Installation Options Research Articles

On a general class of free boundary problems for European-style installment options with continuous payment plan

In this paper we present an integral equation approach for thevaluation of European-style installment derivatives when the paymentplan is assumed to be a continuous function of the asset price andtime. The contribution of this study is threefold. First, we showthat in the Black-Scholes model the option pricing problem can beformulated as a free boundary problem under very general conditionson payoff structure and payment schedule. Second, by applying aFourier transform-based solution technique, we derive a recursiveintegral equation for the free boundary along with an analyticrepresentation of the option price. Third, based on these results,we propose a unified framework which generalizes the existingmethods and is capable of dealing with a wide range of monotonicpayoff functions and continuous payment plans. Finally, by using theillustrative example of European vanilla installment call options,an explicit pricing formula is obtained for time-varying paymentschedules.

한우사 내 송풍팬의 최적 설치에 관한 연구

The fans installed in standard Hanwoo loose barns (room size : 10 m (width) <TEX>$\times$</TEX> 5 m (length)) are frequently used to reduce Hanwoo's heat stress during hot weather and to dry the wet floor. However, the most effective method of installing fans has not been suggested yet. Therefore, this study was carried out to evaluate two methods of installing fans under the ceiling of Hanwoo loose barn by using CFD (Computational Fluid Dynamics) code, FLUENT and to recommend the optimum fan installing method. The fan installation options were fan tilting angles of <TEX>$45^{\circ}$</TEX> and <TEX>$0^{\circ}$</TEX> (horizontal). The fans of 1 m diameter were installed at 3 m above floor. A velocity scale on 10 cm and 110 cm above floor and air flow pattern were used as the parameters to evaluate the fan installing methods. The fans tilted at <TEX>$45^{\circ}$</TEX> angle produced higher wind at 10 cm and 110 cm above floor and more uniform air flow pattern, compared with the fans installed horizontally. Based on these results, fans tilted at <TEX>$45^{\circ}$</TEX> angle may help to reduce Hanwoo's heat stress and will dry the floor better than fans installed horizontally. Therefore, it is suggested that the fans of 1 m diameter in a standard Hanwoo loose barn should be installed at a <TEX>$45^{\circ}$</TEX> tilt angle and 3 m above floor with spacing of 5 m at the center of a room column.

Qualitative Comparison of the Characteristics of Articulated and Non-Articulated Trains and Their Effects on Impact

This article presents a qualitative comparison of the key characteristics and subsequent impact performance for articulated and non-articulated train types. The fundamental purpose of the article is through a review of articulated and non-articulated trains in terms of impact stability to identify and compare the areas referred to as ‘impact worthiness’ design. The major differences between articulated and non-articulated trains are highlighted first. Then, the mechanical reasons leading to the differences and their consequences to impact performance are analysed from three viewpoints: coupling stiffness and freedom, support and coupling patterns, and carbody structural features. The analysis shows that the differences in bogie support positions on the carbody and the effects on coupling devices lead to differences in several structural and compositional characteristics, including height of gravity of the carbody, length of the vehicle, the composition of the end panel, stiffness of coupling device, number of support points to vehicle, and support height of the secondary suspension. These characteristics result in different impact responses for the two types of train and are directly related to subsequent behaviour. Articulated trains show stiff connection and integral performance in collisions but with less capability for absorbing impact energy between vehicles, whereas non-articulated trains show flexible connection with more random behaviour in collisions but with greater options for energy absorber installation between vehicles.

Valuing continuous-installment options

Abstract Installment options are path-dependent contingent claims in which the premium is paid discretely or continuously in installments, instead of paying a lump sum at the time of purchase. This paper deals with valuing European continuous-installment options written on dividend-paying assets in the standard Black–Scholes–Merton framework. The valuation of installment options can be formulated as a free boundary problem, due to the flexibility of continuing or stopping to pay installments. On the basis of a PDE for the initial premium, we derive an integral representation for the initial premium, being expressed as a difference of the corresponding European vanilla value and the expected present value of installment payments along the optimal stopping boundary. Applying the Laplace transform approach to this PDE, we obtain explicit Laplace transforms of the initial premium as well as its Greeks, which include the transformed stopping boundary in a closed form. Abelian theorems of Laplace transforms enable us to characterize asymptotic behaviors of the stopping boundary close and at infinite time to expiry. We show that numerical inversion of these Laplace transforms works well for computing both the option value and the optimal stopping boundary.

