SciComp Calibration Tools: Derivatives pricing model calibration

SciComp's Calibration Tools are robust, standalone calibrators available as ready-to-use Excel spreadsheets and add-ins or Windows/Unix executables. All Calibration Tools can be customized to meet user's particular needs and requirements.

Standard Calibrators

Heston Stochastic Volatility Calibrator is a least-squares calibration of a Heston model via Levenberg-Marquardt. The Heston model assumes that the underlying asset follows a Black-Scholes process with a stochastic volatility. The Heston model may include asset jumps and be piece-wise constant.

Local Volatility Calibrator is a least-square calibration of local volatility surface for Dupire's model. Jim Gatheral's SVI (stochastic volatility inspired) parameterization models are used to fit the volatility smiles to market data by means of Levenberg-Marquardt. The calibration automatically removes arbitrage opportunities inside and across smiles.

1- or 2-Factor Short Rate Calibrator is a least-square calibration of either a 1-factor, constant parameter Gaussian model, or a 2-factor, constant parameter Gaussian model by means of Levenberg-Marquardt.

ATM Gabillion Calibrator ATM Gabillion Calibrator is (in a least-squares sense) a calibrator for a constant coefficient Gabillion model to a collection of at-the-money future contracts.

ATM Schwartz97 Calibrator is (in a least-squares sense) a calibrator for a constant coefficient Schwartz97 model to a collection of at-the-money future contracts.

Credit Calibrators

CDS Calibrator extracts a piecewise constant hazard curve from standard CDS market quotes.

Large Pool Model Calibrator is an implied correlation for the given expected loss specified by the tranche spreads.

Semi-Analytic Implied Base Correlation Calibrator includes index based structures (e.g., DJ Itraxx, etc.)

Custom Calibrators

SciComp can quickly and economically implement custom calibrators for users that want to implement either public domain or proprietary calibration routines that are tailored to their particular needs and requirements. Custom Calibrators are available for a broad range of pricing models including:

• Convertible bond/equity/FX/commodity models including many parameterized local volatility, stochastic volatility (with and without jumps), and pure jump models.
• Generic short rate models (including popular Gaussian and lognormal flavors) with interest rate and/or hazard rate calibration to volatility term structure of cap/swaptions and CDS spreads or corporate bonds.
• LIBOR market model calibration, including exact fit to caps and least square fit to swaptions.
• Credit models, including survival/hazard rates from credit spreads, base correlation and semi-analytic models with deterministic or stochastic factor loading.

Several parameterizations of the correlation matrix are available as well as several approaches for including volatility skew. Many models accommodate time dependent parameters, either exactly through numerical models of the calibration instruments, or through very fast approximate analytic techniques.

Available optimization techniques include a robust Levenberg-Marquardt algorithm and simulated annealing.

Custom Calibrators may include pricing models for the calibration instruments including analytically advanced equity pricers, stochastic volatility models with jumps, stochastic time change, variance gamma models, and cap and swaption pricers under various short rate models. For calibration to instruments that do not have analytic pricing formulae under the desired model, users may elect to incorporate either a SciFinance®-generated or externally developed finite difference (PDE) or Monte Carlo (SDE) pricing code.

SciComp Calibration Tools Benefits:

• State-of-the-art, ready-to-use calibration routines
• Calibrators can be customized to meet particular needs and requirements
• Cross asset class support
• Supports a broad range of pricing models, including cross-asset class
  calibration
• Calibration routines may utilize PDE or MC pricing models for underlying
  calibration instruments
• Available as an Excel spreadsheet and add-in or Windows/Unix executable