CFA® Level II · Fixed Income · free lesson

Valuation and Analysis of Bonds with Embedded Options

Many corporate, agency and bank bonds carry options: issuers' calls, investors' puts, caps and floors on floating coupons and rights to convert into shares. This module shows how each option changes a bond's value and risk, values callable, putable, capped and floored bonds on a calibrated binomial tree, measures relative value with the option-adjusted spread, quantifies interest rate risk with effective, one-sided and key rate durations and convexity, and analyses convertible bonds. Level II item sets require building values node by node and interpreting how volatility and the yield curve move them.

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What you will learn

1. Describe callable, putable, extendible and other bonds with embedded options, and relate their value to the value of the straight bond and the option.

Callable: issuer owns the call; investor is short it and earns a higher yield.
Putable: investor owns the put; accepts a lower yield; an extendible bond is equivalent to a putable bond.
V_callable = V_straight - V_call; V_putable = V_straight + V_put.
Exercise styles: European, American, Bermudan; make-whole calls are rarely used to refinance.
CoCos convert or are written down when capital falls below a trigger or the bank is declared non-viable.

2. Value callable and putable bonds on a binomial interest rate tree and explain how interest rate volatility and the shape of the yield curve affect their value.

Callable: node value = min(computed value, call price); putable: max(computed value, put price).
Compare the option's strike with the value excluding the coupon just paid.
Higher volatility raises both call and put values: callable bond falls, putable bond rises.
A flatter curve raises call values and lowers put values.
Option value = straight value - callable value (call) or putable value - straight value (put).

3. Calculate and interpret option-adjusted spread, effective duration, one-sided and key rate durations, and effective convexity for bonds with embedded options.

OAS = constant spread over the benchmark tree that equates model value to price; higher OAS than peers = cheap.
For callable bonds, a higher volatility assumption gives a lower OAS.
Effective duration and convexity: shift the curve, recalibrate, revalue holding OAS constant.
Callable bonds show negative convexity near the call price; putable bonds keep positive convexity.
One-sided duration: callable less sensitive to falling rates; putable less sensitive to rising rates.

4. Value capped and floored floating-rate bonds on a binomial interest rate tree.

Capped floater = straight floater - cap (investor short the cap; issuer protected).
Floored floater = straight floater + floor (investor long the floor).
On the tree, the coupon set at a node is min(r, cap) or max(r, floor), paid one period later and discounted at that node's rate.
A plain floater with no margin is worth par at every node.
Cap and floor values increase with volatility.

5. Analyse convertible bonds: their components, conversion metrics, minimum value, valuation and risk-return profile.

Conversion value = share price x conversion ratio; minimum value = max(straight value, conversion value).
Market conversion price = convertible price / conversion ratio; premium = market conversion price - share price.
Premium over straight value = convertible price / straight value - 1 measures downside risk.
Value = straight bond + stock call - issuer call + investor put.
Busted convertibles behave like bonds; deep in-the-money convertibles behave like the shares.

Module at a glance

V_callable = V_straight - V_call; V_putable = V_straight + V_put; extendibles are valued like putables.
On the tree, callable nodes take min(value, call price) and putable nodes max(value, put price), before adding the coupon.
Higher volatility lowers callable values and raises putable values; a flatter curve raises call values and lowers put values.
OAS is the spread over the benchmark tree that matches price; overstated volatility understates a callable bond's OAS.
Effective duration and convexity hold OAS constant; callable bonds show negative convexity near the call price.
Capped floater = straight floater - cap; floored floater = straight floater + floor.
Convertible minimum value = max(straight value, conversion value); busted convertibles trade like bonds.

This free module has 5 lessons, 16 practice questions with full explanations.

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