1. http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 FRM Zvi Wiener Following P. Jorion, Financial Risk Manager Handbook Financial Risk Management

2. http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 FRM Chapter 5 Introduction to Derivatives Following P. Jorion 2001 Financial Risk Manager Handbook

3. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 3 Derivatives Financial instruments whose value is derived from some underlying risk factors (asset price, index, etc.). Global Derivatives market had $102T notional in December 1999 (only $14T on exchanges). Securities are usually issued to raise capital. Derivatives are contracts, or private agreements that mainly transfer risk (usually zero-sum game).

4. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 4 Global Derivatives Markets 1999 IR contracts60,091 FRAs6,775 Swaps43,936 Options9,380 FX contracts14,344 Forwards9,593 Swaps2,444 Options2,307 Equity-linked contr.1,809 Forw. and swaps283 Options 1,527 Commodity contr.548 Others11,408 OTC Instruments $88T Exchange traded $13.5T IR contracts11,669 Futures7,914 Options3,756 FX contracts59 Futures37 Options22 Stock-index contr.1,793 Futures 334 Options 1,459 Source BIS World GDP in 99 = 30,000B All stocks and bonds = 70,000 Liquidation value = 2,800B

5. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 5 Forward Contracts Spot - an immediate transaction (T+2 or T+1w). Forward transaction. Long side - who buys the underlying asset, short - seller. Some have physical delivery, others - cash settlement.

6. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 6 t - current time T - delivery time  = T - t, time to maturity S t - current spot price of the asset F t (T) - current forward price for delivery at T V t - value of the contract r t (T) - risk-free rate for delivery at T r t * (T) - foreign rate or dividend n - number of units of the contract face value = notional amount = principal = nF

7. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 7 Valuing Forwards F t e -r  = S t - PV(D) F t e -r  = S t e -r* , interest rate parity V t = S t e -r*  - F t e -r  value of a contract

8. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 8 FRM 99-31 8-month forward contract on a stock with a price of $98/share. The firm is expected to pay a $1.8/share dividend in 4 months. Riskless zero coupon interest rate (continuously compounded) is 4% for maturities of up to 6 months and 4.5% for maturity of 8 months. The forward price is: A. $99.15 B. $99.18 C. $100.98 D. $96.20

9. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 9 FRM 99-31 8-month forward contract on a stock with a price of $98/share. The firm is expected to pay a $1.8/share dividend in 4 months. Riskless zero coupon interest rate (continuously compounded) is 4% for maturities of up to 6 months and 4.5% for maturity of 8 months. The forward price is: A. $99.15, F=(98-1.8e -0.04/3 )e 0.045*8/12 B. $99.18 C. $100.98 D. $96.20

10. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 10 Futures Contracts Similar to forwards but are standardized, negotiable, and exchange-traded. Clearinghouse, marking-to-market, and margins

11. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 11 Convexity Adjustment Relevant for interest rate futures Forward rate = Futures rate - 0.5  2 t 1 t 2 here  is the volatility of the short term rate, t 1 is maturity of the futures contract, t 2 is maturity of the underlying bond.

12. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 12 FRM 00-7 For assets that are strongly positively correlated with interest rates, which one of the following is true? A. Long-dated forward contracts have higher prices than long-dated futures contracts. B. Long-dated futures contracts have higher prices than long-dated forward contracts. C. Prices of forwards and futures are always the same. D. The convexity effect can be ignored for long- dated contracts in this case.

13. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 13 FRM 00-7 For assets that are strongly positively correlated with interest rates, which one of the following is true? A. Long-dated forward contracts have higher prices than long-dated futures contracts. B. Long-dated futures contracts have higher prices than long-dated forward contracts. C. Prices of forwards and futures are always the same. D. The convexity effect can be ignored for long- dated contracts in this case.

14. http://pluto.huji.ac.il/~mswiener/zvi.htmlZvi Wiener slide 14 Swaps Can be viewed as a portfolio of forwards Interest rate swap Currency swap Index amortizing (or accreting) swaps. Asset swaps