âThis is an important development in the interest rate derivatives market, since Monte Carlo solutions are slow, unable to reliably handle American and Bermudan options, and are very difficult to use for hedging and performance measurement,â said Rich Tanenbaum, Savvysoft founder, and developer of the new model. âTrees donât suffer from any of these shortcomings, and are fast enough to use for large portfolio analytics. Weâre extremely excited about being able to offer this brand-new technology.â
Binomial trees are the market standard for pricing derivative instruments in many markets, but until now they have not been viable for the Libor Market Model, since they previously required non-recombining, or bushy, trees. The trees in Savvysoftâs new model are recombining, which means that when considering possible paths of future interest rate moves, a down day followed by an up day leaves the market (and the tree) in the same place as an up day followed by a down day. Trees that donât have this property, and donât recombine, grow exponentially in size, and quickly use up the storage capacity of the computer, and take much too long to calculate. Recombining trees offer the most efficient way to deal with American and Bermudan options. For a typical problem, a non-recombining tree might take 4 months to calculate an option value, but with Savvysoftâs new model that time would be reduced to 7 seconds.
Savvysoftâs model is the first to offer recombining trees with more than one factor. In fact, Savvysoftâs models can handle as many factors as the user wishes. Whereas a one-factor model is equivalent to allowing the yield curve to move up or down in parallel, a two-factor model also allows for changes in slope, and a three-factor model forecasts changes in the curvature of the yield curve, as well. Many complex derivative structures require multi-factor models, and Savvysoftâs new LMM implementation is the only one that can price and hedge these efficiently and accurately.
As with other LMM models, Savvysoftâs is able to calibrate to both the swaption and the cap market. However, Savvysoft has also devised a new method for extracting the correlation of all the points on the yield curve with each other, requiring the user to supply only the cap and swaption volatility surfaces, which are readily available. The calibration is exact, which means that the model does not make a best-fit guess at volatility, as other implementations do. Rather than selecting from a myriad of optimization choices which produce different (and therefore inaccurate) results, the calibration in Savvysoftâs model is exact. This makes Savvysoftâs new model much easier to use than competing products. Simply pass the model the yield curve, the volatility surface (or cube, with skew), and the model calculates the rest.
Savvysoftâs model also allows the user to price derivatives using a blend of normal and lognormal interest rates processes, as in the constant elasticity of variance model (CEV). This helps to capture smiles and skews in the market.
Savvysoftâs new Libor Market Model is part of Savvysoftâs award-winning TOPS suite of derivatives analytics. The model may be used inside Savvysoftâs STARS portfolio management system, or plugged into other open systems. Savvysoft has been voted the number one ranked derivatives analytics vendor three years in a row in customer satisfaction surveys by Risk and Euromoney magazines.