Fixed Income #33 (All)

Question 1

Explain what is meant by arbitrage free valuation of a fixed income instrument.

Answer 1

(LOS 33.a)
Arbitrage-free valuation leads to a security value such that no market participant can earn an arbitrage profit in a trade involving that security.
- The valuation is consistent with the value additivity principle and without dominance of any security relative to others in the market.
- Arbitrage gain is a risk-free profit; hence requires no net investment
>The returns are not simply risk-free rate (as there is no initial investment, the gains cannot be measured as percentage of initial cost)

Question 2

Describe the process of calibrating a binomial interest rate tree to match a specific term structure.

Answer 2

(LOS33.e)
A binomial interest rate tree is calibrated such that:
(1) the values of benchmark bonds using the tree are equal to bond’s market prices
(2) adjacent forward rates at any nodal period are 2 S.D. apart
(3) The midpoint for each nodal period is approximately equal to the implied 1-period forward rate for that period

Question 3

Compare pricing using the zero-coupon yield curve with pricing using an arbitrage-free binomial lattice.

Answer 3

Valuation of bonds using a Zero-Coupon Yield Curve (aka. Spot rate curve) is suitable for option-free bonds.
- However, for bonds with embedded options where value of option varies with outcome of unknown forward rates, a model allows for variability of forward rates is necessary
> Model: Binomial Interest Rate Tree Framework