MultiFactor Valuation of Floating Range Notes

Abstract

Under a one-factor Gaussian Heath-Jarrow-Morton model, Turnbull (1995) as well as Navatte and Quittard-Pinon (1999) have provided explicit pricing solutions for range notes contracts. The present paper generalizes such closed-form solutions for the context of a multifactor Gaussian HJM framework.KEY WORDS: Gaussian HJM multifactor models, change of probability measure, bivariate normal distribution, interest rate digital options, range notes Manuscript

Analytic valuation formulas for range notes and an affine term structure model with jump risks

“…Under a Gaussian model, Nunes (2004) found an analytic representation of C P ðK; t; sÞ by using the distribution of RðX s Þ and a standard probability theory. However, his probabilistic method is not applicable to derive an analytic representation of C P ðK; t; sÞ under non-Gaussian models, thus the Fourier transform method by Carr and Madan (1999) must be used for our further analysis.…”

“…They derive the result by considering a RAN as a portfolio of interest-rate digital options having different maturities. Nunes (2004) also finds an analytic valuation formula under a multi-factor Gaussian model and Eberlein and Kluge (2006) find the formula under a multivariate Levy term structure model, an extension of a Gaussian HJM model with jump processes. However, up to our knowledge, there is no literature on risk analysis or hedging strategies concerning RANs or SRANs, which are primary interest of risk managers and traders, and there is no previous study of valuation of SRANs.…”

Valuation of Quanto Floating Range Notes under the Cross-Currency LIBOR Market Model

“…They decomposed a FRN into a portfolio of a set of options called double delayed digital options. Nunes (2004) adopted the multifactor Gaussian HJM framework to provide an FRN pricing model, which was also regarded as a portfolio of delayed digital options. Eberlein et al (2006) derived an analytical valuation formula for FRNs that generalized the multifactor Gaussian HJM model with a multivariate Lévy process.…”

Pricing and hedging of quanto range accrual notes under Gaussian HJM with cross‐currency Levy processes

“…Then, Navatte and Quittard-Pinon (1999) reevaluated each coupon of a FRAN with the same approach as Turnbull (1995) using a modified numeraire technique. Then, Nunes (2004) generalized the solutions above with a multifactor Gaussian model. However, the aforementioned three studies did not consider the fact that the geometric Brownian motion (GBM) is generally a misspecification of asset prices (Merton, 1976).…”