).

Chapter 3

Uniform random number generators and their uses are comprehensively

treated in Fishman(1996), Fox(1986) with older but valuable treatments of non-

uniform generators in Devroye(1986) and Rubinstein(1981) and a very clear and

concise discussion of random number generation in Ripley(1983, 1987, 1988).

Gentle(2003) also has a nice exposition of di¬erent methods of random number

generation. For speci¬c generators, see Tadikamalla(1978), Cheng(1977, 1979)

for the Gamma and Beta,

For the adequacy of various models for ¬nancial data and alternatives see

Blattberg and Gonedes (1974), Press(1967), Fama(1965) and Fama and Roll,(1968,

1971), Fielitz and Rozelle (1983) (stable distributions), Chan et. al. (1992),

Clark(1973),

Chapter 4

The variance reduction in this chapter is heavily dependent on Hammersley

and Handscomb(1964) and Glasserman(2004) provides a number of applications

speci¬c to ¬nance.

Chapter 5

The material in the last part of this chapter is largely drawn from McLeish

(2002) but there are related results in a number of standard texts and references,

7.13. ALTERNATIVE MODELS 435

including Karatzas and Shreve(1999), Redekop(1995), Shepp(1979).

Chapter 6

An excellent reference for the use of Quasi-Random sequences is Niederre-

iter(1992) and applications to option pricing in the university of Waterloo thesis

of K.S. Tan and Tan and Boyle(2001).

Chapter 7

The problems of ¬nding a root or a maxima of a function when evaluations

are subject to noise is an old one, dating at least to the paper of Robbins

and Monro (1951). The work on Monte Carlo optimization is largely due to

Geyer(1995). Material on the EM algorithm and data augmentation is in the

books of Liu(2001) and Robert and Casella(1999). The estimation of parameters

for di¬usion processes is relatively well known, but in this case much is borrowed

from McLeish and Kolkiewicz(1997) and Kloeden and Platten(1992). The last

section on estimating volatility is largely in McLeish(2002).

Chapter 8

There is a considerable literature on sensitivity analysis in simulation, much

of it for discrete event simulations such as networks and queues. See for example,

Cao(1987) and Cao and Ho(1987), Arsham et. al. (1989), McLeish and Rollans

(1992), Glynn(1989). The treatment here of Monte Carlo optimization is similar

to Rollans(1991) and Reesor(2002).

436 OTHER METHODS AND CONCLUSIONS

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