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FIN 460 Chapter 18
Terms in this set (22)
Static Spread (Zero-Volatility Spread)
The constant spread above the Treasury spot curve that equates the calculated price of the security to the market price.
A measure of the spread that the investor would realize over the entire Treasury spot curve if the bond is held to maturity
Bonds that give the issuer the option to retire them at a stated amount prior to maturity.
Phenomenon caused by that the market will increasingly expect the bond to be redeemed at the call price as interest rates fall
Yield to worst (YTW)
YTW involves the calculation of YTC and YTP for every possible call or put date, and determining which of these results in the lowest expected return.
Least attractive yield option when bond has a call or put option.
Yield to Call (YTC)
The rate of return earned on a bond when it is called before its maturity date
Assumes that the investor will hold the bond to the assumed call date and that the issue will call the bond on that date
Occurs in mortgage-backed securities where duration shortens when rates fall and lengthens when rates rise.
Price appreciation will be less than the price depreciation for a large change in yield of a given number of basis points
Callable Bond Price Formula
Noncallable bond price - call option price
bonds with a provision that allows investors to sell them back to the company prior to maturity at a prearranged price
Putable Bond Price Formula
Nonputable bond price + put option price
Interest-Rate Tree (Lattice)
A graphical depiction of the one-period forward rates over time based on some assumed interest-rate model and interest-rate volatility
A probabilistic description of how interest rates can change over the life of a financial instrument being evaluated. Makes an assumption about the relationship between the level of short-term interest rates and interest-rate volatility
Binomial Interest-Rate Tree
-Set of possible interest rate paths
-Possible paths used to value bonds
Node - point in time when interest rates can take one of two possible paths
Interest rates - one period forward rates corresponding to nodal period
-Relationship among the sets of rates associated with each individual nodal period is a function of the interest rate volatility assumption of the model
-Values for on the run issues generated using an interest rate tree should prohibit arbitrage opportunities
-Value of on the run issue produced by interest tree must equal value of its market price.
-Maintain interest rate volatility
A model for pricing options in which the underlying price can move to only one of two possible new prices.
Valuation models that assume that interest rates can take on three possible rates in the next period
Lognormal Random Walk
Random process that assumes that a 1-year forward rate can evolve over time
Value of a Call Option Formula
Value of a noncallable bond - value of a callable bond
Value of a Put Option Formula
Value of a nonputable bond - value of a putable bond
Risk that the output of the model is incorrect because the assumptions upon which it is based are incorrect. Consequently, it is imperative that the results of a valuation model be stress tested for modeling risk by altering the assumptions
For a callable bond, a higher (lower) volatility assumption lowers (raises) its value. For a putable bond, a higher (lower) volatility assumption raises (lowers) its value
Option-Adjusted Spread (OAS)
-The constant spread added the int rate in every node of the interest rate tree that forces the model price to be equal to the market price.
-Is the 'spread' over Treas secs after removing option risk from cash flows.
All else equal you want to buy bonds with big _______ (big _____ implies low price).
Option Value in Spread Terms
Static spread - OAS
Linearly approximates change in bond price for 100 bp change in yield.
Measure of price sensitivity to changes in yield.
First derivative price/yield function.
Effective Duration = [V- - V+] / [2
V- : Bond price if yield decreases
V+ : Bond price if yield increases
V0: Current Bond Price
▲y : Change in yield (in decimal form)
Note: 1% = 0.01
Preferred measure because it gives a good approximation of interest rate sensitivity for both option-free bonds and bonds with embedded option.
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