Water penetration resistance of residential window installation options for hurricane-prone areas

While recent building code advancements have reduced structural failures in residential buildings during hurricane events, water intrusion through the building envelope is a recurring problem. Water ingress poses a significant threat to the building interior and its contents. The interface between the window and the wall system has been identified as a significant source of this water ingress. The fenestration industry has made extensive efforts to develop installation methods to improve water tightness; however, the body of research needed to guide window installations in high-humidity, hurricane-prone areas is sparse. The goal of this research is to investigate the water penetration resistance of selected window installation options consistent with current construction practice of single-family homes when exposed to wind-driven rain. Static, cyclic, as well as amplitude- and frequency-modulated sinusoidal pressure load sequences were applied with simulated wind-driven rain scenarios to 18 finished wall assemblies with integrated windows. The specimens varied in their unique combination of fenestration, installation methodology, wall structural system, and exterior finish. General conclusions were drawn regarding the effectiveness of the window installation methods to manage water intrusion, as well as the effects that the components of the surrounding wall system have on their performance. The performance of the various sealants used to create the interior moisture/air seal in drainage method window installations is also investigated. It was found that the water barrier and drainage installation methods can provide sufficient water penetration resistance in wood frame construction, while the water barrier method is preferable for windows integrated into masonry walls.

Contractor Perspective on Factors for Evaluating Installation Options for Small-Diameter Utilities

Buried municipal infrastructure is rapidly expanding due to increased urbanization. Subsequently, engineers and contractors are faced with having to designate the most effective method of installing new buried infrastructure while being mindful of cost considerations. In order to determine the most feasible underground construction method, various risks and cost factors must be assessed and analyzed. A comprehensive survey was conducted to solicit input from 28 contractors in various geographical regions throughout the United States and Canada. The intent was to determine specific risk factors and their inherent impacts, as well as to better understand cost comparison between horizontal directional drilling and traditional open-cut construction methods. This paper is relevant to practitioners and researchers because it identifies and describes risks and cost factors from a contractor perspective that can be used for evaluating installation options for small diameter pipelines in an urban environment.

American Continuous-Installment Options: Valuation and Premium Decomposition

Installment options are weakly path-dependent contingent claims in which the premium is paid discretely or continuously in installments, instead of paying a lump sum at the time of purchase. This paper deals with valuing American continuous-installment options written on dividend-paying assets. The setup is a standard Black–Scholes–Merton framework where the price of the underlying asset evolves according to a geometric Brownian motion. The valuation of installment options can be formulated as an optimal stopping problem, due to the flexibility of continuing or stopping to pay installments as well as the chance of early exercise. Analyzing cash flow generated by the optimal stop, we can characterize asymptotic behaviors of the stopping and early exercise boundaries close to expiry. Combining the PDE and Laplace transform approaches, we obtain the Laplace transform of the initial premium in an explicit form, which is decomposed into the value of the associated European vanilla option with the same payoff p...

Risk Assessment of Investment Strategy in Distributed Energy System under Uncertainty of Fuel and Electricity Prices

This paper discusses investment strategies in distributed energy system consisting of cogeneration system and renewable power generation, under uncertainty in the natural gas and the electricity prices as well as related risk assessment of investment strategies. Although incentives for introducing distributed energy system increase these days, volatile natural gas prices make its investment risky. Therefore, it is important to evaluate the risk under uncertainty and find strategies which reduce the exposure to volatility. We take the real option approach to analyze investment decision. By varying the parameters of prices volatility and correlation between uncertainty of natural gas price with that of electricity price, we find that the optimal investment strategy depends on the level of uncertainty and correlation. When volatility is large and correlation is small, strategies with installation option of small renewable power generation, here, photovoltaic generation, and small cogeneration system become attractive in terms of risk reduction.

The Employee Stock Option: An Installment Option

Labor market analysis shows the employee stock option (ESO) is a delayed-payment contract in which the option is exchanged for labor services. Under this delayed-payment approach, the ESO is modeled as an installment option, where the installment premiums are wage concessions determined under an implicit contract at time of option grant. The model explains early exercise, as well as option forfeiture and employee retention. The model shows why, ignoring the wage concessions, the option appears to be a barrier option. Arbitrage pricing is used to determine the wage concessions, as well as value the barrier option at date of grant.

