4.

The use of multiple discount rates (a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in doing so, eliminate any (meaningful) arbitrage opportunities. That's why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.

To compute the value of a bond using spot rates, all you do is calculate the present value of each cash flow (coupon payment or par value) using a spot rate, and then add up the present values.

l: Explain how the process of stripping reconstitution forces the price of a bond toward its arbitrage-free value so that no arbitrage profit is possible.

It is possible to strip coupons from U.S. Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into U.S. Treasury coupon bonds. Therefore, such arbitrage arguments ensure that U.S. Treasury securities trade at or very near their arbitrage-free prices.

The determination of spot rates and the resulting term structure is usually done using risk-free (i.e., sovereign or Treasury) securities. These spot rates then form the basis for valuing non-Treasury securities denominated in the same currency. For example, you find spot rates in Japanese yen using Japanese government bonds, then use these to value non-Treasury securities denominated in yen.

Typically, this is accomplished by adding a credit spread to each treasury spot yield, then using the result to discount the bond's cash flows. The amount of the credit spread is a function of default risk and term to maturity of the cash flow. In other words: 1) the riskier the bond, the greater the spread, and 2) spreads are affected by time to maturity, meaning there is a term structure of credit spreads.

m: Explain how a dealer can generate an arbitrage profit, and compute the arbitrage profit if the market price of a bond differes from its arbitrage-free value.

Using data from LOS 1.A.k, there are three steps (the dollar amounts given are arbitrary):

Buy $1m of the 2-year 8% coupon bonds.

Sell $80,000 of the 1-year 0% coupon bonds at 96.154.

Sell $1.08m of the 2-year 0% coupon bonds at 85.734.

The result is that you receive $2,850.40 (positive income today) in return for no future obligation—an arbitrage opportunity. The selling of the 2-year zeros would force the price down to 85.469% (the price at which the YTM = 8.167%), at which point the arbitrage would cease to exist. 

n: Explain the basic features common to valuation models that can be used to value bonds with embedded options.

The use of multiple discount rates (a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in doing so, eliminate any (meaningful) arbitrage opportunities. That's why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.

To compute the value of a bond using spot rates, all you do is calculate the present value of each cash flow (coupon payment or par value) using a spot rate, and then add up the present values.

l: Explain how the process of stripping reconstitution forces the price of a bond toward its arbitrage-free value so that no arbitrage profit is possible.

It is possible to strip coupons from U.S. Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into U.S. Treasury coupon bonds. Therefore, such arbitrage arguments ensure that U.S. Treasury securities trade at or very near their arbitrage-free prices.

The determination of spot rates and the resulting term structure is usually done using risk-free (i.e., sovereign or Treasury) securities. These spot rates then form the basis for valuing non-Treasury securities denominated in the same currency. For example, you find spot rates in Japanese yen using Japanese government bonds, then use these to value non-Treasury securities denominated in yen.

Typically, this is accomplished by adding a credit spread to each treasury spot yield, then using the result to discount the bond's cash flows. The amount of the credit spread is a function of default risk and term to maturity of the cash flow. In other words: 1) the riskier the bond, the greater the spread, and 2) spreads are affected by time to maturity, meaning there is a term structure of credit spreads.

m: Explain how a dealer can generate an arbitrage profit, and compute the arbitrage profit if the market price of a bond differes from its arbitrage-free value.

Using data from LOS 1.A.k, there are three steps (the dollar amounts given are arbitrary):

Buy $1m of the 2-year 8% coupon bonds.

Sell $80,000 of the 1-year 0% coupon bonds at 96.154.

Sell $1.08m of the 2-year 0% coupon bonds at 85.734.

The result is that you receive $2,850.40 (positive income today) in return for no future obligation—an arbitrage opportunity. The selling of the 2-year zeros would force the price down to 85.469% (the price at which the YTM = 8.167%), at which point the arbitrage would cease to exist. 

n: Explain the basic features common to valuation models that can be used to value bonds with embedded options.