Bond
Management
6TH LECTURE
2020 UPDATED
Valuation and Analysis using
Arbitrage-Free Valuation and
Bonds with Embedded Option
Option-free valuation refresher
Year Spot Rate One-Year
Forward Rate
1 3.5000% 3.500%
2 4.215% 4.935%
3 4.735% 5.784%
4 5.271% 6.893%
Interest rate trees and arbitrage-free
valuation
Benchmark securities are liquid, safe securities whose
yields serve as building blocks for other interest rates in a
particular country or currency.
Market Value of
the Bond
Value of the Bond
using the
Appropriate Spot
Rate
Arbitrage-free Valuation
Arbitrage Opportunity
• An arbitrage opportunity is a transaction that involves no cash outlay that results in a riskless profit.
• 2 Type of Arbitrage Opportunity :
oValue Additivity (risk-free payoff today).
Example :
Asset A is a simple risk-free zero-coupon bond that pays off one dollar and is priced today at
0.952381 ($1/1.05). On the other hand, Asset B is a portfolio of 105 units of Asset A that pays off
$105 one year from today and is priced today at $95.
The portfolio (Asset B) is cheaper than buying 105 units of Asset A at a price of $100 and then
combining.
An arbitrager would sell 105 units of Asset A for 105 × $0.952381 = $100 while simultaneously
buying one portfolio Asset B for $95.
Arbitrage Opportunity
• Another type of arbitrage opportunity :
oDominance (a risk-free payoff in the future)
Consider two assets, C and D, that are risk-free zero-coupon bonds. Asset C is priced at $100 today and
have $105 payoff 1 year from now. Asset D is priced at $200 today and have $220 payoff 1 year from now.
If both assets are risk-free, they should have the same discount rate. To make money, sell two units of
Asset C at a price of $200 and use the proceeds to purchase one unit of Asset D for $200.
