e-book

A Course in Financial Calculus

---

Financial mathematics provides a striking example of successful collaboration
between academia and industry. Advanced mathematical techniques, developed
in both universities and banks, have transformed the derivatives business into a
multi-trillion-dollar market. This has led to demand for highly trained students and
with that demand comes a need for textbooks.

This volume provides a first course in financial mathematics. The influence of
Financial Calculus by Martin Baxter and Andrew Rennie will be obvious. I am
extremely grateful to Martin and Andrew for their guidance and for allowing me
to use some of the material from their book.

The structure of the text largely follows Financial Calculus, but the mathematics,
especially the discussion of stochastic calculus, has been expanded to a level
appropriate to a university mathematics course and the text is supplemented by
a large number of exercises. In order to keep the course to a reasonable length,
some sacrifices have been made. Most notable is that there was not space to discuss
interest rate models, although many of the most popular ones do appear as examples
in the exercises. As partial compensation, the necessary mathematical background
for a rigorous study of interest rate models is included in Chapter 7, where we
briefly discuss some of the topics that one might hope to include in a second
course in financial mathematics. The exercises should be regarded as an integral
part of the course. Solutions to these are available to bona fide teachers from
[email protected].

The emphasis is on stochastic techniques, but not to the exclusion of all other
approaches. In common with practically every other book in the area, we use binomial
trees to introduce the ideas of arbitrage pricing. Following Financial Calculus,
we also present discrete versions of key definitions and results on martingales and
stochastic calculus in this simple framework, where the important ideas are not
obscured by analytic technicalities. This paves the way for the more technical results
of later chapters. The connection with the partial differential equation approach to
arbitrage pricing is made through both delta-hedging arguments and the Feynman–
Kac Stochastic Representation Theorem. Whatever approach one adopts, the key
point that we wish to emphasise is that since the theory rests on the assumption of
absence of arbitrage, hedging is vital. Our pricing formulae only make sense if there
is a ‘replicating portfolio’.

---

Ketersediaan

Tidak ada salinan data

Informasi Detail

Judul Seri

-

No. Panggil

-

Penerbit

Canada : Cambridge University Press., 2002

Deskripsi Fisik

vii, 196 Hlm.

Bahasa

English

ISBN/ISSN

978-0-511-33725-3

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

MATEMATIKA

Info Detail Spesifik

-

Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

Komentar

---

Anda harus masuk sebelum memberikan komentar