Bonus Certificate

A bonus certificate makes a seductive offer: keep the stock's full upside, and if the stock goes nowhere or falls moderately, receive a bonus level anyway — say 115 on a stock bought at 100. The catch lives below: a barrier, perhaps at 70. If the stock ever trades at or below 70 during the certificate's life — even for a minute, even two years before maturity — the bonus vanishes forever and the certificate simply tracks the stock.

So there are two regimes. Barrier intact: you receive max(stock price, bonus level) at maturity — better than the stock in every scenario below the bonus. Barrier touched: you own the stock's fate, including the fall that triggered the touch, and typically without dividends.

Alongside the discount certificate and the reverse convertible, this is the third pillar of the German retail structuring shelf — the one for investors who want to stay bullish but be paid for sideways.

The construction

Under the hood, two pieces:

The exotic put pays \(\max(B_{\text{onus}} - S_T, 0)\) at maturity unless the barrier \(H\) was ever touched, in which case it dies. Its premium is funded almost entirely by the dividends you give up — which is why bonus certificates on high-dividend stocks offer the juiciest terms, and why they thinned out on low-yield stocks.

Reading a quote

• Bonus yield: annualised return if the stock finishes below the bonus level with the barrier intact — the headline number.
• Barrier distance: current spot to barrier, in percent — the real risk number. 30% sounds like a lot until you recall that single stocks fall 30% regularly.
• Aufgeld (premium): certificates usually cost slightly more than the share — the market price of the conditional bonus.

Variants

• Capped bonus: sells away upside beyond a cap to finance a higher bonus or closer barrier — converging toward a discount certificate's profile.
• Reverse bonus: the mirror image for falling markets — barrier above, profits when the stock declines.

Pricing the down-and-out put

The knock-out put has a closed form under Black–Scholes (the reflection principle / image solution — Merton 1973):

— the vanilla put minus its "mirror image" reflected through the barrier. The formula exposes the sensitivities that matter: the certificate is short vol (higher vol raises touch probability, killing the bonus leg), long the dividend cut (lower q cheapens the funding but also the terms), and carries explosive barrier risk: as spot approaches \(H\), delta can exceed 1 — the certificate loses faster than the stock, because price decline and bonus death compound.

Touch probability — the number the flyer omits

Under lognormal dynamics the probability of touching \(H\) before \(T\) is roughly

Plug in a single stock at 30% vol, barrier 30% below, 18 months: touch probability lands near 25–35% — far above the intuition the "safety buffer" framing invites. On indices (lower vol) the same distance is genuinely safer, which is why index bonus certs quote thinner bonuses.

Issuer hedging and the barrier cliff

The issuer's book is short the knock-out put: as spot nears the barrier its hedge concentrates into a discontinuity — at touch, the issuer's obligation drops by the bonus amount at once, forcing an unwind of the delta hedge (selling stock into the fall). Multiply across a crowded barrier level and structured-product hedging demonstrably steepens sell-offs — documented in Asian markets during 2015 and 2018 autocallable/bonus barrier cascades. Retail sees it as "the stock mysteriously plunged straight through every barrier"; the mystery is the hedging.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.