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Chapter 14 of 15
How embedded options create Greek exposures in structured notes
9 min read
What are you really buying when you invest in a structured product?
What Are Structured Products?
A structured product combines a bond with one or more embedded derivatives (usually options). The bond component provides capital protection or income, while the derivative component creates exposure to other assets or market conditions. In Germany, structured products are enormously popular with retail investors. The market for Zertifikate (certificates) exceeds €60 billion in outstanding volume.
Why Structured Products Exist
Bond Volatility Basics
Volatility in fixed income refers to the magnitude of price fluctuations. Two types matter: • Interest rate volatility – How much rates themselves fluctuate (measured by swaption implied vol) • Credit spread volatility – How much spreads widen or tighten Higher volatility increases the value of embedded options, affecting the structured product's price and behavior.
The Greeks: From Equities to Fixed Income
The "Greeks" measure how a derivative's price responds to various factors. In fixed income, familiar concepts take new forms:
Greeks for Fixed Income
| Greek | Equity Definition | Fixed Income Equivalent |
|---|---|---|
| Delta (Δ) | Sensitivity to underlying price | Duration – sensitivity to rate changes |
| Gamma (Γ) | Rate of change of Delta | Convexity – curvature of price-yield relationship |
| Vega (ν) | Sensitivity to volatility | Sensitivity to interest rate or spread volatility |
| Theta (Θ) | Time decay | Time decay of embedded options + accrued interest |
| Rho (ρ) | Sensitivity to interest rates | Already captured in Duration for bonds |
Vega: The Hidden Greek
For plain bonds, Vega is zero—there's no optionality. But structured products with embedded options have significant Vega exposure. Higher volatility → Embedded options worth more → Product price affected Example: A callable bond's issuer holds a call option. Higher vol makes that option more valuable to the issuer, making the bond worth less to you.
German Structured Products
The German Zertifikate market offers various structures. Understanding their Greek profiles helps assess risk:
Common German Structured Products
| Product | Structure | Key Greek Exposures |
|---|---|---|
| Aktienanleihe (Reverse Convertible) | Bond + short put option | Short Vega, negative Gamma at strike |
| Discount-Zertifikat | Long stock + short call | Short Vega, capped upside |
| Bonus-Zertifikat | Long stock + down-and-out put | Long Vega (barrier), path-dependent |
| Callable Bond | Bond + issuer call option | Short Vega, negative convexity |
Aktienanleihe (Reverse Convertible)
Germany's most popular structured product. You receive: • Higher coupon than a comparable bond • At maturity: Either 100% cash OR shares (if stock fell below strike) You're essentially selling a put option. The "enhanced" coupon is your option premium. Your risk: receiving depreciated shares instead of cash.
Aktienanleihe Greeks
Callable Bonds and Negative Convexity
A callable bond gives the issuer the right to redeem early (typically when rates fall). This embedded call option creates negative convexity: • When rates fall significantly, the bond gets called → you lose upside • When rates rise, you keep the bond → full downside exposure The asymmetry works against bondholders. You're compensated with a higher coupon (the option premium you receive).
Reading a Structured Product Term Sheet
Complexity Spectrum
Plain Bonds
Callable Bonds
Discount-Zertifikate
Bonus-Zertifikate
Exotic Structures
AKTIENANLEIHE EXAMPLE
Product: Aktienanleihe on Siemens AG Coupon: 8.5% p.a. (vs. ~3% for plain corporate bond) Strike: €140 (current stock: €160) Maturity: 1 year Scenario Analysis: • Siemens at €180: Receive €1,000 cash + €85 coupon = 8.5% return • Siemens at €140: Receive €1,000 cash + €85 coupon = 8.5% return • Siemens at €120: Receive ~7.1 shares (worth €857) + €85 coupon = -5.8% return The "enhanced" yield compensates for downside equity exposure.
KEY TAKEAWAY
Structured products bundle bonds with options. Understanding the Greeks helps you see what you're really buying.