Derivatives: Replication

If you take opposing positions in the underlying and a derivative, you create a hedge portfolio that is default risk-free and replicates the payoff to a risk-free asset. This means that combining the asset and borrowing or lending at the risk free rate can replicate the payoffs of the derivative. This is called __replication__, where you replicate the payoff to an asset or portfolio using other asset combinations. For example, think about the payoff to a long position in the underlying and borrowing the spot price of the underlying at the risk-free rate. What derivative position do you think that combination of assets replicates?

No, the payoff to an option is kinked at the strike price, but both borrowing at the risk-free rate and a long position in the underlying asset have linear payoffs.

No, a short forward contract has the payoff $$F_0(T) - S_T$$, where $$F_0(T)$$ is the forward price and $$S_T$$ is the value of the underlying asset at maturity.

The equations below summarize the combinations that can be used to replicate the payoff to the risk-free asset, derivative, and the underlying asset. The positive and negative signs reflect opposing positions. Asset + Derivative = Risk-Free Asset Asset - Risk-Free Asset = - Derivative Derivative - Risk-Free Asset = - Asset Why do you think it is useful for an investor to be able to replicate the payoff to an asset using combinations of other assets?

Correct. By the law of one price, two portfolios with the same payoffs should have the same price. If this law is violated then an investor could make an arbitrage profit by entering into a long position in the underpriced asset and a creating a short position using asset combinations. Even if all assets are correctly priced, why do you think being able to replicate asset positions is useful for an investor?

No, since the combination of assets and the replicated asset have the same payoff, they have equal risk.

No, having to buy multiple assets instead of one will likely generate higher, not lower transaction costs.

No, the levered nature of derivative positions makes them very capital efficient. Replicating a position with two assets is more capital intensive. Determining the price of derivatives can be difficult. If the derivative position can be replicated with two assets with known value, then the value of the derivative can be inferred as being the same since it has the same payoff.

Correct. Determining the price of derivatives can be difficult. if the derivative position can be replicated with two assets with known value, then the value of the derivative can be inferred as being the same since it has the same payoff. The levered nature of derivative positions makes them very capital efficient. Replicating a position with two assets is more capital intensive.

To summarize this lesson: [[summary]]

Correct, well done. The payoff to a long forward position is $$S_T - F_0(T)$$, where $$F_0(T)$$ is the forward price and $$S_T$$ is the value of the underlying asset at maturity. The long position in the underlying will be worth $$S_T$$ in the future, and the spot price compounded by the risk-free rate is the forward price in the contract.

A long contract option position

A short forward contract position

A long forward contract position

Realize arbitrage profit

Reduce risk

Reduce transaction costs

Conserve capital while realizing an identical payoff

Method to determine derivative price

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