Utilization and Costs of Antipsychotic Agents: A Canadian Population-Based Study, 1996–2006

This study evaluated the prescribing patterns and costs for antipsychotic agents in the population of the Canadian province of Manitoba over the past decade. A population-based study of antipsychotic utilization and costs was conducted on data collected from the administrative databases of the Manitoba Population Health Data Repository and the Statistics Canada census between index years 1996 and 2006 (April 1, 1995, through March 31, 2006). The total annual number of antipsychotic prescriptions dispensed in Manitoba increased by 227% between 1996 and 2006, and the prevalence of antipsychotic users increased by 62% over the same time interval. The fastest-growing segment of antipsychotic users in Manitoba appears to be young males, who increased from .16% in 1996 to .88% in 2006. The highest numbers of prescriptions were reported for schizophrenia, dementia, and conduct disorder. Annual expenditures for antipsychotics increased from $1.7 million in 1996 to $22.0 million in 2006 (expenditures are in Canadian dollars). The cost of second-generation agents reached 80% of total antipsychotic expenditures in 2006; risperidone was the most prescribed agent in all age groups of patients. The per-patient annual cost of antipsychotic pharmacotherapy increased by approximately 680% between 1996 and 2006 in Manitoba. The number of antipsychotic prescriptions and the prevalence of users of antipsychotic medications increased significantly in Manitoba over the study period, despite a steady-state population of approximately 1.2 million. Incremental costs relative to the use of antipsychotic medications can be explained by the market penetration of the second-generation agents and their expanded use in the treatment of various diagnoses.

Installment options close to expiry

We use an asymptotic expansion to study the behavior of installment options close to expiry. Installment options are contracts where the price is paid over the life of the option rather than as a lump sum at the time of purchase, and where the contract can be allowed to lapse at any time. Series solutions are obtained for the location of the free boundary and the price of the option.

A dynamic programming approach to price installment options

Installment options are Bermudan-style options where the holder periodically decides whether to exercise or not and then to keep the option alive or not (by paying the installment). We develop a dynamic programming procedure to price installment options. We study in particular the geometric Brownian motion case and derive some theoretical properties of the IO contract within this framework. We also characterize the range of installments within which the installment option is not redundant with the European contract. Numerical experiments show the method yields monotonically converging prices, and satisfactory trade-offs between accuracy and computational time. Our approach is finally applied to installment warrants, which are actively traded on the Australian Stock Exchange. Numerical investigation shows the various capital dilution effects resulting from different installment warrant designs.

Fool-proofing firewalls

Firewalls are everywhere. Their increasingly widespread use means they are easier to set up than ever. However, a firewall is not an install and forget device. Their effectiveness still depends heavily on proper configuration. Rules should be careful enforced in a coordinated manner. A rulebase structure should logically reflect the environment where a firewall is deployed. In addition, stealth and ‘drop all’ rules are often omitted by mistake. Everyone has a firewall these days: not just the corporations of yesteryear who pioneered their deployment and subsequent development but also the ‘girl next door’ and even your mother. Firewalls are a key component of nearly every consumer security suite and are becoming default installation options upon desktop systems. The reason for their prevalence is quite simple, no other security technology delivers such a “bang for your buck” as a firewall. If properly configured to restrict access, a firewall protects against the majority of network borne attacks and requires comparatively little maintenance. Such widespread usage can however lead to complacency.

Solar control with thermotropic layers

Innovative means to control the light and energy flux according to demand are desirable for transparent façades and façade elements. One possibility to achieve this is presented by switchable layers that change their optical properties, either actively or passively, according to different control parameters. In addition to inorganic coatings on glass, there are several organic thermotropic systems that can be integrated into façade glazing. Above a certain temperature, thermotropic layers change from a clear to a translucent, light-diffusing state, thus switching from a highly transmitting to a diffusely reflecting state. We shall describe the basic principles of these systems and present an overview of some of the existing prototype systems. Installation options will be discussed and the results of an application in a retrofitted building presented.

