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How to Overcome the Modeling Challenges of Hybrids
By Tony Webb, PhD | January 21, 2016

In the strictest sense, a hybrid is a derivative or security exposed to more than one asset class. For more practical purposes, hybrids are derivatives that are sensitive to correlations between underlyings, whether they are in one asset class or multiple.

An example of a traditional hybrid instrument would be a convertible bond, which is exposed to the value of the underlying equity, interest rates, and credit spread of the issuer. But hybrid modeling is also needed for portfolio-level risk analysis, even for portfolios of vanilla products. For instance, calculating a portfolio’s CVA, to evaluate the effect of counterparty default risk, needs to take into account correlation and non-linear effects, and requires hybrid modeling.

The modeling of hybrids involves detailed analyses of various risk factors, their mathematical properties, and the interplay or correlation among them. The bottom line is that hybrids modeling is difficult. Many firms will create a bespoke model to handle each case separately. However, the need to write code each time a new hybrid model is needed can weigh heavy on a firm’s resources.

Firms will often encounter a few common challenges when endeavoring to model hybrids. These can include:

  • Equity Calibrations Are Destroyed by Stochastic Interest Rates: The pricing formulae for European equity options change when interest rates follow a random process. Often this problem is solved by creating a special calibration setup when modeling hybrid instruments. The issue here is that a new pricing equation for equity options would have to be derived for every random process a firm wants to use for the price of the underlying equity. This could potentially increase staffing resource needs of the firm.    
  • Need for Careful Analysis for a Consistent Measure: Careful analysis of each hybrid model is required to correctly run a Monte Carlo simulation, since the simulation has to be performed relative to a single numeraire and using its associated probability measure. But the detailed analysis required for every combination of dynamics in a hybrid model has much potential for human error if done manually.
  • Inefficient Simulation: Performing simulations on hybrids is often computationally intensive. This is because the drift term can be stochastic, so short time steps are required in the simulation.  But with a careful setup, the drift term can often be eliminated, thereby allowing long time steps, giving much faster performance.
  • Misinterpreting the Inter-process Correlation: It’s often easy to confuse the value of the correlation when modeling a hybrid. The difficulty here is that the correlation observed in the market is between the observable prices or rates, and not the correlation between underlying drivers of the random processes. Problems arise when the correlation between observables is falsely assumed to be a proxy for the inter-process correlation.

A sophisticated valuation and risk analytics solution can let you overcome the aforementioned challenges by helping you build generic hybrid models with a quasi-analytic approach, affording you major improvements in speed and accuracy. FINCAD’s F3 Platform is one of these solutions.  

In F3, the forward price, not the spot price, is modelled as a fundamental variable. This solves many of the challenges around bespoke analysis, and slow performance, that were listed above.  Furthermore, the issue of using a consistent measure is addressed by applying numeraire corrections that are computed automatically in an auxiliary simulation prior to the main simulation. In this way, F3 provides a flexible modeling framework that automates much of the detailed analysis that is normally the domain of expert quants. 

Not only that, but F3 provides building blocks that can be used to represent trades of arbitrary complexity – from vanilla to the most exotic. Those building blocks include concepts like flows, legs, swaps, choice points, and triggers. It also provides convenient ways of specifying standard instrument types. Importantly, the contract representation framework is closely integrated with the Monte Carlo valuation engine, so that once the trade has been defined, the correct Monte Carlo valuation algorithm is automatically induced.

The firm is able to build new valuation models without requiring any new, bespoke code.  All specifications are handled at run time, so it is not necessary to perform a system restart whenever a new hybrid model is needed, or a new instrument is defined. Because of the automatic nature of the process, the firm is free to analyze very complex payoffs that can be based on a range of underlying assets. The result is a highly flexible and automated framework that can value any hybrid contract or portfolio using arbitrary combinations of asset-specific models.

Hybrid models often require much detailed analysis, need careful implementation, and only apply to a particular problem. But the hybrid modeling process in F3 makes it considerably faster, more accurate, more general, and easier. 

For more detail on how a modern valuation and risk analytics solution can help you overcome the four hybrid modeling challenges we’ve discussed here, download our eBook:  The Challenges of Modeling Hybrids and Advanced Structures

About the author
Tony Webb PhD
Tony Webb, PhD
Quantitative Advisor | FINCAD

Tony Webb is an experienced manager and quantitative analyst at FINCAD having held various roles, including Director of Analytics, VP R&D, Product Manager, and manager of technical Pre-Sales Analysts in NYC. He holds an MA in Mathematics from Cambridge University, a PhD in computational fluid dynamics from UBC, and an MBA with a specialization in finance from UBC. He is currently acting as a Quantitative Advisor within the Client Services department.