In addition to SD's benchmark prices for all options, SD includes a number of popular industry models in its pricing applications. So, for example, in SDX Interest Rates the BGM model is available for supported instruments.
Ultimately, this gives users greater insight into how the various prices are obtained. Having the ability to analyze various models allows better understanding of the market price, and will ultimately increase price transparency in the market, resulting in greater liquidity overall.
In SDX Interest Rates the BGM model is calibrated to market observed prices for the cap and swaption, and is currently implemented for the following instruments—Bermudan swaption, range accrual swap, callable swap, callable inverse floater, callable capped floater swap and inverse floater TARN.
The concept behind the BGM (or Brace Gaterek Musiela) model, also known as the LIBOR market model, is that instead of modeling the time evolution of the yield curve via a single short rate, the model describes the evolution of all the forward LIBOR rates simultaneously in a manner that is consistent with the Black volatilities observed in the market place.
In the BGM model the quantity that is modeled is a set of forward rates, which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts.
Each forward rate is modeled by a lognormal process under its forward measure (i.e., a Black model leading to a Black formula for interest rate caps). The Black formula here is the market standard to quote cap prices in terms of implied volatilities, hence the term "market model". However, whereas the Black model deals with a single forward rate, the BGM (or LIBOR market) model may be interpreted as a collection of forward LIBOR dynamics for all points on the yield curve.
The BGM model is intrinsically multi-factor, meaning that it accurately captures various aspects of the curve dynamics—parallel shifts, steepenings/flattenings, curvature, etc.
The advantage of the BGM model is that it lets you impose an approximately stationary volatility and correlation structure of LIBOR forwards. This reflects the view that the volatility structure of interest rates retains its shape over time, without distorting the valuation of instruments sensitive to forward volatility. This is a benefit over the short rate models. One of the main difficulties experienced by short rate models is the fact that they tend to produce unrealistic volatility structures of forward rates. The persistent hump occurring in the short end of the volatility curve leads to overvaluation of instruments depending on forward volatility.
What is SD's BGM model?
SD has developed its own BGM model for the pricing of exotic interest rates derivatives. SD’s BGM model is calibrated to both cap (caplet) and swaption ATM volatilities: the implementation is via American Monte Carlo using the Longstaff-Schwartz treatment.
In the Single Option page, depending on the instrument being priced, the BGM model can optionally be used to calculate the instrument's:
Price as a %
This is for a Bermudan swaption.
Breakeven rate as a %
This result shows by default the fixed rate (in a mid format) that will automatically result in a zero NPV. In this situation the system does not display the NPV. However, if you then define your own fixed rate, via the Market Rate field, SD takes that edited rate as the fixed rate input for the BGM model and then calculates the resultant NPV.
NPV amount
This result is only displayed if you define your own fixed rate, via the Market Rate field.
To improve performance, the BGM model result is not automatically calculated when you click the main Calculate button. Instead to see the relevant result according to the BGM model you must click the Calculate BGM button.