Zvi Wiener

1
Financial Risk Management

• Zvi Wiener
• Following
• P. Jorion, Financial Risk Manager Handbook

2
Chapter 5Introduction to Derivatives

• Following P. Jorion 2001
• Financial Risk Manager Handbook

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).

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Global Derivatives Markets 1999
OTC Instruments 88T
Exchange traded 13.5T

• IR contracts 60,091
• FRAs 6,775
• Swaps 43,936
• Options 9,380
• FX contracts 14,344
• Forwards 9,593
• Swaps 2,444
• Options 2,307
• Equity-linked contr. 1,809
• Forw. and swaps 283
• Options 1,527
• Commodity contr. 548
• Others 11,408

IR contracts 11,669 Futures 7,914 Options 3,756
FX contracts 59 Futures 37 Options 22 Stock-in
dex contr. 1,793 Futures 334 Options 1,459
World GDP in 99 30,000B All stocks and bonds
70,000 Liquidation value 2,800B
Source BIS
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Forward Contracts

• Spot - an immediate transaction (T2 or T1w).
• Forward transaction.
• Long side - who buys the underlying asset, short
  - seller.
• Some have physical delivery, others - cash
  settlement.

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• t - current time
• T - delivery time
• ? T - t, time to maturity
• St - current spot price of the asset
• Ft(T) - current forward price for delivery at T
• Vt - value of the contract
• rt(T) - risk-free rate for delivery at T
• rt(T) - foreign rate or dividend
• n - number of units of the contract
• face value notional amount principal nF

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Valuing Forwards

• Ft e-r? St - PV(D)
• Ft e-r? St e-r?, interest rate parity
• Vt St e-r? - Ft e-r? value of a contract

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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

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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)e0.0458/12
• B. 99.18
• C. 100.98
• D. 96.20

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Futures Contracts

• Similar to forwards but are standardized,
  negotiable, and exchange-traded.
• Clearinghouse, marking-to-market, and margins

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Convexity Adjustment

• Relevant for interest rate futures
• Forward rate Futures rate - 0.5 ?2 t1 t2
• here ? is the volatility of the short term rate,
• t1 is maturity of the futures contract,
• t2 is maturity of the underlying bond.

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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.

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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.

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Swaps

• Can be viewed as a portfolio of forwards
• Interest rate swap
• Currency swap
• Index amortizing (or accreting) swaps.
• Asset swaps