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Subject 1. Principles of Arbitrage-Free Pricing and Valuation of Forward Commitments PDF Download
Pricing vs. Valuation

A forward contract price is the fixed price or rate at which the transaction scheduled to occur at expiration will take place. This price is agreed on the contract initiation date, and is commonly called the forward price or forward rate. Price is different from value, which is what you can sell something for or what you must pay to acquire something.

  • Pricing means determining the forward price or forward rate.

  • Valuation is the process of determining the value of an asset or service. It means determining the amount of money one would need to pay or would expect to receive to engage in the transaction. For example, if one already held a position, valuation would mean determining the amount of money one would either pay or expect to receive in order to get out of the position.

The Non-Arbitrage Approach

The arbitrageur abides by two fundamental rules:

  • Do not use your own money.
  • Do not take any price risk.

The non-arbitrage approach is based on the law of one price. If two securities have the same future cash flows, they should have the same current price. Forward commitments are generally priced so no arbitrage profits are possible.

Key assumptions:

  • Replicating instruments are identifiable and investable.
  • Market frictions are nil.
  • Short selling is allowed with full use of proceeds.
  • Borrowing and lending is available at a known risk-free rate.

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