Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation

In this paper we review the renowned constant elasticity of variance (CEV) option pricing model and give the detailed derivations. There are two purposes of this article. First, we show the details of the formulae needed in deriving the option pricing and bridge the gaps in deriving the necessary formulae for the model. Second, we use a result by Feller to obtain the transition probability density function of the stock price at time T given its price at time t   with t<T$t<T$. In addition, some computational considerations are given for the facilitation of computing the CEV option pricing formula.     

A class of nonlinear stochastic volatility models and its implications for pricing currency options

A class of stochastic volatility (SV) models is proposed by applying the Box-Cox transformation to the volatility equation. This class of nonlinear SV (N-SV) models encompasses all standard SV models, including the well-known lognormal (LN) SV model. It allows to empirically compare and test all standard specifications in a very convenient way and provides a measure of the degree of departure from the classical models. A likelihood-based technique is developed for analyzing the model. Daily dollar/pound exchange rate data provide some evidence against LN model and strong evidence against all the other classical specifications. An efficient algorithm is proposed to study the economic importance of the proposed model on pricing currency options.     

Bond pricing in APL2: A study in numerical solution of the Brennan and Schwartz bond pricing model using a vector processor

This paper is a unification of two earlier papers: the original model of the bond pricing algorithm developed by Foote, Kraemer, and the author [4] and a later paper reported at the Third Supercomputer Conference [5]. This paper briefly discusses the Brennan and Schwartz bond pricing model which was the application studied, presents its finite difference representation and describes three APL2 implementations. Problems in computation are discussed briefly and the three methods for a fixed size grid are compared with and without the IBM 3090 Vector Facility.     

A method of time–time analysis: The TT-transform

A novel technique of analysis of an arbitrary primary time series into a set of secondary, time-limited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform of the primary time series. Similarly, when summed over the primary time variable, the TT-transform reverts to the primary time series. The invertibility of the TT-transform points to the possibility of filtering and signal to noise improvements in the time domain, and some insight into the localized spectra of the S-transform.     

Analysis of a multigrid method for a transport equation by numerical Fourier analysis

In this paper, we perform Fourier analysis for a multigrid method with two-cell μ-line relaxation for solving isotropic transport equations. Our numerical results show that the Fourier analysis prediction for convergence rates is more accurate than that previously found by matrix analysis.     

A real-time road pricing system: The case of a two-link parallel network

A real-time road pricing system in the case of a two-link parallel network is proposed in this paper. The system that is based on a combination of Dynamic Programming and Neural Networks makes “on-line” decisions about road toll values. In the first phase of the proposed model, the best road toll sequences during certain time period are calculated off-line for many different patterns of vehicle arrivals. These toll sequences are computed using Dynamic Programming approach. In the second phase, learning from vehicle arrival patterns and the corresponding optimal toll sequences, neural network is trained. The results obtained during on-line tests are close to the best solution obtained off-line assuming that the arrival pattern is known.     

Estimation of fog utility pricing: a bio-inspired optimisation techniques' perspective

ABSTRACT

Due to the limited data storage capacity available to Internet service providers and large-scale enterprises, the concept of resource sharing arises. The services can be given on lease to enterprises through Service Level Agreements. Being the extension of the cloud computing, fog computing architecture brings the resources near end users. In order to get the services on lease, the enterprises are supposed to pay for the resources or services which are being used by them. In this paper, four nature inspired algorithms are analysed in order to determine the efficient management of services or resources so that the cost of resources can be reduced and the billing can be attained through calculation of the utilised resources. Pigeon inspired optimization, enhanced differential evolution, binary bat algorithm and simple human learning optimization are used to evaluate the energy consumed by the edge nodes or cloudlets that in turn can be used for estimating the bill through the Time of Use pricing variable. We evaluate the aforementioned techniques to analyse their performance regarding the bill calculation on the basis of fog servers usage. Simulation results demonstrate that BAT algorithm gives significantly better results than other three algorithms in terms of resource utilisation and bill reduction.     

Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model

In this paper, we discuss the numerical analysis and the pricing and hedging of European Spread options on correlated assets when, in contrast to the standard framework and consistent with a market with imperfect liquidity, the option trader's trading in the stock market has a direct impact on one of the stocks price. We consider a first-order feedback model which leads to a linear partial differential equation. The Peaceman–Rachford scheme is applied as an alternating direction implicit method to solve the equation numerically. We also discuss the stability and convergence of this numerical scheme. Finally, we provide a numerical analysis of the effect of the illiquidity in the underlying asset market on the replication of an European Spread option; compared to the Black–Scholes case, a trader generally buys less stock to replicate a call option.     

