Pricing Convertible Bonds: Universal Convertible Bond Pricing Model

SciComp’s Universal Convertible Bond Pricing Model is a fast, accurate, and flexible PDE-based solution for computing fair value, sensitivities, and implied quantities for convertibles. All standard and a wide range of exotic features of modern convertible bonds are included:

pricing convertible bonds

  • Fixed, proportional, or mixed fixed/proportional dividend models. Explicit dividend schedules or specified frequency. Dividend growth. Multiple choices for dividend protection.
  • Fixed, floating or mixed fixed/floating coupon models. Explicit coupon schedules or specified frequency with initial fixed coupon period. Specified coupon growth rates.
  • Contingent coupons based upon underlying stock or convertible bond prices.
  • Conversion rate resets contingent on stock price, hypers.
  • Separate yield curve (discount) and benchmark curves.
  • Hazard rate and credit spread models. Hazard rate calibrated from CDS spreads or specified. Distinct CDS and bond recovery, stock price reset upon default.
  • Convertibles written on foreign stocks.
  • Hard call and discrete put schedules. Call notice periods.
  • Soft calls based on average stock price or days exceeding protection price. Call price/protection price schedules.
  • Contingent conversion (CoCos) including: forced or voluntary conversions; instantaneous, average, or days exceeding CoCo trigger.
  • Many types of make whole provisions including coupon make whole, premium make whole, take out table conversion ratio adjustment matrices and change of control provisions.
  • Funding spread, borrow rate spread, choice of day count basis and holiday calendar support, switches for inclusion of accrued interest upon call, conversion, put, or default.
  • Outputs include theoretical price, all standard Greeks, interest, hazard, credit spread curve sensitivities, and many market implied quantities.

Test drive the Universal Convertible Bond Pricing Model

The Universal Convertible Bond Pricing Model can generate sensitivity to any model parameter. Standard CB model output includes:

  • Theoretical Price
  • Accrued Interest
  • Dirty Theoretical Price
  • Parity
  • Premium
  • Straight Bond Price
  • Delta
  • Gamma
  • Theta
  • Vega
  • Volga
  • Vanna
  • DV01
  • RR01
  • HR01
  • CS01
  • Implied Vol
  • Implied Hazard Rate
  • Implied CB Recovery
  • Implied Credit Spread
  • YieldToMaturity

The Universal Convertible Bond Pricing Model has been designed to facilitate all functionality required for pricing, risk management and valuation (P&L and P&L attribution) activities by traders, risk managers, portfolio managers, product controllers and end-of-day trade support.

Like all SciComp solutions, the Universal Convertible Bond Pricing Model can easily be enhanced to meet customer needs and requirements. The Universal Convertible Bond Pricing Model is available as Excel spreadsheet and add-ins, Windows/Linux executable or C/C++ source code files.

Convertibles bonds are complex financial instruments with many parameters. The Universal Convertible Bond Pricing Model is organized by functional blocks (e.g., stock block, call block, make whole block, etc.) that provide for an intuitive organization of the CBs inputs/outputs. If a particular block is applicable for the modeling of a given CB, enter the data. If not, leave the fields blank.

In addition, users may enter the parameters of the convertible bond and have all model outputs reported in a single row of the Excel spreadsheet.

Summary of Model Input

Stock Block: Valuation Stock Price, Calibration Stock Price, Borrow Rate Spread, Stock Volatility.

Bond Block: Issue Date, Maturity Date, Face Value, Minimum Denomination, Issue Price, Trades Clean, Funding Spread, Treasury Compound Freq., Benchmark Compound Freq.

Credit Block: Hazard Rate, Hazard Rate Exponent, Hazard Rate Ref Price, Credit Spread, CB Recovery, Default Accrued Interest, Stock Fall Upon Default, Hazard Rate Compound Freq., Cred Spread Compound Freq. Note: Both hazard rate or credit spread credit models are supported. Hazard rate parameters can be obtained from CDS spreads via an included calibrator. The hazard rate may be given stock price dependence to model a collapsing bond floor.

