Interest-Rate Products Pricing Problems with Uncertain Jump Processes

Yiyao Sun,Filippo Cacace,Shiqin Liu

doi:10.1155/2021/7398770

Abstract

Uncertain differential equations (UDEs) with jumps are an essential tool to model the dynamic uncertain systems with dramatic changes. The interest rates, impacted heavily by human uncertainty, are assumed to follow UDEs with jumps in ideal markets. Based on this assumption, two derivatives, namely, interest-rate caps (IRCs) and interest-rate floors (IRFs), are investigated. Some formulas are presented to calculate their prices, which are of too complex forms for calculation in practice. For this reason, numerical algorithms are designed by using the formulas in order to compute the prices of these structured products. Numerical experiments are performed to illustrate the effectiveness and efficiency, which also show the prices of IRCs are strictly increasing with respect to the diffusion parameter while the prices of IRFs are strictly decreasing with respect to the diffusion parameter.

Highlights

Du [7] considered the existence of embedded options under the assumption that the fluctuation of interest rate follows fuzzy stochastic process
The Uncertain differential equations (UDEs) was firstly introduced to the financial models by Liu [9], in which the Discrete Dynamics in Nature and Society price of a stock is described by an exponential Liu process, and the European options of the stock are priced. en, Sun and Su [11] modeled the price of a stock and the interest rate in long run by means of mean-reverting processes
Sheng and Shi [13] and Gao et al [14] calculated the prices of Asian options and lookback options, respectively. ese works were generalized by Hassanzadeh and Mehrdoust [15] and Yang et al [16]. e UDEs were used to model the interest rate in the uncertain environment by Chen and Gao [17], in which the zero-coupon bond is priced in an analytic form

Summary

Introduction

Du [7] considered the existence of embedded options under the assumption that the fluctuation of interest rate follows fuzzy stochastic process. E UDEs were used to model the interest rate in the uncertain environment by Chen and Gao [17], in which the zero-coupon bond is priced in an analytic form. For the purpose of deriving the European currency options, Wang [19] supposed a currency model in which interest rate and exchange rate follow stochastic process and uncertain process, respectively.

Results

Conclusion