Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks

Abstract

As an important economic index, interest rates are assumed to be constant in the Black and Scholes model (1973); however, they actually fluctuate due to economic factors. Using a constant interest rate to evaluate derivatives in a stochastic model will produce biased results.This research derives the LIBOR market model with jump risks, assuming that interest rates follow a continuous time path and tend to jump in response to sudden economic shocks. We then use the LIBOR model with jump risk to price a Range Accrual Interest Rate Swap (RAIRS). Given that the multiple jump processes are independent, we employ numerical analysis to further demonstrate the influence of jump size, jump volatility, and jump frequency on the pricing of RAIRS. Our results show a negative relation between jump size, jump frequency, and the swap rate of RAIRS, but a positive relation between jump volatility and the swap rate of RAIRS. When new information emerges, the resulting increase in jump size reduces the value of LIBOR, which in turn lowers the value of RAIRS. Similarly, the value of RAIRS declines when the jump frequency of LIBOR increases. This is because jump frequency is associated with higher uncertainty risk, and the market pays out a premium for bearing such risk. On the other hand, when jump volatility increases, both parties must agree to a higher swap rate because the floating rate payer is subsidized by the fixed rate payer for bearing risk.

Medical Decision-Making by Patients and Providers Under Uncertainty and in the Presence of Antibiotic Resistance

“…The approach used in this section shows one way to model and study a public policy issue of considerable importance, namely, how to provide health care to sick individuals at the lowest possible cost. consistent with our observation in the last paragraph of section 3.5, it would be worthwhile to determine whether methods of the sort utilized by Lin et al (2017) or other similar methods can be employed to solve equation (1) numerically and to see how sensitive the obtained solution is…”

Medical decision-making by patients and providers under uncertainty and in the presence of antibiotic resistance

“…Here are two suggestions for extending the research described in this paper. First, consistent with our observation in the last paragraph of section 3.5, it would be worthwhile to determine whether methods of the sort utilized byLin et al (2017) or other similar methods can be employed to solve equation (1) numerically and to see how sensitive the obtained solution is to alternate specifications of, for instance, the parameter . Second, it would also be interesting to use game theory---possibly as inGreenberg et al (2002)---to analyze the patient-physician interaction as a game in which both players interact with each other repeatedly over time.…”

Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions

“…Traditional models often incorporate stochastic volatility, correlations, and random jumps to capture the inherent complexities of interest rate dynamics (Bouziane 2008). The literature suggests that jumps play a significant role in interest rate dynamics (Balduzzi et al (2001), Glasserman and Kou (2003), and Lin et al (2017)). However, they fail to accurately reflect the precise occurrence of scheduled events such as central bank announcements.…”