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31 Cards in this Set

  • Front
  • Back

Price of T-Period Zero Coupon Bond

Forward price of zero coupon bond

k period bond exchanged at time j

k period bond exchanged at time j

Forward pricing model


Forward Rate Model

Riding the Yield Curve

Buying longer maturity bonds and selling them before maturity to profit on the difference in yield. Better than buying a shorter term bond and holding till maturity

Swap Spread

Spread Spread = swap rate - treasury yield




Swap rate is the fixed rate someone must receive to pay the floating libor rate in exchange

TED Spread

3-month Libor Rate - 3-month T-bill Rate

Libor-OIS Spred

Libor Rate - overnight indexed swap rate

Term Structure of Interest Rates

Unbiased (pure) expectations theory


Local expectations theory


Liquidity preference theory


Segmented markets theory


Preferred habitat theory

Modern term structure models

Cox-Ingersoll-Ross: dr = a(b-r)dt + sigmasqrt(r)dz


Vasicek model: dr = a(b-r)dt + sigmadz


Ho-Lee Model: dr = thetadt + sigmadz

Managing Yield Curve Shape Risk

Yield Volatility

Long Term <-- Uncertainty regarding the real economy and inflation




Short Term <-- Uncertainty regarding economic policy




Long term vol generally < short term vol

Value of options

Value of a call option = Value of straight bond - value of callable bond




Value of put option = Value of putable bond - value of straight bond

Higher interest rate volatility increases

Value of call option increases




Value of put option increases




Value of callable bond decreases (issuer is more protected from volatility)




Value of putable bond increases

Upward sloping yield curve

Results in lower call value and higher put value

Effective duration

ED (Callable Bond) < ED (Straight Bond)


ED (Putable Bond) < ED (Straight Bond)


ED (zero-coupon) ~ maturity of the bond


ED (Fixed Rate Bond) < maturity of the bond

One sided durations

Callables have lower down-duration




Putables have lower up-duration

Minimum value of convertible bond

greater of conversion rate or straight value

Conversion value

market price of stock x conversion ratio

Market Conversion Price

Market Price of convertible bond


-------------------------------------------------


conversion ration

Market Conversion premium per share

Market conversion price - stock's market price

Market Conversion Premium Ratio

Market Conversion premium per share


--------------------------------------------------------


market price of common stock

Premium over straight value

market price of convertible bond


---------------------------------------------- - 1


Straight value

Callable and Putable Bond Value

Straight Value of bond


+ value of call on stock


- value of call option on bond


+ value of put option on bond

Recovery Rate

% of money received upon default




money received over money owed

Loss given default (%)

100 - recovery rate

Expected Loss

probability of default x loss given default

Present value of expected loss

Risky Bond Value - risk free bond value

Corporate Credit Risk

value of risky debt = value of risk free debt - value of put option on company's assets




equity = European call on company asset's

Reduced Form Models

Impose assumptions on the output of a structural model

Credit Analysis of ABS

ABS do not default but lose value w/ defaults




Modeled w/ probability of loss, loss give default, expected loss, present value of the loss