Relative Guarantees

Many real-world financial contracts have some sort of minimum rate of return guarantee included. One class of these guarantees is so-called relative guarantees, i.e., guarantees where the minimum guaranteed rate of return is given as a function of the stochastic return on a reference portfolio. These guarantees are the topic of this paper. We analyse a wide range of different functional specifications for the minimum guaranteed rate of return, hereunder both so-called maturity and multi-period guarantees. Several closed form solutions are presented.     

WHEN IS THE SHORT RATE MARKOVIAN?

We answer this question in the very general context of the n-factor Heath, Jarrow, and Morton model for the evolution of the term structure of interest rates, with nonrandom volatility. the answer is that a constraint is imposed on the behavior of the volatility structure. We explain the importance of this result for the design of efficient numerical algorithms for the valuation of options on the term structure.     

A Generalization of the Formulas for Options on the Maximum or the Minimum of Several Assets

Abstract

This paper generalizes the option on the maximum or the minimum of two assets (several assets) within a stochastic interest rate framework. A Gaussian model is used to describe the interest rates. Closed-form solutions for the market values are presented. The use of the options is illustrated with numerical examples.     

石油企业制定和执行健康,安全与环境管理体系标准的必要性

本文介绍了石油天然气工业健康、安全与环境管理体系标准的主要内容,简述了制定和执行该标准在国际竞争和国内自身管理两方面的重要性。指出,制定和执行健康、安全与环境管理体系标准是国际发展的大趋势,是石油工业自身管理的需要。     

Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes

We study a continuous trading bond model where the associated forward rate curve follows a multidimensional Poisson-Gaussian process. the bond market is complete, and the unique arbitrage-free interest rate call option price is explicitly derived.     

The Markov-switching jump diffusion LIBOR market model

In this paper, we introduce an extension to the LIBOR Market Model (LMM) that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LMM by a regime-switching jump diffusion. We demonstrate that the new Markov-switching jump diffusion (MSJD) LMM can be embedded into a generalized regime-switching Heath–Jarrow–Morton model and prove that the considered market is arbitrage-free. We derive pricing formulas for caps, floors and swaptions using Fourier pricing techniques and show how the model can be calibrated to real market data.     

VOLATILITY STRUCTURES OF FORWARD RATES AND THE DYNAMICS OF THE TERM STRUCTURE1

For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.