Duplication principle

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In financial market theory, the duplication principle describes the synthetic creation of a portfolio that generates the same cash flows as the security to be duplicated. It plays a role particularly in trading and the valuation of derivatives . A distinction is made between static and dynamic duplication.

The requirement that the duplication portfolio must generate the same series of payments as the duplicated instrument, if the freedom from arbitrage is valid , means that portfolio and security have the same value at all times. In order to be able to duplicate any securities, there must be the possibility of being able to sell stocks short and to be able to borrow and invest money risk-free at a uniform interest rate . Since derivatives are usually duplicated with a specific maturity date, the duplication also has a finite time horizon. The following applies to the duplication of bonds:

Duplication principle : create a portfolio of other investments that will make the same payments as the bond at all future points in time.

Static duplication

When it comes to duplication, a distinction is made between static and dynamic duplication. For example , an index certificate on a stock index can be statically duplicated by buying all stocks in the index for the corresponding shares. The portfolio only needs to be adjusted if the weights in the index change, but often not during the term of the index certificates until the due date.

Dynamic duplication

In the case of options and other derivatives, however, a dynamic trading strategy as duplication is necessary, since the price of an option does not develop linearly to the price of other securities. It is therefore necessary to constantly adjust the portfolio so that it can at least track the price movement of the derivative at the relevant point in time. Key figures such as delta , gamma and vega are often used for dynamic duplication (see also option ). These ratios are calculated for the derivative to be duplicated and for the individual securities in the portfolio. The portfolio is then put together in such a way that the individual key figures of the derivative and the portfolio are the same. Since the key figures of the derivative are constantly changing, the portfolio must be adjusted regularly.