Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.     

Investment and the dynamic cost of income uncertainty: The case of diminishing expectations in agriculture

This paper studies optimal investment and the dynamic cost of income uncertainty, applying a stochastic programming approach. The motivation is given by a case study in Finnish agriculture. The investment decision of a representative farm is modelled as a Markov decision process, extended to account for risk. A numerical framework for studying the dynamic uncertainty cost is presented, modifying the classical expected value of perfect information to a dynamic setting. The uncertainty cost depends on the volatility of income: e.g. with stationary income, the dynamic uncertainty cost corresponds to a dynamic option value of postponing investment. The model can be applied to agricultural policy planning. In the case study, the investment decision is sensitive to risk.     

Some Properties of CIR Processes

Abstract

This article derives some properties of variants of squared Bessel processes known as CIR processes in the finance literature. We derive the transition probability density function of a square-root process and compute the resolvent density of CIR processes. As a consequence, we derive the density of CIR processes sampled at an independent exponential time. Moreover, we derive explicit expressions of the Laplace transforms (LTs) of first hitting times by martingale methods.     

Exercise Boundary Near Maturity for an American Option on Several Assets

We consider an American put option on a linear function of d dividend-paying assets. The value function of this option is given as the solution of a free boundary problem. When d = 1, the behavior of the free boundary near the maturity of the option is well known. In this article, we extend to the case d > 1 the study of the free boundary near maturity. A parameterization of the stopping region at time t is given. That enables us to define and give a convergence rate for this region when t goes to the maturity.     

MC方差减小技术在算术平均亚式外汇期权定价中的应用

建立了利率和汇率波动率均为随机情形下算术平均亚式外汇期权的定价模型.由于其定价问题求解十分困难,运用蒙特卡罗(Monte Carlo)方法并结合控制变量方差减小技术进行模拟,有效地减小了模拟方差,得到了期权定价问题的数值结果.     

市场化改革、经济战略与中国外汇储备积累:实证研究

对中国外汇储备成因的传统研究在很大程度上忽略了市场化进程因素对中国外汇储备积累的历史性和制度化影响。而外汇储备的决定因素分为两大类:战略性因素和制度性因素。战略性因素包括预防性需求、重商主义动机和机会成本;制度性因素包括对外贸易发展和市场化程度。通过一个改进的外汇储备需求函数模型对该因素进行实证研究,发现中国的外汇储备积累主要是外向型经济发展模式和市场化改革这一历史进程的客观结果,而非货币当局基于主观动机所追求的战略目标。     

基于指数障碍期权的抛物方程的存在性和唯一性

考虑了一类基于指数障碍期权的拟线性抛物型方程.首先在b(t,x)=c(t,x)=0情形下运用标准的Schauder理论证明了该抛物型方程问题存在一个属于Cα,1+α/2的唯一解.其次,运用变换的方法将该结论推广到了一般方程.     

Two Exotic Lookback Options

This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look‐barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look‐barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed‐form representations in the Black–Scholes framework.     

Computing the Volume of n-Dimensional Copulas

Abstract

A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put–call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance.     

Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility

Abstract

We show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously sampled fixed-strike arithmetic Asian call option, in the presence of non-zero time-dependent interest rates (Theorem 1.2). We also propose a model-independent lognormal moment-matching procedure for approximating the price of an Asian call, and we show how to apply these approximations under the Black–Scholes and Heston models (subsection 1.3). We then apply a similar analysis to a time-dependent Heston stochastic volatility model, and we show how to construct a time-dependent mean reversion and volatility-of-variance function, so as to be consistent with the observed variance swap curve and a pre-specified term structure for the variance of the integrated variance (Theorem 2.1). We characterize the small-time asymptotics of the first and second moments of the integrated variance (Proposition 2.2) and derive an approximation for the price of a volatility swap under the time-dependent Heston model ( Equation (52)), using the Brockhaus–Long approximation (Brockhaus, and Long, 2000 Brockhaus, O. and Long, D. 2000. Volatility Swaps made simple. Risk, 13(1) January: 92–96.  [Google Scholar]). We also outline a bootstrapping procedure for calibrating a piecewise-linear mean reversion level and volatility-of-volatility function (Subsection 2.3.2).