Jamshidian's trick

Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989.

The trick relies on the following simple, but very useful mathematical observation. Consider a sequence of monotone (increasing) functions ${\displaystyle f_{i}}$ of one real variable (which map onto ${\displaystyle [0,\infty )}$), a random variable ${\displaystyle W}$, and a constant ${\displaystyle K\geq 0}$.

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