Arbitrage Pricing

Arbitrage pricing determines the market price of financial securities given a risk-free "bank" that takes deposits and lends at a known interest rate.

Assumptions:  Bond A pays a risk-free \$1000 in one year.  Banks take deposits and make loans at a 10% interest rate.

Case 1:  The bond currently sells for \$900.  To secure immediate arbitrage profits, borrow 1000/1.10 = 909.09.  Buy the bond, and put a 9.09 arbitrage profit in your pocket.  In one year, you will receive 1000 from the bond, which will pay off what you owe the bank.

Case 2:  The bond currently sells for \$920.  To secure an immediate arbitrage profit, sell bonds at 920.  Put 909.09 of the proceeds in the bank at 10%, and put a 10.91 arbitrage profit in your pocket.  In one year, your bank account will contain 1000, which will just pay off the bondholder.

The arbitrage profit opportunity will exist unless the bond sells for \$909.09.  If the bank interest rate is fixed, efforts to secure infinite arbitrage profits will very quickly push the bond price to \$909.09.

See arbitrage profit.

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