Numerix Blog

Powering Pre-Trade Analytics and Modeling

Yesterday, attendees at the A-Team Insight Exchange 2010 here in New York were witness to a lively and informative panel discussion on “Powering Pre-Trade Analytics and Modeling,” which included our own Satyam Kancharla, Senior Vice President - Client Solutions Management Group.

Grid Power + Excel Flexibility?
Among the items Mr. Kancharla highlighted was Numerix’s partnership with Microsoft HPC (grid computing) as a real-world working example. HPC technology has been successfully applied to portfolios containing several thousand Excel spreadsheet trades at a global insurance company as part of the firm’s pre-trade risk management process. The end result: taking a process that would have taken days, down to two minutes. Traditionally, analytics users have had to make a tradeoff between the flexibility of Excel and the performance and scalability of a custom gridding solution. What’s unique about the Numerix Excel/HPC solution is that users get both.

Consistent Pricing/Risk Analytics
The discussion on pricing provided a good forum for highlighting Numerix’s strategic partnership with Bloomberg and how we’re working towards creating an industry standard for pricing and valuations. For example, because Numerix analytics are already embedded into the Bloomberg platform, everyone looking at a deal — issuers, dealers, investors, compliance, risk management, auditors — operate on a common, transparent analytic foundation. And with Numerix Bloomberg Edition and NXDL, users can upload bespoke instruments into the BLOOMBERG PROFESSIONAL® service, where they can take advantage of all the Bloomberg functions they already use, such as on-demand pricing and Greeks, messaging, changing data contributors, and outputting to order management systems.

Counterparty Credit
Risk management also took center stage, with the importance of Counterparty Valuation Adjustments (CVA) and Monte Carlo simulations in the pre-trade process. To do CVA, firms need a solution that is flexible and scalable.

In the end, all panel participants agreed that pricing analytics and software as a service (SAAS) were poised for continued growth, with service and vendor firms standing to gain increased revenues from the SAAS value proposition.

Numerix and the UTS Master of Quantitative Finance Program

Check out this short video by Prof. Schlogl from the Quantitative Finance Research Centre at the University of Technology, Sydney. Graduate students in the program have the advantage of using Numerix software for teaching and non-commercial research related to pricing and risk management of OTC derivatives.

Comparing Market Model Accuracy to the Volatility Smile

Following up from yesterday’s post on LIBOR Market Models in Numerix, I thought it would be valuable to show how the incorporation of shifts and stochastic volatility enables more accurate pricing for instruments with high market skew.

To measure the calibration fit of various models in use today, we tested the standard BGM model, a shifted BGM (SBGM) model and a LMM with stochastic volatility (LMM-SV) for a grid of 55 call swaptions at various expiry/maturity combinations (from 1Y/1Y to 25Y/5Y) and relative strikes (-2% to +2%). (Note: The plotted implied model vols are obtained from Monte Carlo simulation pricing of the swaptions.)

Ideally, a model should track the market swaption volatility (representing the market-quoted price of the swaption) as close as possible across expirations, maturities and relative strikes. The better the fit, the more accurate the calculations for pricing and risk analysis.

Findings:

• LMM-SV provided the best overall fit to the market volatility smile across all expiry/maturity combinations
• SBGM accuracy declined for shorter-dated maturities
• BGM was generally only effective for ATM options (0% relative strike)

LIBOR Market Models for Smile-Dependent Exotics

Continuing our series on the use of advanced models (see The Bates Model), today we address the issue of pricing complex trades that are heavily dependent on the volatility smile, such as CMS, LIBOR-linked structures and hybrids. For these exotics, the Numerix includes a suite of LIBOR Market Models (LMM), with support for stochastic volatility, which is required to calibrate to the entire volatility surface.

To understand why this model is necessary, let’s look at recent advances in market models for pricing interest-rate derivatives.

Tracing the Evolution of the LMM
In 1997, Brace, Gatarek and Musiela [1] introduced the BGM model—a standard formulation of the LIBOR market model using a lognormal diffusion of the underlying forward LIBORs. By modeling observable rates directly and enabling correlation between observable rates, BGM offered a major advantage over short-rate models that relied on unobservable instantaneous rates.

This multi-factor model allowed de-correlation of LIBOR/CMS rates and provided analytical formulas for European caplets/swaptions, which are necessary for effective calibration. However, lognormal modeling of the underlying LIBORs implies a flat volatility smile. This limitation made BGM ineffective for pricing smile-dependent exotics, such as range accrual notes.

The need for more-complex calibration algorithms led to two key extensions of the classic formulation. First came the shifted BGM, which introduced the ability to reproduce an implied volatility skew [2]. Further, a stochastic volatility process was added to the LIBORs’ evolution to calibrate both the skew and curvature of the smile [3].

Visit Us at the ERM Symposium, April 12-15

by Saul Stepner, Senior Vice President, Sales/ALM Solutions

Next week, we’ll be attending the Enterprise Risk Management Symposium in Chicago, hosted by the Society of Actuaries. This is the eighth year the SOA has held this well-attended event, and it usually offers some helpful insights on the current state of ERM.

Among the many great sessions taking place, the one I’ll be most interested in is “Successes and Challenges in Integrating an Economic Capital Allocation and Risk/Return Framework,” held on Tuesday the 13th at 2:00pm.

This topic has been one of the major challenges facing Numerix clients today. As a result of the last couple of years, regulators have imposed a number capital and reporting requirements on our clients, and most are trying to understand the impact and interactions of GAAP, statutory accounting and economic frameworks.

The good news is that Numerix is helping its clients work through the advanced modeling aspects of this changing landscape through its Economic Scenario Generator (ESG). The ESG can generate consistent real world and risk neutral scenarios across “n” economies leveraging the Numerix hybrid modeling framework.

If you’ll be at the symposium next week, please stop by our booth and say hi!