# Expert, Cost-Effective Derivatives Consulting

## Ready-n-Customizable Calibrators

**Ready-n-Customizable Calibrators** are a suite of robust, standalone, ready-to-use calibration functions any of which can be tailored to meet customer requirements. In addition, SciComp Consulting can quickly and economically implement custom calibrators for customers looking for either public domain or proprietary calibration routines that are tailored to their specific requirements.

**Ready-n-Customizable Calibrators** are available as C++ source code, as Windows or Unix executables, or embedded in Java, Python, .xll, COM, or .NET wrappers.

### Pricing Model Calibration Functions

The **Futures Volatility Surface Calibrator** utilizes the SciComp extended classical log-normal model to incorporate volatility smiles. This new approach improves the accuracy of derivatives valuations:

- Calibration of volatility term structure and volatility smiles
- Construction of arbitrage-free volatility surfaces and marginal distributions
- Robust and accurate algorithms to construct local volatility surfaces
- Separation of Samuelson effect, volatility smiles and correlations
- Simulation algorithm based on copula techniques to value path-dependent options

Test drive the Futures Volatility Surface Calibrator

Watch the Webinar: Construction of Volatility Surface for Commodity Futures

The** Stochastic Local Volatility Calibrator** (**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 then mixes the two models together either by a)
calibrating to selected exotics, or b) using historical data.

**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 Gabillon Calibrator** is
(in a least-squares sense) a calibrator for a constant coefficient
Gabillon 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 looking for either public domain or proprietary calibration routines that are tailored to their specific needs and requirements. Custom Calibrators are available for a broad range of pricing models including:

- 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. Several parameterizations of the correlation matrix are available as well as several approaches for including volatility skew.
- Credit models, including survival/hazard rates from credit spreads, base correlation and semi-analytic models with deterministic or stochastic factor loading.

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.

**Why use SciComp Consulting?
**

**Expertise:**Our expert quant/developer staff has years of derivatives experience developing pricing models for financial institutions around the globe.**Industry standard or customized derivatives solutions:**Comprehensive selection of industry standard derivatives pricing models and calibrators, any of which can be customized to meet your exact needs.**Pricing models tailored to customer requirements:**Customers may specify model features such as the underlying dynamics, the market data and formats, and model output, or they may default such decisions to our expert quant/developer staff.**Performance enhanced pricing models:**GPU-enabled or OpenMP-compliant derivatives pricing models.

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