Derivative Solutions

F3 4.1 Release Highlights

The most recent release of F3 includes a new framework for pricing American Options, enhancements to its treatment of inflation curves and instruments, and numerous other extensions and improvements to usability and performance.

New American Option Pricing Framework

The new framework for pricing American equity options uses backwards evolution of the characteristic function of the probability distribution of the underlying stock returns. This approach uses Fast Fourier Transform (FFT) techniques, which are computationally efficient, and it allows for a wide range of random processes to be modelled, including Log-normal (aka, Black), Merton jump diffusion, Heston, Bates, Variance Gamma, and diffusion-extended CGMY. The same characteristic function framework can be used to efficiently price European options for any of these random processes, thereby enabling their calibration to the volatility surface. The framework also provides an extrapolation method to increase the accuracy of pricing an American Option using a sequence of Bermudan options with an increasing number of exercise dates. As with all pricing algorithms in F3, sensitivities of price to all market inputs, as well as the corresponding hedge factors, are precisely and rapidly calculated using Universal Risk Technology™ (no bumping, or finite difference, required).

This framework will be of interest to traders and risk managers of American equity options who are looking for more accurate and efficient pricing, greeks, and hedge factors. Furthermore, risk managers or traders concerned with assessing model risk can do so easily by substituting the characteristic function for a different random process within the same framework. The characteristic function approach allows different random processes to be implemented more easily and hence more reliably then a tree- or PDE-based approach, with the same result at the small time-step limit.

Inflation Curves and Instruments

The infrastructure to build inflation curves from inflation market instruments (e.g., YoY or ZC swaps) was enhanced to provide greater flexibility in the shape of the curve, so that a monthly step can be combined with a smoother overall interpolation method. In addition, the seasonality adjustment can now be more simply and conveniently applied. These enhancements will provide traders and risk managers of inflation swaps with more accurate and convenient pricing and risk, including sensitivity to the seasonality adjustment factors as well as the swap rates used to build the curve.

Bond traders will also benefit from the convenience of pre-defined bond types for US TIPS and UK Inflation-Linked Gilts, in addition to new example workbooks that can either use an assumed flat inflation rate (per Bloomberg), or use more realistic inflation curves. Cash-flows can be based on lagged monthly levels (e.g., US TIPS), or on interpolated lagged levels (e.g., UK Treasury I/L Gilts after 2005).

Additional Enhancements

IR Swap futures

Convenient pricing and risk metrics for deliverable IR swap futures, such as those traded on the CME. This new financial product allows interest rate swaps to be traded on a forward basis, with the advantages of exchange trading, including lower margin requirements than for OTC derivatives. The new convenient functionality in F3 will benefit to rates traders and risk managers.

SVI Volatility surface

The ability to represent and calibrate the "stochastic volatility inspired" (SVI) parameterization of the implied volatility smile. This widely-used arbitrage-free parameterization was originally devised at Merrill Lynch in 1999, and more recently publicized by J. Gatheral. It allows traders of equity options to fit a smooth volatility surface to observed European option prices, enabling more accurate pricing that is free of arbitrage.

Ultimate Forward Rate (UFR)

Tools to extrapolate a discount factor curve beyond the longest-dated market instrument, to a prescribed Ultimate Forward Rate (e.g., 4.2%), using the Smith-Wilson method. This technique has been published by EIOPA for use by insurance and pension companies when discounting long-dated liabilities (e.g., 60 or 100 years) for ALM purposes.

Parameterized Curves

The ability to support user-supplied formulae for any type of curve, such as a rate curve, a discount factor curve, an inflation curve, a volatility smile, etc. This technology is integrated with F3's calibration framework, so that you can define your own shape for a curve using a mathematical formula, then calibrate the parameters in that formula to the observed price of relevant market instruments. The formula is parsed at run time, with no need to pre-compile. The technology works seamlessly with F3's Universal Risk Technology™, allowing price sensitivities to be calculated with respect to market quotes, not curve parameters. Example applications that could be implemented using F3's Parameterized Curves technology include the SVI Volatility surface (see above), the Smith-Wilson method of extrapolating to a UFR (see above), and the Nelson-Siegel yield curve. This advanced capability will allow quants to extend F3 to use their own proprietary or favorite parameterizations, and allows FINCAD to offer such customization services without requiring a special installation.

Bond duration simplification

A convenient way to request the duration of a bond or bond portfolio with respect to z-spread (or with respect to yield), even when the bond quote is provided in a different form, such as price. Internally, the price is converted to an equivalent z-spread (or yield) value, before calculating sensitivity to the new value using Universal Risk Technology™. This makes it easier for asset managers to get the metrics they need to manage the risk of their bond holdings.

Cheapest-to-Deliver (CTD) curve simplification

The calculation of the CTD curve implied by a multi-currency collateral agreement has been simplified by providing a high-level wrapper. Fewer steps are now required to calculate this discount curve from XC basis spreads. This simplification will be of benefit for practitioners that need accurate pricing of derivatives in all asset classes, in cases where the collateral agreement allows a party to post collateral in one of a number of currencies.

Since I am able to work with the granular components of the trade, I can re-use the building blocks across multiple trades. My spreadsheets are significantly smaller and workbook management is much easier than before.

Orlando Calvo Treasury Risk Analyst, Global Bank Corporation