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 functions of one real variable, a random variable, and a constant.
Since the function is also increasing and maps onto, there is a unique solution to the equation
Since the functions are increasing:
In financial applications, each of the random variables represents an asset value, the number is the strike of the option on the portfolio of assets. We can therefore express the payoff of an option on a portfolio of assets in terms of a portfolio of options on the individual assets with corresponding strikes.
