In mathematical financea replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties especially cash flows. This is meant in two distinct senses: Dynamic replication requires continual adjustment, as the asset and portfolio are only assumed to behave similarly at a single point mathematically, their partial derivatives are equal at a single point.

Given an asset or liability, an offsetting replicating portfolio a " hedge " is called a static hedge or dynamic hedgeand constructing such a portfolio by selling or purchasing is called static hedging or dynamic hedging. The notion of a replicating portfolio is fundamental to rational pricingwhich assumes that market prices are arbitrage-free — concretely, arbitrage opportunities are exploited by constructing a replicating portfolio.

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In practice, replicating portfolios are seldom, if ever, exact replications. Most significantly, unless they are claims against the same counterpartiesthere is credit risk. Further, dynamic replication is invariably imperfect, since actual price movements are not infinitesimal — they may in fact be large — and transaction costs to change the hedge are not zero.

Dynamic replication is fundamental to the Black—Scholes model of derivatives pricingwhich assumes that derivatives can be replicated by portfolios of other securities, and thus their prices determined. See explication under Rational pricing The replicating portfolio. In limited cases static replication is sufficient, notably in put—call parity.

An important technical detail is how cash is treated. Most often one considers a self-financing portfoliowhere any required cash such as for stock broker nashville tn payments is borrowed, binary options fixed odds financial bets download game excess cash is loaned.

In the valuation of a life insurance company, the actuary considers a series of future uncertain cashflows including incoming premiums and outgoing claims, for example and attempts to put a value on these cashflows.

There are many ways of calculating such a value such as a net premium valuationbut these approaches are often arbitrary in free day trading simulators online the interest rate chosen for discounting is itself rather arbitrarily chosen. One possible approach, and one that is gaining increasing attention, is the use of replicating portfolios or hedge portfolios.

The theory is that we can choose a call option cash flow hedge of assets fixed interest bonds, zero coupon bonds, index-linked bonds, etc. Such a construction, which requires only fixed-income securities, is even possible for participating contracts at least when bonuses are based on the performance call option cash flow hedge the backing assets.

The proof relies on a fixed point argument.

Valuing options and guarantees can require complex nested stochastic calculations. Replicating portfolios can be set up to replicate such options and guarantees. It may be easier to value the replicating portfolio than to value the underlying feature options and guarantees.

For example, bonds and equities can be used to replicate a call option. For additional information on economic valuations and replicating portfolios can be found here: The Economics of Insurance. From Wikipedia, the free encyclopedia.

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