Science and Technology Studies Commons^™

Pricing Of Barrier Options On Underlying Assets With Jump-Diffusion Dynamics: A Mellin Transform Approach, Marianito R. Rodrigo

Faculty of Engineering and Information Sciences - Papers: Part B

A barrier option is an exotic path-dependent option contract where the right to buy or sell is activated or extinguished when the underlying asset reaches a certain barrier price during the lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing formulas for barrier options with general payoffs and exponential barriers on underlying assets that have jump-diffusion dynamics. With the same approach we also price barrier options on underlying futures contracts.

An Accurate Approximation Formula For Pricing European Options With Discrete Dividend Payments, Song-Ping Zhu, Xinjiang He

Faculty of Engineering and Information Sciences - Papers: Part A

In this article, two relevant problems related to pricing European options with discrete dividend under the classic Black-Scholes framework are considered. For the case when a discrete dividend payment is proportional to the underlying asset value, we discuss an interesting phenomenon observed; the option price is independent of the dividend payment date. This appears to be at odds with one's intuition that dividend amount, as well as the dividend date, should both affect the price of a European call or put option. We reveal the fundamental reasons, from both mathematical and financial viewpoints, why this occurs. When the amount of …

Pricing Parisian And Parasian Options Analytically, Song-Ping Zhu, Wen-Ting Chen

Professor Song-Ping Zhu

In this paper, two analytic solutions for the valuation of European-style Parisian and Par. asian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previous analytical solutions, which still require a numerical inversion of Laplace transform, our solutions, written in terms of double integral for the case of Parisian options but multiple integrals for the case of Par. asian options, are both of explicit form; numerical evaluation …

Residential And Business Broadband Prices Part 1: An Empirical Analysis Of Metering And Other Price Determinants, Scott J. Wallsten, James Riso

Scott J. Wallsten

For this project, we assemble a new dataset consisting of more than 25,000 residential and business broadband plans from all OECD countries from 2007–2009. We explore three issues: the relationship between plan components—such as metering—and consumer prices, price changes over time, and how broadband prices vary across countries.

This paper, part 1 of the project, discusses pricing for broadband plans and, specifically, the relationship between plan components and pricing. We find that residential broadband plans with data caps—plans in which consumers pay a base price for a set amount of data—cost less than plans with unlimited data, other things being …

The Pricing Of Credit Default Swaps Under A Generalized Mixed Fractional Brownian Motion, Xinjiang He, Wenting Chen

Faculty of Engineering and Information Sciences - Papers: Part A

In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two …

Global Optimization Method For Robust Pricing Of Transportation Networks Under Uncertain Demand, Shuaian Wang, Lauren Gardner, S.Travis Waller

Faculty of Engineering and Information Sciences - Papers: Part A

We extend the existing toll pricing studies with fixed demand to stochastic demand. A new and practical second-best pricing problem with uncertain demand is proposed and formulated as a stochastic mathematical program with equilibrium constraints. In view of the problem structure, we develop a tailored global optimization algorithm. This algorithm incorporates a sample average approximation scheme, a relaxation-strengthening method, and a linearization approach. The proposed global optimization algorithm is applied to three networks: a two-link network, a seven-eleven network and the Sioux-Falls network. The results demonstrate that using a single fixed estimation of future demand may overestimate the future system …

Variational Inequality Model For Cordon-Based Congestion Pricing Under Side Constrained Stochastic User Equilibrium Conditions, Zhiyuan Liu, Qiang Meng, Shuaian Wang

Faculty of Engineering and Information Sciences - Papers: Part A

A major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behaviour is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown …

Pricing Variance Swaps With Stochastic Volatility, Song-Ping Zhu, Guang-Hua Lian

Professor Song-Ping Zhu

Following the pricing approach proposed by Zhu & Lian [19], we present an exact solution for pricing variance swaps with the realized variance in the payoff function being a logarithmic return of the underlying asset at some pre-specified discrete sampling points. Our newly-found pricing formula is based on the Heston's [8] two-factor stochastic volatility model. The discovery of this exact and closed-form solution has significantly improved the computational efficiency involved in computing the value of variance swaps with discrete sampling points.

