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Marketing strategy

Callable Libor exotics are among the most challenging interest rate derivatives to price and risk-manage. These derivative contracts are loosely defined by the provision that the holder has a Bermuda-style (i.e. multiple-exercise) option to exercise into various underlying interest rate instruments. The instruments into which one can exercise can be, for instance, interest rate swaps (for Bermuda swaptions), interest rate caps (for captions, callable capped floaters, callable inverse floaters), collections of digital call and put options on Libor rates (callable range accruals), collections of options on spreads between various CMS rates (callable CMS coupon diffs), and so on.

From a modeling prospective, callable Libor exotics are difficult to handle. Simple, "first

generation" interest rate models like Ho-Lee, Hull-White, Black-Karasinsky cannot be used because of their inability to calibrate to a rich enough set of market instruments. One has to use "second generation" models with richer, more flexible volatility structures. Among the latter, forward Libor models (also known as Libor Market and BGM models) are arguably the best suited for the job.

Building a pricing and risk management framework for callable Libor exotics based on

forward Libor models is a formidable task. Conceptual and technical issues abound. Calibration, valuation and risk sensitivities calculations all present unique challenges.

This paper takes a look at these problems and possible ways that may be used to address these challenges. We aim to present a comprehensive review of problems one has to deal with when developing the callable Libor exotics capability for forward Libor models.

To get an idea of the scope of the paper, one just needs to ask why using forward Libor

models for callable Libor exotics (CLE for short) is so hard? Problems start with volatility calibration. Multiple types of optionality embedded in CLEs mean that they depend on volatilities of many different rates. What market instruments do we calibrate the model to?

Matching today's prices of market instruments is just one part of the solution. Choices affecting the dynamics of the volatility structure have a significant impact on CLE prices. Questions arising out of this situation though in the domain of general interest rate modeling, have profound importance for callable Libor exotics.

After calibration comes pricing. Pricing must be done using Monte-Carlo, as it is the

only viable numerical method available for forward Libor models. Successful pricing of

Bermuda-style options in Monte-Carlo hinges on the ability



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