Fixed Income: Valuing Bonds with Embedded Options

Question 1

Nominal / z-Spread / OAS (fixed income)
Benchmark / Compensation for risk

Answer 1

1. Nominal: T-yield curve / credit, liquidity, option (a one time view on the spread)
2. z-Spread: T-spot rate curve / credit, liquidity, option (the spread that when added to the treasury spot rate will make the bond’s value equal to the price of the bond)
3. Option-adjusted: T-spot rate curve / credit, liquidity

Question 2

Price of Callable Bond
Price of a Putable Bond

Answer 2

Callable Price = Price of Option Free Bond - Price of embedded call

Putable Price = Price of option free bond + price of embedded put

Question 3

Effective Bond Duration

Answer 3

Duration = (V₋ - V₊) / [2V₀(Δy)]

- used to value bonds with or without an option

Question 4

Effective Bond Convexity

Answer 4

Convexity = [V₋ + V₊ - 2V₀] / [2V₀(Δy)²]

Question 5

Most Appropriate Model for Valuing Models on Mortgage Backed Securities

Answer 5

Monte Carlo for bonds with options

Question 6

Bond Equivalent Yield

Answer 6

BEY = 2[(1+i)^n -1]

- i: interest rate per period… monthly would lead to an exponent of 6

Question 7

Appropriate Spread Measure for…

1. Callable corporate bonds and MBS
2. Credit card or autoloan ABS
3. Option free corporate bonds

Answer 7

1. Callable = Option adjusted/removed spread
2. Credit card or auto loan ABS = Z-spread
3. Option free corporate bonds = Z-spread

Question 8

Market Conversion Premium Per Share (convertible bond)

Answer 8

MCPPS = (Market price of bond / Conversion factor) - Market price of stock

• Bond = 950 / converts to 10 shares / stock trading at 50*
• MCPPS = (950/10) - 50 = $45*

Question 9

Steps to Value Bond (1 year) with %r Tree

Answer 9

1: Value of bond with up and down change in interest rate one period forward.
2. If value of bond in one branch is greater than callable value… use that
3. Add coupon payment(s) in branches
4. Discount at one-year treasury rate

[(V1+C$)/(1+%r) + (V2+C$)/(1+%r)] / 2

Question 10

Use OAS spread to determine of callable bond is over, under or fairly valued.

Answer 10

1. OAS is negative compared to corp spot rate curve = overvalued
2. OAS is zero compared to corp spot rate curve = Fairly valued
3. OAS is positive compared to corp spot rate curve = undervalued