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Financial Derivatives - Options, Forwards, Futures, Swaps

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Financial Derivative module notes including futures, options, forwards, rate swaps. Pricing structures for options including Binomial pricing model and Black Scholes model. No guarantees of a particular grade are provided with the purchase of these notes, but I personally got 95% on this exam us...

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  • April 9, 2022
  • 44
  • 2020/2021
  • Lecture notes
  • Unknown
  • Financial derivatives
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Financial Derivatives CONTENTS


Contents

1 Mathematical Concepts 4


2 Introduction 4

2.1 Exchange Traded Markets . . . . . . . . . . . . . . . . . . . . . 4

2.2 Types of Traders . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Dangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7


3 Mechanics of Futures Markets 8

3.1 Specification of a Futures Contract . . . . . . . . . . . . . . . . . 8

3.2 Operation of Margin . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3 Market Quotes . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Types of Traders and Types of Orders . . . . . . . . . . . . . . . 13

3.5 Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.6 Forward vs Futures Contracts . . . . . . . . . . . . . . . . . . . 15

3.7 Pricing Forwards by Replication . . . . . . . . . . . . . . . . . . 16

3.8 Futures Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . 19


4 Pricing Forwards and Futures II 19


5 Trading Strategies Involving Options 22

5.1 Introduction to Options . . . . . . . . . . . . . . . . . . . . . . . 22

5.2 Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23




Page 1

,Financial Derivatives CONTENTS


6 Interest Rates 24


7 Bounds on option prices 26

7.1 Insurance value of an option . . . . . . . . . . . . . . . . . . . . 28


8 Put-Call parity 30

8.1 Put-Call Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

8.2 Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . . 31

8.3 Option delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

8.4 Portfolio Insurance . . . . . . . . . . . . . . . . . . . . . . . . . 33

8.5 Risk Neutral Pricing . . . . . . . . . . . . . . . . . . . . . . . . 34


9 Binomial Pricing 34

9.1 Two Period Binomial Tree . . . . . . . . . . . . . . . . . . . . . 35

9.2 European Option Pricing in Binomial Trees . . . . . . . . . . . . . 37


10 Black Scholes 37

10.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

10.2 Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

10.3 Closed form call pricing formula . . . . . . . . . . . . . . . . . . 40

10.4 Interpretation of factors . . . . . . . . . . . . . . . . . . . . . . . 40

10.5 Put option prices in the model . . . . . . . . . . . . . . . . . . . 42

10.6 Options on Indices and Currencies . . . . . . . . . . . . . . . . . 42

10.7 Estimating Volatility . . . . . . . . . . . . . . . . . . . . . . . . 43



Page 2

,Financial Derivatives CONTENTS


11 Swaps 43

11.1 LIBOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44




Page 3

, Financial Derivatives 2 INTRODUCTION


1 Mathematical Concepts

A matrix is a rectangular array of numbers, called elements. The matrix itself is
denoted by a boldface letter. When specific numbers are not used, the elements
are denoted by italicised lower-case letters, having a double subscript.

Matrices having a single row are referred to as row vectors; matrices having a single
column are referred to as column vectors. Vectors of either type are usually denoted
by lower-case boldface letters.

If the determinant of A is zero, then A is said to be singular. If the determinant of
A is not zero, then A is called nonsingular


2 Introduction

2.1 Exchange Traded Markets

A derivatives exchange is a market where individuals trade standardised contracts
that have been defined by the exchange. Initially their main task was to standardise
the quantities and qualities of the grains that were traded. Traditionally derivatives
exchanges have used what is known as the open outcry system, a system of in per-
son communication on the trading floor using hand signals. This has been replaced
by an electronic system.

Derivatives
A derivative security is a financial security whose value depends on (or derives
from) other, more fundamental, underlying financial variables such as the price of
a stock, an interest rate, an index level, a commodity price or an exchange rate. It
is a contract or contingent claim between two parties that specifies conditions, i.e.
dates and values of the underlying variables, that trigger the payoffs and payments
made between the parties.

Over-the-counter Markets
OTC markets are not over the exchange transactions, they are done over a com-
puter network of dealers. Trades are done over the phone and are usually between
two financial institutions or between a financial institution and one of its clients.


Page 4

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