Library/CFA (Chartered Financial Analyst)/JuiceNotes 2024: Derivatives - Chartered Financial Analyst Level I/Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

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Arbitrage and the Law of One Price5 min

Arbitrage is described as a mechanism ensuring market efficiency by exploiting price discrepancies to earn riskless profits. The text highlights two main arbitrage arguments: the Law of One Price and the comparison of returns against the risk-free rate. The Law of One Price asserts that assets or portfolios with identical future payoffs must have the same current price. This is exemplified by the equation S + P = B + C, equating a portfolio of a Stock and Put option to a portfolio of a Bond and Call option. If these values diverge, an arbitrageur can buy the cheaper portfolio and sell the expensive one.

Key Points

Arbitrage is the earning of riskless profit.
Law of One Price: Identical cash flows must have the same price.
Equation: S + P = B + C (Protective Put = Fiduciary Call).
Arbitrage exists if a riskless portfolio yields more than the risk-free rate.

Replication5 min

Replication involves constructing a portfolio using the underlying asset and cash (via borrowing or lending) to mimic the cash flow profile of a derivative. The purpose of replication is to determine the fair price of a derivative; since the replicating portfolio and the derivative have the same payoff, they must have the same cost. This concept is foundational to pricing models and allows investors to exploit mispricing through arbitrage if the derivative's market price deviates from its replicated value.

Key Points

Replication recreates a derivative's cash flow.
Uses positions in the underlying asset and cash (borrowing/lending).
Prevents riskless arbitrage opportunities.
Eliminates mispricing by forcing price convergence.

Costs, Benefits, and Net Cost of Carry5 min

Owning an underlying asset incurs specific costs and generates benefits. Costs include storage, insurance, and the opportunity cost of capital. Benefits can be monetary, such as dividends or interest, or non-monetary, known as convenience yield. The concept of Net Cost of Carry is introduced to synthesize these factors. The notes define Net Cost of Carry as the Future Value of Benefits minus the Future Value of Costs. Consequently, the Net Cost of Carry is positive when benefits exceed costs, zero when they are equal, and negative when costs exceed benefits.

Key Points

Costs: Storage, Insurance, Opportunity cost.
Benefits: Monetary (Dividends/Interest), Non-monetary (Convenience yield).
Net Cost of Carry = FV Benefits - FV Costs (per source notes).
Positive Net Cost of Carry implies Benefits > Costs.
Negative Net Cost of Carry implies Benefits < Costs.

Questions

Question 1

What is the primary definition of arbitrage as provided in the reading?

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

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