This paper examines the contribution of Leonardo of Pisa [Fibonacci] to the history of financial mathematics. Evidence in Leonardo's Liber Abaci (1202) suggests that he was the first to develop present value analysis for comparing the economic value of alternative contractual cash flows. He also...

History is important to the study of financial bubbles precisely because they are extremely rare events, but history can be misleading. The rarity of bubbles in the historical record makes the sample size for inference small. Restricting attention to crashes that followed a large increase in...