Constant Maturity Swap Spread Research Articles

Valuation of certain CMS spreads

In this paper, we derive an approximate lognormal process for the swap rate under the multifactor LIBOR market model using a Levy approach. Using the approximate dynamics for the swap rate, the constant maturity swap spread digital range notes with different strike rates are valued in analytic and semi-analytic form. The CMS spread digital range notes are widely traded in the marketplace, or embedded in structure notes.

Pricing a Callable Leveraged Constant Maturity Swap Spread Note

A callable leveraged constant maturity swap (CMS) spread note allows the holder to benefit from future changes in the spread between two swap interest rates. The issues retains the right to call the note at pre-specified times in the future. The note is priced via Monte Carlo simulation using the current term structure of interest rates and at-the-money implied swaption volatilities.

On Valuing Constant Maturity Swap Spread Derivatives

Motivated by statistical tests on historical data that confirm the normal distribution assumption on the spreads between major constant maturity swap (CMS) indexes, we propose an easy-to-implement two-factor model for valuing CMS spread link instruments, in which each forward CMS spread rate is modeled as a Gaussian process under its relevant measure, and is related to the lognormal martingale process of a corresponding maturity forward LIBOR rate through a Brownian motion. An illustrating example is provided. Closed-form solutions for CMS spread options are derived.

Pricing Callable Constant Maturity Swap Spread Range Accruals Under the Two Factor Linear Gaussian Martingale Model Using Fast Fourier Transform

I propose an efficient method to price callable constant maturity swap spread range accruals using fast Fourier transforms. I illustrate the model calibration method and pricing procedure based on a two-factor linear Gaussian Martingale model.

Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options

This work discusses the calibration of instantaneous Libor correlations in the Libor market model. We extend the existing calibration strategies by the incorporation of spread option implied correlation information. The correlation structure implied by constant maturity swap (CMS) spread options observed in the present-day market motivates us to extend the existing parameterizations of ratio correlations by a new three-parameter approach. For the first time, this paper presents an extensive empirical study of different parameterizations and their capability to match market correlations. We can show that our approach leads to stable calibrations and gives a satisfactory fit to the market. We conclude our investigation with the pricing of a callable swap on CMS spread using the parameterizations compared before.

Option Valuation in Multivariate SMM/SABR Models (with an Application to the CMS Spread)

We consider the joint dynamic of a basket of n-assets where each asset itself follows a Swap Market Model or SABR stochastic volatility model. Using the Markovian Projection methodology we approximate it by a univariate displaced diffusion SMM/SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but, in the case of the SABR model, as well the skew, the cross-skew and the decorrelation in our approximation. If for example spread options are considered the latter is not possible in alternative approximations.We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.

Analytical Formulas for Pricing CMS Products in the LIBOR Market Model with the Stochastic Volatility

In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for model calibration to the market, including European swaptions and CMS products. The first technical achievement of this work is related to the optimal calculation of the measure change. For single-rate CMS products, we have used the standard linear regression of the measure change, with optimally calculated coefficients. For the CMS spread options, where the linear procedure does not work, we propose a new effective 'non-linear' measure change technique. The fit quality of the new results is confirmed numerically using Monte Carlo simulations. The second technical advance of the article is a theoretical derivation of the generalized spread option price via two-dimensional Laplace transform presented in a closed form in terms of the complex Gamma-functions.