Financial Engineering

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Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Introduction

Markus Leippold
University of Zurich

Chris Bardgett
University of Zurich

Elise Gourier
University of Zurich

Financial Engineering – September, 2012

Introduction 1 / 97

Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Outline

1

Historical Degression Setting the Stage No-Arbitrage Bounds Relations between Puts and Calls Itô Refresher Appendix*

2

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Introduction 2 / 97

Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Timeline

In Ancient Times “Deducing from his knowledge of the stars that there would be a good crop of olives, while it was still winter and he had a little money to spare, used it to pay deposits on all the oil-presses in Miletus and Chios, thus securing their hire. This cost him only a small sum, as there were no other bidders. Then the time of the olive-harvest came and, as there was a sudden and simultaneous demand for oil-presses, he hired them out at any price he liked to ask.” (Aristotle, The Politics, Book I,xi)

Thales of Miletus

Introduction 3 / 97

Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Timeline

How did we get here?
Risk and Chance in the Greek and Roman culture The Early Christianity: ”The good Christian should beware of mathematicians. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.” (Augustinus, 354 - 430)

“Secularization” of Chance
1494 Luca Paccioli and his “brainteaser” (1494) 1550 Cardano: “liber de ludo alea” 1654 Chevalier de Méré and the letters of Pascal and Fermat. 1686 Newton’s Infinitesimal Calculus 1731 Daniel Bernoulli “Specimen Theoriae Novae de Mensura Sortis” and the beginning of utility theory.

Introduction 4 / 97

Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Chevalier de Méré’s Problem
Example A 17th century gambler, the Chevalier de Méré, turned to Blaise Pascal for an explanation of his unexpected losses. Pascal teamed up with Pierre de Fermat and the two of them laid out mathematical foundations for the theory of probability. Gamblers in the 1717 France were used to bet on the event of getting at least one 1 (ace) in four rolls of a dice. As a more trying variation, two die were rolled 24 times with a bet on having at least one double ace. According to Chevalier de Méré, two aces in two rolls are 1/6 as likely as 1 ace in one roll. (Which is correct.) To compensate, de Méré thought, the two die should be rolled 6 times. And to achieve the probability of 1 ace in four rolls, the number of the rolls should be increased four fold - to 24. Thus reasoned Chevalier de Méré who expected a couple of aces to turn up in 24 double rolls with the frequency of an ace in 4 single rolls. However, he lost consistently.

Introduction 5 / 97

Historical Degression

Setting the Stage

No-Arbitrage Bounds

Relations between Puts and Calls

Itô Refresher

Appendix*

Timeline
South Sea Company
The South Sea Company was a British joint stock company that traded in South America during the 18th century. Founded in 1711, the company was granted a monopoly to trade in Spain’s South American colonies as part of a treaty during the War of Spanish Succession. In return, the company assumed the national debt England had incurred during the war. Speculation in the company’s stock led to a great economic bubble known as the South Sea Bubble in 1720, which caused financial ruin for many. “I can calculate the movements of heavenly...
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