FIBI

1
Fixed Income Instruments 6

• Zvi Wiener
• 02-588-3049
• mswiener_at_mscc.huji.ac.il

2
IR derivatives

• Forward and Futures
• Options
• Caps, Floors
• Swaps
• Structured notes
• Hedging
• Mathematical models

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Interest rate futures

• Legal agreement
• settlement, delivery date
• quantity and quality of deliverable asset
• futures price (it is NOT a price!)
• long and short positions
• margin requirements

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Margin requirements

• Initial margin
• Maintenance margin - margin call trigger
• Variation margin - after a margin call
• Mark to market procedure reduces counterparty
  risk!

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Marking to Market
Your balance
Initial margin
Maint. margin
margin call
time
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Futures Contract

• T-Bills
• T-Notes
• T-Bonds
• notional is typically 100,000
• deliverable bond is unknown, CTD option
• timing option (during the delivery month)
• wild card option

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Options

• This type of contract is an obligation of one
  side only, but it requires a payment to purchase
  the right to choose.

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Call Value before Expiration
E. Call
X Underlying
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Put Value before Expiration
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IR Options

• Call
• Put
• European
• American
• Bermudian
• Exotic Asian, Digital, Knock-In, Knock-Out, path
  dependent and multiple asset options.

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Various IR Options

• Futures options
• Caps
• Floors
• Exchange options
• Swaptions

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Cap

• Is priced as a sequence of caplets

cap
time
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Floor
floor
time
14
Collar
cap
floor
time
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Option pricing

• Time value, intrinsic value
• underlying
• time to maturity
• interest rates
• strike
• coupons
• volatility

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Swaps

• Currency swap
• Interest rate swap
• Amortizing swap
• Swaption

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Currency swap
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Currency Swap
10,000Y
300Y 300Y 300Y 300Y 300Y 300Y
5 5 5 5 5 5
100
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IR swap
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IR Swap
100
3 3 3 3 3 3
L1 L1 L1 L1 L1 L1
100
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IR Swap
L1 L1 L1 L1 L1 L1
100
a regular LIBOR loan for one year!
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Term Structure Models

• Binomial trees
• Short-term based analytical models
• LIBOR based analytical models
• Multi-factor models
• Simulations

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Binomial Trees
6
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Interest rates
6
Bond prices
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Typical yield curves
yield
time to maturity
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Analytic Term Structure Models
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Analytic Term Structure Models

• Hull, White
• Black-Karasinsky
• Black-Derman-Toy
• Heath-Jarrow-Morton
• Affine TS modles
• Gaussian models

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Arithmetic BM dX ? dt ? dW
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Geometric BM dX ?Xdt ?XdW
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Mean Reverting Process dX ?(?-X)dt ?X?dW
X
?
time
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Ho and Lee Model

• Rates are normally distributed.
• All rates have the same variability.
• The model has an analytic solution.

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Bond Prices under Ho and Lee

• Where

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Option Prices under Ho and Lee

• A discount bond matures at s, a call option
  matures at T

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Monte Carlo
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Monte Carlo Simulation
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Callable Bond
Straight Debt
Payoff
Callable Bond
Debt
Value of the firms call option
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Convertible Bond
Stock
Payoff
Convertible Bond
Straight Bond
Stock
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Protective Put
Payoff
Protective Put
X
Put
Stock
X Underlying
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Covered Call
Stock
Payoff
X
Covered Call
X
Written Call
40
Straddle
Payoff
X
Call
Straddle
Put
X