CDS Block: Notional, Coupon, UpFront, CDS Recovery, Day Count, Roll Convention, Tenor. Trade Date, Step In Date, Settlement Date, Maturity Date, Accrual Start Date. These data are used by the hazard rate calibrator.

Coupon Block: Day Count Basis, Coupon Frequency, Number Initial Fixed Coupons, Initial Fixed Rate CoPay Type, CoPay Lower Premium, CoPay Upper Premium. Note: Both fixed and floating (geared Libor) coupons are supported. CoPay features are supported, with contingent coupon payments paid above or below lower and upper trigger prices. Trigger prices may be with respect to either stock price or bond price.

Coupon and CoPay Schedules: Users may enter an explicit schedule of coupon dates, amounts and Libor gearings or just the next date and let the model build a schedule. CoPays are specified by Trigger Start Dates, Trigger End Dates, CoPay Lower Triggers, and CoPay Upper Triggers.

Call Block: Call Accrued Interest, Call Notice Period, Call Date Certain, Soft Call Type, Soft Call Trigger Days, Soft Call Window Days. Note: The model provides comprehensive support for different types of call features on the CBs including call notice periods, call accrued interest, user-defined call schedules and call protection. Soft calls may be may be based on spot price, average price, or number of days above the protection price in a rolling window.

Call Schedule: Call Start Dates, Call End Dates, Call Prices, and Call Protection Prices.

Conversion Block: Conversion Ratio, Lower Strike Price (for Mandatory Convertibles), Forced Conversion Type, Conversion Accrued Interest, CoCo Type, CoCo Trigger Days, CoCo Window Days. Note: Contingent conversions may be may be based on spot price, average price, or number of days above the protection price in a rolling window. Forced conversion types include, no forced conversion, conversion on call without restriction, contingent conversion on call.

Conversion Schedule: Conversion Start Dates, Conversion End Dtaes, CoCo Triggers.

Dividend Block: Stock Dividend Type, (Fixed or Proportional) Stock Dividend Frequency, Dividend Growth Rate, Dividend Protection Type, Dividend Protection Trigger. Note: Several types of dividend protection are supported, including pass through.

Dividend Schedule: Users may enter an explicit schedule of dividend dates and amounts or just the next date and let the model build a schedule.

Put Block and Schedule: Users may specify the treatment of accrued interest and a put schedule comprising discrete put dates and corresponding put amounts.

FX Block: Spot FX, FX Volatility, FX-Stock Correlation for modeling bonds convertible into foreign stock.

MakeWhole Block: MakeWhole Type, First MakeWhole Date, Last MakeWhole Date, MakeWhole Premium, MakeWhole Coupon Discount, Change Of Control Date, Change Of Control Amount, Change Of Control Accrued Interest, Change Of Control Shares, Redemption Stock Discount, Conversion Cash Discount. Note: Seven types of MakeWhole features are supported including Coupon MakeWhole, Premium MakeWhole, Conversion Ratio Increase with MakeWhole TakeOut table. This latter type of MakeWhole can be invoked at Change Of Control, upon call, or both.

TakeOut Table:TakeOut Table is used in conjunction with certain MakeWhole provisions to adjust the Conversion Ratio.

Yield Curve and Benchmark Curve Blocks: The Yield Curve used for discounting the convertible bond cash flows. The Benchmark Curve is used for the benchmark rates in floating rate coupons.

Holiday Block: The Holiday Block contains a list of holidays for the domestic currency.

Modeling Block: Modeling Block contains an accuracy specification and a list of switches for turning on/off computation of stock sensitivities (Delta, Gamma, Theta, Vega, Volga, Vanna), rate sensitivities (DV01, HR01, RR01, CS01) implied quantities (Implied Vol, Implied hazard Rate, Implied Recovery, Implied Credit Spread) and MakeWhole Value.

Test drive the Universal Convertible Bond Pricing Model

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