Financial Engineering with Stochastic Calculus I
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Financial Engineering with Stochastic Calculus I
Andreea Minca
Cornell University
Fall 2019

Financial Engineering with Stochastic Calculus I
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Introduction
0. Introduction

Financial Engineering with Stochastic Calculus I
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Introduction
Course syllabus
I:
Introduction: financial engineering, binomial model
II:
Background in probability: information and
σ
-algebras, independence, general
conditional expectations, martingales, fundamental theorem of asset pricing
III:
Brownian motion (BM): scaled random walks, definition of BM, distribution of BM,
filtration for BM, martingale property of BM, quadratic variation
IV:
Stochastic calculus: stochastic integral, Itˆ
o processes, Itˆ
o formula,
Black-Scholes-Merton equation, multivariable stochastic calculus
V:
Risk-neutral pricing: Girsanov’s theorem, risk-neutral measure, martingale
representation, fundamental theorems of asset pricing, dividend paying assets.
VI:
Miscellaneous topics (if time permits): dividends, forwards and futures.

Financial Engineering with Stochastic Calculus I
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Introduction
August 29, 2019
Outline
Overview of financial markets
Overview of main types of financial derivatives and their use in the market
Size of the derivative market
Modeling financial markets - the main assumptions: efficiency and absence of
arbitrage
Pricing derivatives: the philosophy

Financial Engineering with Stochastic Calculus I
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Introduction
Financial markets
Throughout the course, we assume that there is exists a
financial market
, where securities
are traded.
In a
primary financial market
, securities are issued. For example, the debt of a company,
government, etc., initial public offerings (IPO) for equity.
On a
secondary financial market
a
large
number of investors trade securities through an
exchange. E.g. New York Stock Exchange, Nasdaq, American Stock Exchange and all
major exchanges in the world.
These are the closest to the markets we consider in theory in this course. We call
e
fficiency of the market the capacity of the market to determine a ”fair value” for the
traded securities.
When the market is efficient, the market forces (supply and demand) determine
the price of the primary assets, e.g., stocks, bonds.
There are also over-the-counter markets, in which a (small) number of large investors
trade directly, without passing through an exchange. When pricing a security traded in
this markets, special attention must be given to
counterparty risk
.

Financial Engineering with Stochastic Calculus I
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Introduction
Derivative contracts
Contrary to primary assets (such as commodities, stocks, interest rates, foreign
exchange),
derivative contracts
depend on the performance of these primary assets.

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