## Arbitrage spot rate

Once we have the spot rate curve, we can easily use it to derive the forward rates.The key idea is to satisfy the no arbitrage condition – no two investors should be able to earn a return from arbitraging between different interest periods.

Spot-Forward Arbitrage Example: More Realistic Case This is a revised version of the material on slide 13 of “Index Models and APT”. Suppose that the one year Canadian risk free interest rate is 4%, and that the one year U.K. risk free interest rate is 5%. Further assume that the spot exchange rate is £1 00 \$2 25, and that the Spot interest rate for maturity of X years refers to the yield to maturity on a zero-coupon bond with X years till maturity. They are used to (a) determine the no-arbitrage value of a bond, (b) determine the implied forward interest rates through the process called bootstrapping and (c) plot the yield curve. The discount rates used should be the rates of multiple zero-coupon bonds with maturity dates the same as each cash flow and similar risk as the instrument being valued. By using multiple discount rates, the arbitrage-free price is the sum of the discounted cash flows. Arbitrage-free price refers to the price at which no price arbitrage is Spot Rates, Forward Rates, and Bootstrapping. The spot rate is the current yield for a given term. Market spot rates for certain terms are equal to the yield to maturity of zero-coupon bonds with those terms. Generally, the spot rate increases as the term increases, but there are many deviations from this pattern. Despite the impeccable logic, interest rate arbitrage isn't without risk. The foreign exchange markets are fraught with risk due to the lack of cohesive regulation and tax agreements. In fact, some economists argue that covered interest rate arbitrage is no longer a profitable business unless transaction costs can be reduced to below-market rates. Arbitrage Futures Trading: Arbitrage Opportunities on Futures & Spot, Buying in one market and simultaneously selling in another market to make risk free profits, arbitrage opportunities in Near

## A better way to price the bonds is to discount each cash flow with the spot rate (zero coupon rate) for its respective maturity. This is called the arbitrage-free valuation approach. According to this approach the value of a Treasury bond based on spot rates must be equal to the sum of the present values of all cash flows.

Interest Rate Parity (IRP) in Spot vs. Forward. The interest rate parity is a theory which states that the difference between the interest rates of two countries is the same as the difference between the spot exchange rate and the forward exchange rate. This theory plays a major role in foreign exchange markets since it connects the dots An arbitrageur executes a covered interest arbitrage strategy by exchanging domestic currency for foreign currency at the current spot exchange rate, then investing the foreign currency at the foreign interest rate.Simultaneously, the arbitrageur negotiates a forward contract to sell the amount of the future value of the foreign investment at a delivery date consistent with the foreign Spot-Forward Arbitrage Example: More Realistic Case This is a revised version of the material on slide 13 of “Index Models and APT”. Suppose that the one year Canadian risk free interest rate is 4%, and that the one year U.K. risk free interest rate is 5%. Further assume that the spot exchange rate is £1 00 \$2 25, and that the Spot interest rate for maturity of X years refers to the yield to maturity on a zero-coupon bond with X years till maturity. They are used to (a) determine the no-arbitrage value of a bond, (b) determine the implied forward interest rates through the process called bootstrapping and (c) plot the yield curve.

### With the spot trade, the rollover interest will be realized daily and that can be reinvested. In a real scenario the nightly rollover interest would be lower to account for this reinvestment possibility. Swap rates would have broker markups added to them as well. Finding Interest Rate Arbitrage Opportunities

Forward and Spot Rates: No Arbitrage A forward rate constructed in this way is arbitrage free to the extent that any discrepancy between the prevailing forward at the future date 1 and the above calculated forward would raise risk-free profit opportunities. Spot interest rate for maturity of X years refers to the yield to maturity on a zero-coupon bond with X years till maturity. They are used to (a) determine the no-arbitrage value of a bond, (b) determine the implied forward interest rates through the process called bootstrapping and (c) plot the yield curve. A better way to price the bonds is to discount each cash flow with the spot rate (zero coupon rate) for its respective maturity. This is called the arbitrage-free valuation approach. According to this approach the value of a Treasury bond based on spot rates must be equal to the sum of the present values of all cash flows. With the spot trade, the rollover interest will be realized daily and that can be reinvested. In a real scenario the nightly rollover interest would be lower to account for this reinvestment possibility. Swap rates would have broker markups added to them as well. Finding Interest Rate Arbitrage Opportunities Currency Cross Rates and Triangular Arbitrage in the FX Spot Market. Cross rates are the exchange rates of 1 currency with other currencies, and those currencies with each other. Cross rates are equalized among all currencies through a process called triangular arbitrage. Below is a table of key cross rates of some major currencies.

### A better way to price the bonds is to discount each cash flow with the spot rate (zero coupon rate) for its respective maturity. This is called the arbitrage-free valuation approach. According to this approach the value of a Treasury bond based on spot rates must be equal to the sum of the present values of all cash flows.

An arbitrageur executes a covered interest arbitrage strategy by exchanging domestic currency for foreign currency at the current spot exchange rate, then investing the foreign currency at the foreign interest rate.Simultaneously, the arbitrageur negotiates a forward contract to sell the amount of the future value of the foreign investment at a delivery date consistent with the foreign Spot-Forward Arbitrage Example: More Realistic Case This is a revised version of the material on slide 13 of “Index Models and APT”. Suppose that the one year Canadian risk free interest rate is 4%, and that the one year U.K. risk free interest rate is 5%. Further assume that the spot exchange rate is £1 00 \$2 25, and that the Spot interest rate for maturity of X years refers to the yield to maturity on a zero-coupon bond with X years till maturity. They are used to (a) determine the no-arbitrage value of a bond, (b) determine the implied forward interest rates through the process called bootstrapping and (c) plot the yield curve.

## Arbitrage-Free Valuation: 1. The theoretical future price of a security or commodity based on the relationship between spot prices, interest rates, carrying costs , convenience yields , exchange

Arbitrage Futures Trading: Arbitrage Opportunities on Futures & Spot, Buying in one market and simultaneously selling in another market to make risk free profits, arbitrage opportunities in Near

Despite the impeccable logic, interest rate arbitrage isn't without risk. The foreign exchange markets are fraught with risk due to the lack of cohesive regulation and tax agreements. In fact, some economists argue that covered interest rate arbitrage is no longer a profitable business unless transaction costs can be reduced to below-market rates. Arbitrage Futures Trading: Arbitrage Opportunities on Futures & Spot, Buying in one market and simultaneously selling in another market to make risk free profits, arbitrage opportunities in Near Forward and Spot Rates: No Arbitrage A forward rate constructed in this way is arbitrage free to the extent that any discrepancy between the prevailing forward at the future date 1 and the above calculated forward would raise risk-free profit opportunities. Spot interest rate for maturity of X years refers to the yield to maturity on a zero-coupon bond with X years till maturity. They are used to (a) determine the no-arbitrage value of a bond, (b) determine the implied forward interest rates through the process called bootstrapping and (c) plot the yield curve.