Derivatives Models on Models

It is easy to forget that many of today's financial models are based on ancient models. For example, an important ingredient in the binomial tree model is Pascal's triangle and the binomial coefficient. The Chinese knew Pascal's triangle long before the Europeans. Figure 0.1 shows a drawing from Chu Shih-chien's book published in (1303). However reading Chinese from right to left we will see that he already in 1303 called this an ancient old method. Chu Shih-chien is actually referring to Yanghui (1261), even today the Chinese mathematical literature refer to this triangle as Yanghui's (or Yang Hui's) triangle. In India there is a book called “Bhagabati Sutra” published 300 years before the birth of Christ that indicates that already back then there was some knowledge of the binomial coefficient. Mahavira (circa 850 A.D.), writing in “Ganita Sara Sangraha” generalized the rule found in the Bhagabati Sutra.

The illustration to your left is an oil painting by Wenling Wang, a hedge fund artist in Greenwich Connecticut. She was inspired by the ancient Yanghui triangle, and the painting is full of ancient wisdom and mystery.

Figure 0.1: Drawing from Chu Shih-chien (1303)

Here together with Nassim Taleb and Benoit Mandelbrot