Pricing Parisian And Parasian Options Analytically, Song-Ping Zhu, Wen-Ting Chen

Faculty of Engineering and Information Sciences - Papers: Part A

In this paper, two analytic solutions for the valuation of European-style Parisian and Par. asian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previous analytical solutions, which still require a numerical inversion of Laplace transform, our solutions, written in terms of double integral for the case of Parisian options but multiple integrals for the case of Par. asian options, are both of explicit form; numerical evaluation …

Stochastic Volatility Models And The Pricing Of Vix Options, Joanna Goard, Mathew Mazur

Faculty of Engineering and Information Sciences - Papers: Part A

In this paper we examine and compare the performance of a variety of continuous- time volatility models in their ability to capture the behaviour of the VIX. The `3/2- model' with a di®usion structure which allows the volatility of volatility changes to be highly sensitive to the actual level of volatility is found to outperform all other popular models tested. Analytic solutions for option prices on the VIX under the 3/2- model are developed and then used to calibrate at-the-money market option prices.

Speed-Based Toll Design For Cordon-Based Congestion Pricing Scheme, Zhiyuan Liu, Qiang Meng, Shuaian Wang

Faculty of Engineering and Information Sciences - Papers: Part A

The cordon-based Electronic Road Pricing (ERP) system in Singapore adopts the average travel speed as an index for evaluating the traffic congestion within a cordon area, and the maintenance of the average travel speed within a satisfactory range is taken as the objective of the toll adjustment. To formulate this practical speed-based toll design problem, this paper proposes a mathematical programming with equilibrium constraint (MPEC) model with the objective of maintaining the traffic condition in the cordon area. In the model, the network users' route choice behavior is assumed to follow probit-based stochastic user equilibrium with elastic demand, asymmetric link …

Pricing Strategies In A Digital World, Laura Martin, Scott J. Wallsten

Scott J. Wallsten

No abstract provided.

Residential And Business Broadband Prices Part 2: International Comparisons, Scott J. Wallsten, James Riso

Scott J. Wallsten

For this project, we assemble a new dataset consisting of more than 25,000 residential and business broadband plans from all OECD countries from 2007–2009. We explore three issues: the relationship between plan components—such as metering—and consumer prices, price changes over time, and how broadband prices vary across countries.

This paper, part 2 of the project, studies prices and price changes over time in the United States and other OECD countries. We find that residential prices in the U.S. remained fairly stable overall in this time period for both standalone and triple play (voice, video, and data) plans, though prices for …

Residential And Business Broadband Prices: Data Appendix, Scott J. Wallsten, James Riso

Scott J. Wallsten

No abstract provided.

Residential Broadband Competition In The United States, Scott J. Wallsten, Colleen Mallahan

Scott J. Wallsten

This paper uses a new FCC dataset on residential broadband subscribership and speeds at the census tract level combined with data from a number of additional sources to explore the state of broadband competition in the U.S. and test the effects of competition on speeds, penetration, and prices.

We find that the number of wireline providers in a census tract is positively correlated with the highest available broadband speeds, even when controlling for housing density, household income, state fixed effects, and endogenizing the number of providers. That is, we find that DSL, cable, and fiber speeds are each significantly higher …

Pricing Variance Swaps With Stochastic Volatility, Song-Ping Zhu, Guang-Hua Lian

Faculty of Engineering and Information Sciences - Papers: Part A

Following the pricing approach proposed by Zhu & Lian [19], we present an exact solution for pricing variance swaps with the realized variance in the payoff function being a logarithmic return of the underlying asset at some pre-specified discrete sampling points. Our newly-found pricing formula is based on the Heston's [8] two-factor stochastic volatility model. The discovery of this exact and closed-form solution has significantly improved the computational efficiency involved in computing the value of variance swaps with discrete sampling points.

The Economics Of Pacific Bell V. Linkline Communications, Scott J. Wallsten

Scott J. Wallsten

No abstract provided.