Not to forex uncovered confused with Arbitration. The term is mainly applied to trading in financial instruments, such as bonds, stocks, derivatives, commodities and currencies.
Arbitrage” is a French word and denotes a decision by an arbitrator or arbitration tribunal. If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium, or arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. This refers to the method of valuing a coupon-bearing financial instrument by discounting its future cash flows by multiple discount rates. By doing so, a more accurate price can be obtained than if the price is calculated with a present-value pricing approach. Arbitrage-free pricing is used for bond valuation and to detect arbitrage opportunities for investors.
For the purpose of valuing the price of a bond, its cash flows can each be thought of as packets of incremental cash flows with a large packet upon maturity, being the principal. Since the cash flows are dispersed throughout future periods, they must be discounted back to the present. In the present-value approach, the cash flows are discounted with one discount rate to find the price of the bond. In arbitrage-free pricing, multiple discount rates are used.
The present-value approach assumes that the yield of the bond will stay the same until maturity. This is a simplified model because interest rates may fluctuate in the future, which in turn affects the yield on the bond. The discount rate may be different for each of the cash flows for this reason. Each cash flow can be considered a zero-coupon instrument that pays one payment upon maturity. The ideas of using multiple discount rates obtained from zero-coupon bonds and discount a similar bonds cash flow to find its price is derived from the yield curve.
The yield curve is a curve of the yields of the same bond with different maturities. This curve can be used to view trends in market expectations of how interest rates will move in the future. In arbitrage-free pricing of a bond, a yield curve of similar zero-coupon bonds with different maturities is created. Since the yield curve displays market expectations on how yields and interest rates may move, the arbitrage-free pricing approach is more realistic than using only one discount rate. Investors can use this approach to value bonds and find mismatches in prices, resulting in an arbitrage opportunity.
Investor goes short the bond at price at time t1. Investor goes long the zero-coupon bonds making up the related yield curve and strip and sell any coupon payments at t1. 1 the price spread between the prices will decrease. At maturity the prices will converge and be equal.
Investor exits both the long and short position, realizing a profit. If the outcome from the valuation were the reversed case, the opposite positions would be taken in the bonds. This arbitrage opportunity comes from the assumption that the prices of bonds with the same properties will converge upon maturity. This can be explained through market efficiency, which states that arbitrage opportunities will eventually be discovered and corrected accordingly. Two assets with identical cash flows do not trade at the same price.