Fitting an Intuitionistic Fuzzy Black-Derman-Toy Model of Yield Curve to Price Interest Rate Derivatives

Identifier:  imarina:9632981

Handle: https://hdl.handle.net/20.500.11797/imarina9632981

Authors:  de Andrés-Sánchez J

Abstract:
Since the early 21st century, the Fuzzy Random Option Pricing (FROP) literature has emerged as an active field within fuzzy mathematics. Mainstream contributions model the epistemic uncertainty of parameters governing the stochastic variation of underlying asset prices through Fuzzy Numbers (FNs). Within discrete-time models, virtually all FROP contributions assume the analytical framework of the Cox, Ross, and Rubinstein model (CRR), introducing uncertainty associated with volatility through FNs, with analyses focusing on options on stock and real options. This work falls within this setting, as we extend the nonarbitrage model of the Black, Derman, and Toy (BDT) interest rate term structure to the hypothesis that short-term interest rate volatility is estimated through Intuitionistic Fuzzy Numbers (IFNs), a generalization of FNs that allows the introduction of bipolar uncertainty. As a preliminary step, we propose a methodology to estimate short-term interest rate volatility as an IFN based on transforming probabilistic information into possibilistic information using empirical data and adopting the historical volatility approach. Additionally, we apply the intuitionistic BDT estimate of the yield curve to price options on zero coupon bonds, which is a novelty in the field. We believe that introducing information through IFNs is of particular interest in fixed-income derivative instruments, as they are traded in over-the-counter markets, which are less liquid than exchange markets, and negotiated contracts are usually not standardized.