考虑需求响应的纳网双向定价斯坦伯格博弈模型 (英文）

新能源发电和负荷需求的波动性使得纳网内能源盈馀不同,从而影响本地新能源消纳水平和运行成本。本文针对纳网内暖通空调潜在的热弹性调节能力,阐述了一种基于用户舒适度偏好和环境因素的需求响应和双向定价策略,来优化纳网与公共管理中心间的能源双向交易及时均收益。所构建的双层交易随机优化模型中由于存在不确定参数和时间耦合温度队列使得长期优化问题求解复杂。为此设计了一种基于李雅普诺夫优化方法的松弛形式对原问题进行时间解耦,重构主从博弈框架来刻画参与者能量交易决策间的相互影响关系,并进一步对博弈均衡点的存在与唯一性给出严格的证明。在此基础上提出了一种优化响应算法使得决策者间能以较少的信息交换达到博弈均衡。最后通过仿真实验验证了该能量管理算法的有效性。     

Parametric models and non-parametric machine learning models for predicting option prices: Empirical comparison study over KOSPI 200 Index options

We investigated the performance of parametric and non-parametric methods concerning the in-sample pricing and out-of-sample prediction performances of index options. Comparisons were performed on the KOSPI 200 Index options from January 2001 to December 2010. To verify the statistical differences between the compared methods, we tested the following null hypothesis: two series of forecasting errors have the same mean-squared value. The experimental study reveals that non-parametric methods significantly outperform parametric methods on both in-sample pricing and out-of-sample pricing. The outperforming non-parametric method is statistically different from the other models, and significantly different from the parametric models. The Gaussian process model delivers the most outstanding performance in forecasting, and also provides the predictive distribution of option prices.     

Multitasking across generations: Multitasking choices and difficulty ratings in three generations of Americans

This study investigated whether changes in the technological/social environment in the United States over time have resulted in concomitant changes in the multitasking skills of younger generations. One thousand, three hundred and nineteen Americans from three generations were queried to determine their at-home multitasking behaviors. An anonymous online questionnaire asked respondents to indicate which everyday and technology-based tasks they choose to combine for multitasking and to indicate how difficult it is to multitask when combining the tasks. Combining tasks occurred frequently, especially while listening to music or eating. Members of the “Net Generation” reported more multitasking than members of “Generation X,” who reported more multitasking than members of the “Baby Boomer” generation. The choices of which tasks to combine for multitasking were highly correlated across generations, as were difficulty ratings of specific multitasking combinations. The results are consistent with a greater amount of general multitasking resources in younger generations, but similar mental limitations in the types of tasks that can be multitasked.     

SipaaS: Spot instance pricing as a Service framework and its implementation in OpenStack

Designing dynamic pricing mechanisms that efficiently price resources in line with a provider's profit maximization goal is a key challenge in cloud computing environments. Despite the large volume of research published on this topic, there is no publicly available software system implementing dynamic pricing for Infrastructure as a Service cloud spot markets. This paper presents the implementation of a framework called Spot instance pricing as a Service (SipaaS) that supports an auction mechanism to price and allocate virtual machine instances. SipaaS is an open‐source project offering a set of web services to price and sell virtual machine instances in a spot market resembling the Amazon EC2 spot instances. Cloud providers, who aim at utilizing SipaaS, should install add‐ons in their existing platform to make use of the framework. As an instance, we provide an extension to the Horizon – the OpenStack dashboard project – to employ SipaaS web services and to add a spot market environment to OpenStack. To validate and evaluate the system, we conducted an experimental study with a group of 10 users utilizing the provided spot market in a real environment. Results show that the system performs reliably in a practical test environment. Copyright © 2015 John Wiley & Sons, Ltd.     

Equilibrium allocation and pricing of variable resources among user-suppliers

We propose a novel model of resource sharing schemes that provide each user with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. At equilibrium, if it exists, all users optimize their utility and resource demand equals supply, i.e., the marginal increase in user utility due to higher return on variable resources is balanced by the marginal decrease in utility due to their variability. We show how an equilibrium might be approached using a simple price adjustment rule that does not require any knowledge on the part of the network about user utilities. We further show that at equilibrium every user holds strictly positive amounts of variable bandwidth and variable buffer, and in the same ratio. We characterize the equilibrium prices to lie in a hyperplane that can be computed by the network without having to know user utilities. We illustrate with an example how this characterization might significantly speed up convergence towards an equilibrium.     

