A coupon advantage can make a convertible look attractive even when its issuer can call away the premium before the income is earned. The desk needs a screen that acknowledges its limits and a valuation method that honours the contract. This lesson connects income break-even to convexity and explains why the running contract requires a lattice rather than a static bond-plus-call price.
Learning objectives. Compute both break-even measures, distinguish convexity from profitable hedging, and identify the contract decisions that need backward induction.
Setup 1 (The running contract). All amounts are dollars per bond. Face is , conversion ratio is 16 shares, spot is , maturity is five years, and annual coupons are at years 1–5. Conversion is available at every lattice date. The issuer can call for from year 2 inclusive to maturity exclusive, only when spot is at least . The holder has a put at year 3. Rates are continuously compounded: , dividend yield , volatility , and credit spread .
Coupons are paid before same-date exercise, including conversion; call and put prices exclude that coupon. Between dates there is no accrued-interest payment on conversion. At maturity the payoff is . This explicit teaching convention differs from contracts that forfeit the final coupon on conversion. The spot trigger is a simplified soft call: it does not claim to implement a rolling 20-of-30-day test.
In this lesson
- Income is a screen, not a price
- Convexity and paid hedging
- Why the European package is insufficient
Before you start
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