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Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 6

The Wide World of Futures Contracts

YTF

註解

Please read and understand slides 2 to slides 6 (inclusive).

Copyright © 2009 Pearson Prentice Hall. All rights reserved. 6-2

• Widely used to hedge against changes in exchange rates

• WSJ listing

Currency Contracts

Figure 6.1 Listings for various currency futures contracts from the Wall Street Journal, August 10, 2007.


Currency Contracts: Pricing

• Currency prepaid forward– Suppose you want to purchase ¥1 one year from today

using $s–

• Where x0 is current ($/ ¥) exchange rate, and ry is the yen-denominated interest rate

• Why? By deferring delivery of the currency one loses interest income from bonds denominated I that currency

• Currency forward–

• r is the $-denominated domestic interest rate• F0, T > x0 if r > ry (domestic risk-free rate exceeds

foreign risk-free rate)

FP0,T = x0e

−ryT

F0,T = x0e(r− ry )t


Currency Contracts: Pricing (cont’d)

• Example 6.1– ¥-denominated interest rate is 2% and current ($/ ¥)

exchange rate is 0.009. To have ¥1 in one year one needs to invest today

• 0.009/¥ x ¥1 x e-0.02 = $0.008822

• Example 6.2– ¥-denominated interest rate is 2% and $-denominated

rate is 6%. The current ($/ ¥) exchange rate is 0.009. The 1-year forward rate

• 0.009e0.06-0.02 = 0.009367


Covered Interest Arbitrage

Synthetically creating a yen forward contract by borrowing in dollars and lending in yen. The payoff at time 1 is ¥1−$0.009367.


Eurodollar Futures

• WSJ listing• Contract SpecificationsFigure 6.2 Listing for interest rate futures contracts, including the 1-month LIBOR and 3-month Eurodollar contracts, from the Wall Street Journal, August 10, 2007.

Figure 6.3 Specifications for the Eurodollar futures contract.


Introduction to Commodity Futures

• Different commodities have their distinct forward curves, reflecting different properties of

– Storability– Storage costs– Production– Demand


The Commodity Lease Rate

• The lease rate is the difference between the commodity discount rate, α, and the expected growth rate of the commodity price, g

• For a commodity owner who lends the commodity, the lease rate islike a dividend

– With the stock, the dividend yield, δ, is an observable characteristic of the stock

– With a commodity, the lease rate, δl, is income earned only if the commodity is loaned. It is not directly observable, except if there is a lease market

δ l = α − g


Forward Prices and the Lease Rate

• The lease rate has to be consistent with the forward price

• Therefore, when we observe the forward price, we can infer what the lease rate would have to be if a lease market existed

• The annualized lease rate

• The effective annual lease rate

δ l = r −1T

In (F0,T / S)

δ l =(1+ r)

(F0,T / S)1/T −1


The Commodity Lease Rate

• Contango occurs when the lease rate is less than the risk-free rate

• Backwardation occurs when the lease rate exceeds the risk-free rate


Energy Futures

• Corn, electricity, natural gas, and oil all have distinctforward curves, reflecting the different characteristics of their physical markets.

• When there are seasonalities in either the demand or supply of a commodity, the commodity will be stored (assuming this is physically feasible), and the forward curve for the commodity will reflect storage costs.


Electricity

• Because electricity cannot be stored,its price is set by demand and supply at a point in time.

Table 6.2 Day-ahead price, by hour, for 1 megawatt-hour of electricityin New York City, October 1, 2007.


Natural Gas

• The natural gas futures contract is one of the most heavily traded futures contracts in the United States.

Figure 6.5 Listing for the NYMEX crude oil, heating oil, gasoline, and natural gas futures contracts from the Wall Street Journal, August10, 2007.


Crude Oil

• Both oil and natural gas produce energy and are extracted from wells, but the different physical characteristics and uses of oil lead to very different forward prices than for gas.

Figure 6.7Specifications for the NYMEX light sweet crudeoil contract.


Weather Derivatives

• A heating degree-day is the maximum of zero and the difference between 65°F and the average daily temperature.

• A cooling degree-day is the maximum of zero and the difference between the average daily temperature and 65°F.


Table 6.3 Heating degree-day futures prices, October 1, 2007. Source: Chicago Mercantile Exchange

• In all three cities, the period December through February is expected to be the coldest, and the futures price rises with latitude.


Housing Futures

• Residential real estate futures, introduced by the CME in May 2006, are futures contracts that settle based on city-specific indexes of real estate prices.

• These contracts settle quarterly and are based on indexes constructed by S&P/Case-Shiller for 20 metropolitan areas in the United States.

Figure 6.8Specifications for the CME housing futures index contract.

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 6

Additional Art


Equation 6.1


Equation 6.2


Equation 6.3


Figure 6.4 A hypothetical forward curve for corn, assuming the harvest occurs at years0, 1, 2, etc.


Equation 6.4


Equation 6.5


Equation 6.6


Equation 6.7


Equation 6.8


Figure 6.6 Specifications for theNYMEX Henry Hub natural gas contract.


Equation 6.9


Table 6.4 Real estate futures prices for several cities, October 1, 2007.Source: Chicago Mercantile Exchange


Equation 6.10

m06 mcd 548160 01 pp c06 [唯讀] - stanford university...title: microsoft powerpoint -...

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