Pricing convertible bonds

SciComp offers two solutions for pricing convertible bonds, SciFinance and SciCMD.

SciFinance is an automated coding technology for rapidly developing derivatives pricing and risk models. SciFinance models can be created by simply modifying one of hundreds of model templates provided with the system or by writing a model specification comprised of arbitrary partial differential equation (PDE) or stochastic differential equation (SDE), numerical algorithms and the use of key words. SciFinance does the rest by automating the programming task via the SciPDE and SciMC modules to produce fully documented C/C++ source code or Excel spreadsheets and add-ins.

SciCMD meets the needs of users looking for "off-the-shelf" convertible bond pricing and risk models as well as those seeking a customized model approach that captures particular instrument features and modeling needs. SciCMD models are state-of-the-art convertible bond pricing and risk models comparable to those found on the desks of traders and risk managers within Tier-1 financial organizations. Like SciFinance, SciCMD supports the modeling of any financial instrument that can be priced using a PDE or SDE and the deliverable may include a ready-to-use Excel add-in or C/C++ source code pricing library.

SciComp's modeling flexibility and transparency provides:

• Support for any interest rate derivative (including sensitivity to any model parameter) that can be priced using a PDE or SDE
• Support for both market standard and proprietary pricing models
• Robust calibration routines
• Pricing model C/C++ source code

Pricing models for convertible bonds

• Local volatility models
• Stochastic volatility models
  • Heston, Hull & White, etc
  • Arbitrarily user defined
• Stochastic volatility with asset jumps (SVJ)
  • Bates, etc
  • Arbitrarily user defined
• Stochastic volatility with asset and volatility jumps (SVJJ)
  • Matytsin
  • Duffy, Singleton and Pan
  • Arbitrarily user defined
• Variance gamma, CGMY, CGMYSA, etc
  

Pricing model calibration

SciCalibrator is an automated coding technology for translating calibration specifications into C/C++ source code calibration routines and ready-to-use, standalone Calibration Spreadsheets.

Calibration routines include:

• Local volatility
• Heston SV
• Heston SV + jumps
• Kou double exponential jump model
• VG and CGMY models
• VGSA and CMGYSA (VG and CMGY + stochastic time change)
• Generic short rate calibration
  • Single-factor Gaussian models
  • Generic single factor models (e.g. G1,HW,EEV,BK,CIR)

Processes for convertible bond pricing

SciComp technology can generate PDE codes for an arbitrary number of factors, but execution of the codes is typically practical for 1-3 factors. How these factors are allocated is up to the user. For example, a three factor model could be:

• A stochastic stock, a stochastic interest rate, a stochastic default process.
• A stochastic stock, a stochastic volatility, a stochastic default process.
• Two stochastic stocks with simple credit spreads, and a stochastic interest rate.
• Three stochastic stocks with simple credit spreads and deterministic interest rate.
  

Credit factor

SciComp solutions support deterministic credit spreads in the convertible bond pricing model including those implemented as a PDE. SciComp solutions handle stochastic credit factors by making the pricing equation 2D or 3D. SciComp’s ADI solvers for handling multi-D PDEs are state of the art, and extremely fast (100x100 grid x 50 time steps in O(1 sec) They are second order accurate, unconditionally stable, and handle any physical correlation.

Convertible bond features

• Term structure of volatility, rates, credit risk
• Local volatility surface
• Stochastic volatility, jump diffusion models
• Arbitrary one or two factor short rate models (Hull-White, Gaussian, CIR, BK, etc.)
• Term structure of conversion rates, put and call prices
• Contingent conversion and soft calls including Asian and Parisian features
• Stochastic conversion rate (resets according to arbitrary formula involving current and past spots, current and past conversion rates, etc.)
• Arbitrary coupon sizes and schedules, contingent coupons
• Arbitrary dividend sizes and schedules, contingent dividends
• Embedded optionality, e.g., call notice period
• Convertible into best/worst/basket of two or three
• Cross currency features
• Transaction costs
• Credit spreads, recovery rates, arbitrary functions of time and stock prices
• Sensitivities to any model parameter
• Wide variety of grid, solvers, algorithm choices for fastest/most accurate possible code
  

Conversion features

SciComp solutions support the modeling of any convertible bond conversion feature and no list can be complete (partial list below).

• Simple structures
• LYON
• Protected call
• Discrete call/put
• Resetting conversion ratios
• Best of asset conversions
• Call notice period
• Contingent conversion
• Parisian conversion
• Zero coupon conversion
• Conversion into foreign stock