Derivatives Calibration Tools

SciComp Consulting provides robust, standalone calibration tools that can be customized to meet a user's particular needs and requirements. Calibrators are available as Windows/Unix executables or Excel spreadsheets and add-ins.

Pricing Model Calibration

Stochastic Local Volatility Calibrator

The SLV Calibrator is based on the work of Ren, Madan and Qian [Risk, Sept 2007], Lipton [Risk, Feb 2002], Jex, Henderson and Wang [J.P.Morgan, 1999], and the Bloomberg paper "Stochastic Local Volatility" by Tataru & Fisher. The SLV Calibrator takes any calibrated LV surface that matches vanillas. Then, using a non-linear Fokker-Planck equation, one adds a SV component and for any given set of SV parameters computes a new "leveraged local volatility surface" that still matches the vanillas, while accommodating SV. The SLV Calibrator then applies to this PDE solution a Levenberg-Marquardt optimizer and finds the (time bucketed) SV parameters that yield a maximally flat leveraged local volatility surface. At this point you have the pure LV model (the original LV surface) and the pure SV model (the SV parameters that yield a nearly flat leveraged LV surface). Both models fit the vanillas. The SLV Calibrator then solves for a mixing fraction the mixes the two models together either by a) calibrating to selected exotics, or b) using historical data.

Test drive the Stochastic Local Volatility Calibrator

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.

The Local Volatility Calibrator is applicable to any portfolio of European options written on a single asset. This includes equity and FX options and commodity options written on spot prices. The input option market prices and output calibrated option prices are entered in terms of Black-Scholes implied volatility. The calibrated local volatility surface is parameterized in expiration and forward log moneyness. The calibration is a two step process. In the first step, the implied volatility vs. log-moneyness curve is fit to Gatheral's SVI (Stochastic Volatility Inspired) functional form. In the second step, the smoothed implied volatility surface is transformed into the calibrated local volatility surface using Dupire's equation in an inverse fashion, i.e., computing local volatility from derivatives of the implied volatility surface. Care is taken with the required interpolation, extrapolation and differentiation to produce a smooth stable local volatility surface while observing no-arbitrage constraints.

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 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 credit default swap (CDS) market quotes.

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

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

Custom Calibrators

SciComp Consulting can quickly and economically implement Custom Calibrators for users that want to implement either public domain or proprietary calibration routines. Custom Calibrators that meet your particular needs and requirements 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.

Calibrator Benefits:

• Expertise: Our expert quant/developer staff has years of derivatives experience, developing derivatives calibration models for financial institutions around the globe.
• Ready-to-use or customized derivatives solutions: Comprehensive selection of ready-to-use calibrators, any of which can be customized to meet your exact needs.
• Comprehensive derivatives calibration model development:
  • Design
  • Implementation
  • Testing
• Performance enhanced pricing models: GPU-enabled or OpenMP-compliant derivatives calibration models.