Hybrid Securities
Convertible Bonds
Bifurcation & Greeks
Convertible Bond Pricing & Greeks Lab
Price convertible bonds, model conversion parity and straight debt floors, quantify option premiums, calculate delta hedge ratios, and analyze Tsiveriotis-Fernandes hybrid risk sensitivities.
Conversion Parity: P_{\text{parity}} = \text{CR} \times S |
Straight Bond Floor: B_0 = \sum_{t=1}^T \frac{C}{(1 + r_d)^t} + \frac{M}{(1 + r_d)^T} |
Convertible Value: V_{\text{CB}} = B_0 + \text{CR} \times c_{\text{BS}}(S, K, T)
Market Presets:
Convertible Bond Parameters
$
%
Y
Conversion & Equity Terms
$
sh
%
%
Discount & Credit Spread
%
bps
Balanced Convertible Regime
Hybrid behavior with balanced equity delta and downside bond floor protection.
CONVERTIBLE FAIR VALUE
$1,142.50
114.25% of Par
CONVERSION PARITY
$1,000.00
CR 25.0 × $40.00
STRAIGHT BOND FLOOR
$852.40
Yield 6.50% (r + 250bps)
CONVERSION PREMIUM
+14.25%
Spread over Parity ($142.50)
Convertible Metrics & Greeks Decomposition
| Metric Parameter | Value | Benchmark / Context | Description |
|---|---|---|---|
| Conversion Price (CP) | $40.00 | Par / CR ($1,000 / 25.0) | Effective stock purchase price upon conversion |
| Premium over Bond Floor | +34.03% | +$290.10 | Option value excess paid above straight debt floor |
| Embedded Option Value | $290.10 | $11.60 per share | Warrant component value via Black-Scholes framework |
| Convertible Delta (Δ) | 0.582 | Hedge: 14.55 shares | ∂V / ∂S; sensitivity to $1 move in underlying stock |
| Convertible Gamma (Γ) | 0.0162 | ∂²V / ∂S² | Rate of change in Delta as equity price moves |
| Convertible Vega (ν) | $3.85 | per +1% volatility | Sensitivity of convertible bond price to stock volatility |
| Credit Duration (Mod. Dur.) | 4.18 Y | Floor DV01: $0.36 | Interest rate / spread duration of straight bond floor |
Interactive convertible pricing curve illustrating downside bond floor protection and upside equity parity tracking.
Stock Price vs. Volatility on Fair Price ($)
Rows: Stock Price ($S$), Columns: Volatility ($\sigma$). Shows convexity and equity sensitivity.
Stock Price vs. Credit Spread on Delta (Δ)
Rows: Stock Price ($S$), Columns: Credit Spread ($s$ bps). Evaluates hybrid equity exposure.
Convertible Bond Mastery Self-Assessment
Related Derivatives & Capital Structure Simulators
Frequently Asked Questions: Convertible Bond Valuation
A convertible bond is a hybrid financial security that pays regular coupon interest like a traditional corporate bond but gives the holder the contractual right to convert the bond into a predetermined number of common stock shares. It offers investors downside protection via the bond floor while providing upside participation in equity price gains.
Conversion parity (also known as parity value or conversion value) is the immediate market value of the underlying common stock into which the bond can be converted. It is calculated as Conversion Parity = Conversion Ratio × Current Stock Price. For example, if a bond converts into 25 shares and the stock is trading at $45, the conversion parity is $1,125.
The straight debt investment value (or bond floor) is the present value of the convertible bond's contractual coupon payments and principal repayment discounted at the market yield of an equivalent non-convertible bond of the same issuer and credit rating. The bond floor represents the theoretical minimum value of the convertible security if the embedded conversion option expires worthless.
Conversion premium is the excess price that investors pay for a convertible bond over its immediate conversion parity value, expressed as Conversion Premium (%) = (Convertible Market Price - Conversion Parity) / Conversion Parity. It reflects the value of the downside protection provided by the coupon payments and principal floor relative to owning the common stock directly.
Convertible arbitrage is an institutional trading strategy where a hedge fund buys an undervalued convertible bond and simultaneously sells short delta shares of the underlying equity. By neutralizing equity price risk (delta hedging), the arbitrageur captures cheap implied volatility, collects positive bond carry, or profits from tightening credit spreads without bearing directional equity exposure.