Perpetual Bermudan Continuity Corrections and a Multi-Dimensional Wiener–Hopf Type Result

Abstract

In this article, Wiener–Hopf type results by Feller are generalized to higher dimensions, in order to derive bounds on the continuity corrections at the exercise boundary for certain perpetual Bermudan options on multiple assets. We assume that the vector of logarithmic price processes of the underlyings is a Lévy process under some risk-neutral measure. In addition, we have to impose the condition that the payoff functions of these perpetual Bermudans have been chosen in such a way that the corresponding optimal exercise regions of the Bermudan options are, up to translation, a half-space. (This is, of course, a fairly restrictive assumption for higher dimensions, but none for dimension one.)     

Pricing American currency options in an exponential Lévy model

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Lévy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone‐Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.     

Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree

In this paper, we present a natural mathematical framework to model trader behavior as a continuous time discrete event process, and derive stochastic differential equations for aggregate behavior and price dynamics by passing to diffusion limits. In particular, we model extraneous, value, momentum and hedge traders. Through analysis and numerical simulation we explore some of the effects these trading strategies have on price dynamics.     

Numerical Methods and Volatility Models for Valuing Cliquet Options

Several numerical issues for valuing cliquet options using PDE methods are investigated. The use of a running sum of returns formulation is compared to an average return formulation. Methods for grid construction, interpolation of jump conditions, and application of boundary conditions are compared. The effect of various volatility modelling assumptions on the value of cliquet options is also studied. Numerical results are reported for jump diffusion models, calibrated volatility surface models, and uncertain volatility models.     

Comment on ‘Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Lévy Processes’ by C. Ribeiro and N. Webber

Abstract

This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Lévy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic function of the intertemporal joint distribution of the time-changed Lévy process. Using the derived representation of the characteristic function, we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader and lookback options, all of which are discretely monitored.     

The pricing of Asian options under stochastic interest rates

The purpose of this paper is to analyse the effect of stochastic interest rates on the pricing of Asian options. It is shown that a stochastic, in contrast to a deterministic, development of the term structure of interest rates has a significant influence. The price of the underlying asset, e.g. a stock or oil, and the prices of bonds are assumed to follow correlated two-dimensional Itô processes. The averages considered in the Asian options are calculated on a discrete time grid, e.g. all closing prices on Wednesdays during the lifetime of the contract. The value of an Asian option will be obtained through the application of Monte Carlo simulation, and for this purpose the stochastic processes for the basic assets need not be severely restricted. However, to make comparison with published results originating from models with deterministic interest rates, we will stay within the setting of a Gaussian framework.     

Options on Realized Variance in Log-OU Models

Abstract

We study the pricing of options on realized variance in a general class of Log-OU (Ornstein–Ühlenbeck) stochastic volatility models. The class includes several important models proposed in the literature. Having as common feature the log-normal law of instantaneous variance, the application of standard Fourier–Laplace transform methods is not feasible. We derive extensions of Asian pricing methods, to obtain bounds, in particular, a very tight lower bound for options on realized variance.     

Multivariate option pricing using copulae

The complexity of financial products significantly increased in the past 10 years. In this paper, we investigate the pricing of basket options and more generally of complex exotic contracts depending on multiple indices. Our approach assumes that the underlying assets evolve as dependent GARCH(1, 1) processes. The dependence among the assets is modeled using a copula based on pair‐copula constructions. Unlike most previous studies on this topic, we do not assume that the dependence observed between historical asset prices is similar to the dependence under the risk‐neutral probability. The method is illustrated with US market data on basket options written on two or three international indices. Copyright © 2012 John Wiley & Sons, Ltd.     

异物致损铁道车轴的疲劳强度及寿命评估

车轴是高速列车关键承载部件, 承受着源自车体、轨道的各种载荷,其疲劳行为直接关乎列车运行安全. 疲劳裂纹往往具有较强的隐蔽性和突然性,由车轴断裂发生的列车脱轨事件具有灾难性,因此确保车轴在运行中不发生失效事故, 对高速列车可靠运行至关重要.高速列车实际运营中, 车轴外表面受到各种异物击打, 会形成深度达毫米级的缺陷,破坏车轴表面完整性, 严重威胁车辆安全.本研究采用空气炮装置预制合金钢车轴小试样异物致损(foreign object damage, FOD)缺陷,采用扫描电子显微镜和体视显微镜观测损伤特征.开展高周疲劳试验获得光滑试样和FOD损伤小试样的疲劳S-N曲线,考虑载荷模式、表面质量和尺寸系数推证出全尺寸车轴的疲劳性能.断口分析表明, 裂纹于FOD附近多处位置萌生, 并在不同平面内连续扩展,最终汇聚为一个半椭圆形裂纹. 基于Peterson公式和El Haddad模型估算异物冲击速度100 m/s和138 m/s试样的理论疲劳极限远低于试验结果, 过于保守; 同时也远低于标准推荐值, 偏于危险. 最后,采用修正的Miner理论公式估算含FOD实物车轴的服役寿命,满足最低25年的服役寿命.      

汇改与外汇市场波动性:大玩家理论的视角

央行在外汇市场的行动对市场波动性有重要影响。本文从主观预期概念出发,基于“大玩家”理论解释了2005年和2015年中国外汇管理体制两次改革前后人民币外汇市场的波动性差异。汇改前,央行积极地承担着“大玩家”的角色,人民币对美元汇率波动性较强;汇改后,央行的“大玩家”角色减弱,汇率波动性程度显著下降,市场效率增强。利用汇率数据进行的R/S分析支持了前述解释。