Unified discount pricing models of a two-echelon channel with a monopolistic manufacturer and heterogeneous retailers

This paper considers a two‐echelon channel in which a monopolistic manufacturer supplies a single product to multiple heterogeneous retailers who are in separate markets. The present paper studies the problem of how the manufacturer in a manufacturer‐Stackelberg game designs a unified quantity‐discount pricing scheme to improve the whole channel's profit as well as each partner's profit. Considered in the paper are two types of unified quantity‐discount pricing schemes: the regular quantity‐discount pricing scheme and the incremental volume discount pricing scheme. Each of the two types of schemes includes a single price‐break discount policy and a non‐linear quantity discount policy. Optimal solutions are derived and numerical examples presented to illustrate the efficiency of each discount policy.     

Vertical pricing competition in supply chains: the effect of production experience and coordination

We consider a two‐echelon supply chain consisting of a single supplier (producer) and a retailer. The supplier determines the wholesale price with a production cost decreasing with experience. The retailer orders products from the supplier to meet demands. Negative effects of a vertical competition in static supply chain models are typically attributed to a double marginalization. Using an intertemporal supply chain problem, defined by a differential game, we show that in addition to the “cost” of double marginalization, the margin gained from reducing production costs affects the supply chain performance as well. In our analysis, performance is shown to deteriorate even more than the deterioration observed in static problems with no learning (experience). To improve the performance, we provide a time‐variant version to the well‐known, pure, two‐part tariff strategy, which in its dynamic framework may coordinate the supply chain only partially. Efficient coordination in a supply chain is shown to be possible if a mixed two‐part tariff strategy is employed, however.     

The effect of firm number on equilibrium product positioning and pricing: a marketing–production perspective

We examine how product design and pricing are affected when the number of firms in the market increases by considering marketing and production variables. We employ a model that adopts marketing notions such as market shares and ideal points to dictate the attraction of the product to consumers. The model also incorporates production costs where the cost of the product increases linearly with increasing product attribute levels. The modeling framework facilitates the existence of a Nash equilibrium in prices and product positions. The number of firms in the market is exogenously defined. When the number of firms in the market increases, firms lower their prices and design their product with features closer to the market's ideal point. This results in lower profits.     

Effect of information,uncertainty and parameter variability on profits in a queue with various pricing strategies

This paper presents an unobservable single-server queueing system with three types of uncertainty, where the service rate, or waiting cost or service quality is random variable that may obtain n(n > 2) values. The information about the realised values of parameters is only known to the server. We are concerned about the server’s behaviour: revealing or concealing the information to customers. The n-value assumption and the server’s behaviour enable us to consider various pricing strategies. In this paper, we analyse the effect of information and uncertainty on profits and make comparisons between the profits under different pricing strategies. Moreover, as for parameter variability reflected by the number of each parameter’s possible choices n, we observe the effect of variable n on all types of profits and find that revealing the parameter information can much more benefit the server with the increase of n.     

Marketplace or reselling: the pricing decisions and face value of the coupons under the Cap-and-Trade regulation

This paper considers a manufacturer selling his products with the marketplace or the reselling mode under the cap-and-trade regulation. Coupons are allocated when selling the products. We explore the optimal decisions, the selection and the coordination with the two modes. First, we analytically find that the increase of the cap and platform power (commission rate) increases (decreases) the total production quantity and the optimal production quantity for coupon-sensitive consumers, and interestingly find that it reduces (increases) the production quantity for coupon-insensitive consumers when the sensitivity of the coupons is high. Furthermore, the optimal profit of the manufacturer first increases and then decreases with the cap when the emission intensity is low, and it increases with the cap when the emission intensity is high. Second, the marketplace mode creates more (less) profits for the manufacturer if the order-fulfillment cost is low (high). Whether the marketplace mode or the reselling mode will generate more carbon emission depends on the commission rate and the platform power. Finally, the marketplace mode is not capable of coordinating the manufacturer and the platform at all times, while the reselling mode can coordinate the two firms after considering a coupon-sharing contract under considerable platform power, and they can achieve Pareto improvement with a two-part tariff contract under the generalized Nash bargaining framework.