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PolyPaths’ trading-quality models and analytical tools help you manage yield- and volatility- sensitive positions, including:

  • Mortgage-related securities
  • European and Bermudan options on or embedded in bonds and derivatives 
  • Caps and floors
  • Various exotic instruments like callable capped floaters and range notes

PolyPaths provides these models and other tools for use in pricing and hedging for virtually all security types found in fixed income portfolios. In addition, we supply a complete set of Greeks and other risk measures, as well as a flexible interface for compound and multi-horizon scenario analysis at the portfolio, sector, and individual security level.

Models

Mortgages/CMOs

We use a Three-Factor BGM Interest-Rate Process (LIBOR Market Model), which features:

  • Simultaneous calibration to a complete set of caps and swaptions volatility term structures
  • Fast calibration, which can be done in real time within 30 seconds
  • CEV adjustment on a continuous scale from lognormal to near normal for approximating the observed volatility skew
  • A volatility-dependent current coupon model

Integrate Intex cashflows and user-supplied or third-party prepayment and default models

Bermudan Bonds and Derivatives

  • Lognormal Trinomial Tree
  • Square root Trinomial Tree
  • Normal Trinomial Tree
  • Monte-Carlo – least squares implementation

Cap/Floors, European Swaption

  • Monte Carlo
  • Black

Risk Measures

The risk measures available at the portfolio, user-defined sector, and the security level are

  • Static: Cash flow duration, user-supplied duration, treasury/swap equivalents.
  • Option Adjusted: OAS, OA duration, OA convexity, current coupon duration, OA spread duration, volatility duration, prepay duration, user-modified OA duration, option Greeks.
  • Key Rate Duration: Partial and adjusted-partial duration and convexity, Treasury/swap equivalents.

Scenario Analysis

  • Curve shifts parallel, steepening, flattening, and twists
  • Current coupon shifts
  • Prepayment multipliers
  • Volatility shifts
  • Basis/spread scenario at security or sector level