A finely spaced tree can still misprice a soft-callable convertible if it has discarded the contract's history. The desk must distinguish numerical refinement from additional state. This lesson reads the running engine's convergence, explains multinomial refinements, and identifies what a real rolling-day call trigger would require.
Learning objectives. Separate distribution and exercise-boundary errors, test event-aligned grids, and describe sufficient state for consecutive-day and rolling-window triggers.
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
- Refine the grid before changing the model
- A spot trigger is not a rolling trigger
- Other refinements have different jobs
Before you start
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