תמחור חוזים עתידיים וחוזה החלף

1. תמחור חוזים עתידיים וחוזה החלף

2. Stock Index Futures • The most active contract is the S&P500 futures contract traded on the CME, where the contract notional is defined as $250 times the index level. • If we actually invested in the S&P500 index, our rate of return would be higher than the index, because we would receive the cash dividends. • The pricing formula is derived by the no-arbitrage argument, using a strategy composed of buying the Index , selling a futures contract, and borrowing. such that the net investment is zero

3. If we have annualized and continuing compounded dividend and interest:

4. Numerical Example Suppose the NISE Index closed at 342. If dividend yield is 2% and the current risk-free interest rate is 4%, what is the equilibrium value of a six-month futures contract on the NYSE Index? Assume that the futures contract is traded at $347, show arbitrage strategy!

6. Currency Futures • Currency futures contracts are used by firms having exposure to foreign exchange risk. • For example, a Israeli firm sell its goods in US and therefore receives USD in exchange for its product. • To minimize the effect of FX risk on the value of the product sold, the firm may enter into a futures contract to sell USD in the future with predetermined NIS/$ exchange rate.

7. If we have annualized and continuing compounded interest:

8. Numerical Example Suppose you are an arbitrage trader in the Swiss franc foreign exchange rate. You observe the following information: Are these prices in equilibrium?How will you profit if they are not? The equilibrium futures price should be:

9. Thus, the current future price is lower than the equilibrium price.

10. Numerical Example Assume that the British pound Des 2004 futures contract settled at $1.6664/£ and Mar 2005 contract settled at $1.6604/£What is the implied interest rate difference between the pound and dollar?

12. Commodity Futures • To price commodity futures, we need to consider storage costs and insurance costs. • The pricing formula is derived by using a strategy composed of buying the asset , selling a futures contract, and borrowing.

13. Numerical Example Assume that the spot price of gold is $340 per ounce and the one year futures price is $357. If the risk-free interest is 3%, what is the implied storage cost for gold in percent?

14. Swap Contracts • Swap contracts are OTC agreements to exchange a series of cash flow according to some pre-specified terms. • The underlying asset can be : • an interest rate, an exchange rate, an equity, a commodity price or any other index. • The most common swap contracts are: an Interest Rate Swap (IRS), a Foreign Exchange Swap (FES) and a Credit Default Swap (CDS)

15. Interest Rate Swap • Consider the case of a firm that has issued long term bonds with total par value of $10M at a fixed interest rate of 8%. However, it can change the nature of its obligation from fixed rate to floating rate by entering a swap agreement to pay a floating rate and to receive a fixed rate. • A swap with notional principle of $10M that exchanges LIBOR for an 8% fixed rate: • $800K ↔ $10M * rLIBOR • Suppose that the swap is for three years and the LIBOR rates turns out to be 7%, 8% and 9% in the next three years

16. $900K $800K $700K Floating rate payments Fixed rate payments $800K $800K $800K LIBOR 7% 8% 9%

17. IRS - Pricing • A swap contract can be viewed as a portfolio of forward transactions, but instead of each transaction being priced independently, on forward price is applied to all of the transactions. • The Yield and the Forward Curve

18. F* – Fixed rate yt, is the appropriate yield from the yield curve for discounting dollars cash flows.

19. IRS – Quotations • Swaps are quoted in terms of spreads relative to the yield of similar-maturity Treasury notes. • For instance, a dealer quote 10 years swap rates as 31/35bp against LIBOR. • If the current note yield is 7%: • The dealer is willing to pay 7%+0.31%=7.31% against receiving LIBOR and to receive 7%+0.35%= 7.35% against paying LIBOR.

20. Interest Rate Swap – Motivation Consider two firms, A and B that can raise funds either at fixed or floating rates, $100M over 10 years. A want to raise floating and B want to raise fixed. Cost of Capital Comparison

21. Interest Rate Swap – Motivation • Firm A has an absolute advantage in both markets • However, it has a comparative advantage in raising fixed • If both will directly issue funds in their desired market, the total cost: LIBOR+0.3% (for A) + 11.2% (for B) = LIBOR + 11.5% • If they will raise funds where each has a comparative advantage, the total cost: 10% (for A) + LIBOR+ 1% (for B) = LIBOR + 11%. • Thus, the gain to both firms from entering a swap is: • 11.5%-11%= 0.5%.

22. A swap that splits the benefit equally between the two parties: Swap to firm A Firm A issues fixed debt at 10% and enters a swap whereby it promises to pay LIBOR+0.05% in exchange to receiving 10% fixed payments, which will offset the required debt payments.

23. A swap that splits the benefit equally between the two parties: Swap to firm B Firm B issues floating debt at LIBOR+1% and enters a swap whereby it promises to pay 10% fixed payments in exchange to receiving LIBOR+0.05%, which is less than the direct cost by 0.25%

24. Foreign Exchange Swap • Foreign Exchange Swaps are agreements between to parties to exchange currencies according to a pre-determined formula. • FES enable the firm to quickly and cheaply hedge its currency exposure. • For Instants, a U.S. firm sell its goods in UK and therefore receives British pound in exchange for its product. • To minimize the effect of FX risk on the value of the product sold, the firm may enter into a swap contract to sell British pound in the future with predetermined $/£ exchange rate.

25. Foreign Exchange Swap • A U.S. firm has a 3 years contract of selling goods to UK firm for £100M each year. The U.S. firm can enter to a FES whereby it promises to pay £100M in exchange to receiving $X. • The current exchange rate is: $1.8/£ • The term structure of US and UK interest rate

26. £100M £100M £100M $176M $176.6M $177.4M The Forward rates: Therefore,

27. Alternatively, we can calculate a constant rate of F* dollars per pound to be exchanged each year: where y1, y2 and y3 are the appropriate yields from the yield curve for discounting dollars cash flows.

28. £100M £100M £100M $176.65M $176.65M $176.65M In this case the swap agreement will be:

29. Credit Default Swap • In a credit default swap contract, a protection buyer pays a premium to the protection seller in exchange of payment if credit event – default - occurs. • Buyer Periodic Payment Seller • Contingent Payment • The contingent payment is triggered by a Credit Event on the underlying credit • Investing in a risky bond is equivalent to investing in a risk-free bond plus selling a credit default.

30. Numerical Example • A protection buyer enters a 1-year CDS on a notional of $100M worth of 10-year bonds issued by XYZ. The swap entails an annual payment of 50bp. • At the beginning of the year, the buyer pays $500K to the protection seller. • At the end of the year, XYZ defaults on this bond, which now traded at 40% of the notional value (Recovery Rate) The seller has to pay $60M (Loss Given Default).