EC3070 FINANCIAL DERIVATIVES
SPECULATION
Speculation Speculation entails running the risk of a loss in the expectation of
a high reward. A pure investment is devoid of risk and, therefore, of any spec
EC3070 FINANCIAL DERIVATIVES
CONTINUOUS-TIME STOCHASTIC PROCESSES
Discrete-Time Random Walk The concept of a Wiener process is an extrapolation of that of a discrete-time random walk. A standardised r
EC3070 FINANCIAL DERIVATIVES
PRESENT VALUES
The Initial Value of a Forward Contract. One of the parties to a forward
contract assumes a long position and agrees to buy the underlying asset at a
certai
EC3070 FINANCIAL DERIVATIVES
OPTIONS
Options consist of rights to buy or rights to sell, which can be exercised or
foregone at the discretion of the holder. The right to sell is called a put option
an
EC3070 FINANCIAL DERIVATIVES
OPTIMAL HEDGE RATIO
If an asset has been hedged, then the movements in its spot price and in the
accompanying short hedge should constitute compensating variations. The
op
EC3070 FINANCIAL DERIVATIVES
The Mean Value Theorem
Rolles Theorem. If f (x) is continuous in the closed interval [a, b] and
dierentiable in the open interval (a, b), and if f (a) = f (b) = 0, then th
EC3070 FINANCIAL DERIVATIVES
MARKING TO MARKET
Imagine a futures contract that has been written at time t = 0, which obliges
a party to supply an asset or a commodity at time for a settlement price
of
EC3070 FINANCIAL DERIVATIVES
SPECULATION AND CRISES
Speculation Speculation entails running the risk of a loss in the expectation of a high reward. Financial speculation involves the buying, holding,
EC3070 FINANCIAL DERIVATIVES
BINOMIAL OPTION PRICING MODEL
A One-Step Binomial Model Suppose that a portfolio consists of N
units of stock as assets, with a spot price of S0 per unit, together with a
EC3070 FINANCIAL DERIVATIVES
CONTINUOUS-TIME STOCHASTIC PROCESSES
Discrete-Time Random Walk . A standardised random walk dened
over the set of integers cfw_t = 0, 1, 2, . . ., is a sequence by w(t) =
EC3070 FINANCIAL DERIVATIVES
FUTURES: MARKING TO MARKET
The holder of a futures contract will be required to deposit with the brokers
a sum of money described as the margin, which will be calculated a
EC3070 FINANCIAL DERIVATIVES
ITOS LEMMA
Preliminaries Itos lemma enables us to deduce the properties of a wide variety of continuous-time processes that are driven by a standard Wiener process
w(t).
W
EC3070 FINANCIAL DERIVATIVES
COMPOUND INTEREST
Investments
Imagine that a sum of y0 = 100 is invested at an annual rate of interest
of r = 5% per annum. After one year has elapsed, the sum will have g
EC3070 FINANCIAL DERIVATIVES
HEDGING VIA FORWARD CONTRACTS
Example 1. Hedging a Long Forward Contract. Acme Metals buys 10 Comex
gold contracts at 100 ounces each for June delivery at 11.a.m Monday at
EC3070 FINANCIAL DERIVATIVES
GLOSSARY
Ask price The bid price.
Arbitrage An arbitrage is a nancial strategy yielding a riskless prot and
requiring no investment. It commonly amounts to the successive
EC3070 FINANCIAL DERIVATIVES
FORWARD CONTRACTS
In a forward contract, a party agrees to buy or sell an asset at a given price
at a future date . The party that agrees to buy the asset, is taking a lon
EC3070 FINANCIAL DERIVATIVES
Exercise 2
1. A stock price is currently S0 = 40. At the end of the month, it will be
u
d
either S1 = 42 or S1 = 38. The risk-free rate of continuously compounded
interest
EC3070 FINANCIAL DERIVATIVES
Exercise 1
1. A credit card company charges an annual interest rate of 15%, which is
eective only if the interest on the outstanding debts is paid in monthly
instalments.
EC3070 FINANCIAL DERIVATIVES
PUTCALL PARITY
Upper Bounds Let p |0 be the current price at time t = 0 of a put option
eective at time , and let c |0 be the current price of a corresponding call
option.
EC3070 FINANCIAL DERIVATIVES
BLACKSCHOLES OPTION PRICING
The Dierential Equation The Black-Scholes model of option pricing assumes that the price St of the underlying asset has a geometric Brownian
mo
EC3070 FINANCIAL DERIVATIVES
THE BINOMIAL THEOREM
Pascals Triangle and the Binomial Expansion. To prove the binomial
theorem, it is necessary to invoke some fundamental principles of combinatorial cal
EC3070 FINANCIAL DERIVATIVES
BINOMIAL OPTION PRICING MODEL
A One-Step Binomial Model The Binomial Option Pricing Model is a simple device that is used for determining the price c |0 that should be att
EC3070 FINANCIAL DERIVATIVES
BIBLIOGRAPHY
Textbooks
Chance, D.M. and R. Brooks, (2008), An Introduction to Derivatives and Risk
Management: Seventh Edition, Thompson South-Western Publishers.
Hull, J.
EC3070 FINANCIAL DERIVATIVES
Yesterday, upon the stair,
I saw a man who wasnt there.
He wasnt there again today.
I wish, I wish, hed go away.
Antigonish (1899), by William Hughes Mearns (18751965)
The
EC3070 FINANCIAL DERIVATIVES
Exercise 2
u
1. A stock price is currently S0 = 40. At the end of the month, it will be either S1 = 42
d
or S1 = 38. The risk-free rate of continuously compounded interest
EC3070 FINANCIAL DERIVATIVES
Exercise 1
1. A credit card company charges an annual interest rate of 15%, which is eective only
if the interest on the outstanding debts is paid in monthly instalments.
Hull: Chapter 10
Options, Futures, and Other Derivatives, 7th
1
Take
a position in the option and the
underlying.
Take
a position in 2 or more options of
the same type (A spread) .
Combination: Tak
Introduction
Options, Futures, and Other Derivatives, 7th
Edition, Copyright John C. Hull 2008
1
Derivative: a
financial instrument whose
value depends (or derives from) the
values of other, more bas
EC3070 FINANCIAL DERIATIVES
TAYLORS THEOREM AND SERIES EXPANSIONS
Taylors Theorem. If f is a function continuous and n times dierentiable in
an interval [x, x + h], then there exists some point in thi