Financial Engineering
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
3
4
5
6
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
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
3
4
5
6
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