Technical note: a comparison of antiscatter grids for digital radiography

The use of digital radiography (DR) systems offers a number of advantages over film-screen detectors. One potential disadvantage, however, is that some fixed DR systems do not allow the user to change the antiscatter grid to suit the imaging task. Instead, the user must choose the grid at the time of purchase. Six grids, which are offered as installation options for one commercial fixed-room DR system, were experimentally evaluated, using a range of scatter conditions and tube voltages. In addition, three grids, which are available with a portable DR system in which the user can change the grid to suit the imaging task, were also evaluated. The grids were compared using the primary transmission, scatter fraction, and calculated signal-to-noise improvement factor (SIF). It was found that the grids with low atomic number interspace and cover material had an SIF up to 15% higher than did the grids with aluminium interspace and cover material; the grid with a grid ratio of 12:1 had the highest SIF for all tube voltages and scatter conditions tested here. This 12:1 grid probably represents a good general-purpose non-removable grid in DR.

Engine configurations for the Silent Aircraft

The Silent Aircraft Initiative is a Cambridge-MIT Institute research project aimed at reducing aircraft noise to the point where it would be unnoticeable in the urban areas around airports. This talk investigates viable engine and installation options that can meet the Silent Aircraft noise requirements. To reduce the transmitted jet noise sufficiently, it is found that a very large exhaust nozzle area is required. If this is achieved with a conventional turbofan it leads to a very high engine diameter and low fan pressure ratio. The large diameter results in greater engine weight and unacceptably high installation drag at cruise. The low fan pressure ratio makes the engine more susceptible to operability problems such as fan stall and vibration, which lead to a further increase in weight. This presentation demonstrates how these problems can be mitigated with a propulsion system that has a variable cycle combined with a novel installation that is embedded into the airframe. Several suitable engine concepts are considered in detail and each configuration is assessed in terms of its relative performance, weight, noise emission, and operability.

LAPLACE TRANSFORMS AND INSTALLMENT OPTIONS

An installment option is a derivative financial security where the price is paid in installments instead of as a lump sum at the time of purchase. The valuation of these options involves a free boundary problem in that at each installment date, the holder of the derivative has the option of continuing to pay the premiums or allowing the contract to lapse, and the decision will depend upon whether the present value of the expected pay-off is greater or less than the present value of the remaining premiums. Using a model installment option where the premiums are paid continuously rather than on discrete dates, an integral equation is derived for the position of this free boundary by applying a partial Laplace transform to the underlying partial differential equation for the value of the security. Asymptotic analysis of this integral equation allows us to deduce the behavior of the free boundary close to expiry.

Pricing Installment Options with an Application to ASX Installment Warrants

Installment options are Bermudan-style options where the holder periodically decides whether to exercise or not and then to keep the option alive or not (by paying the installment). We develop a dynamic programming procedure to price installment options. We derive the range of installments within which the installment option is not redundant with the European contract. Simulations analysis shows the method yields monotonically converging prices, and satisfactory trade-offs between accuracy and computational time. In addition, we examine the flexibility in installment option design that yields various hedging properties. Our approach is applied to installment warrants, which are actively traded on the Australian Stock Exchange. Numerical investigation shows the various capital dilution effects resulting from different installment warrant designs.

A CASE STUDY OF DRYING WET FLOORS WITH MIXING FANS IN FREE–STALL DAIRY HOUSING

The effectiveness of mixing fans installed under the ceilings of freestall dairy housing was evaluated as a methodto dry a highmoisture manure litter mixture on the floors. The fan installation options were fan tilting angles of 45., 90.(horizontal), or no fan. The litter materials tested on the floor were recycled compost and sawdust or chopped wheat strawwhose initial average moisture contents on a wet basis were 44%, 17.5%, and 5.4%, respectively. It was found that fans tiltedat a 45. angle dried the floor better than fans installed horizontally or the drying obtained without mechanical ventilation.The effect of tilting fans on removing moisture from the house was about 5 times larger than horizontal installations and30 times larger than without mechanical ventilation. The moisture content of the floor was reduced to less than 70% for afan tilt angle of 45.. Tilting fans not only dried the floors better, but also improved the air exchange rate, reducing aerial NH3 concentrations.

Installment Options and Static Hedging

This article discusses static hedges for installment options, which are finding broad application in cases where the option‐buyer may reduce up‐front premium costs via early termination of an option. An installment option is a European option in which the premium, instead of being paid up front, is paid in a series of installments. If all installments are paid, the holder receives the exercise value, but the holder has the right terminate payments on any payment date, in which case the option lapses with no further payments on either side. The authors summarize pricing and risk management concepts for these options, in particular, using static hedges to obtain both no‐arbitrage pricing bounds and very effective hedging strategies with almost no vega risk.