A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Strategic options of firms considering private label production

Private labels are a growing phenomenon globaly. Retailers become stronger and stronger by offering their own quality private label product for customers in all segments. Certainly they do not open factories to produce these items but rather search for dedicated private label producers or pressure branded goods manufacturers to produce it for them. The article deals with the strategic choices manufacturers can have and suggest the necessary factors that need to be evaluated to decide on the winning business model- in considering wether or not to enter in private label production- through literature and a case study on the ice cream market in Hungary.

A geometriai Brown-mozgás feltevésének elfogadhatósága a reálopciók értékelésében (The acceptability of the assumption of geometric brownian motion in the valuation of real options)

A reálopciók a döntési rugalmasság megtestesítőiként jelen vannak a vállalatvezetők mindennapjaiban, és cégtől függően jelentős értéket képviselhetnek. Értékelésük a hagyományos diszkontált pénzáramlás módszerekkel csak korlátozottan lehetséges, ezért alternatívaként felmerül a pénzügyi opcióárazás módszertana, amelynek hagyományos változatai az alaptermék alakulásáról geometriai Brown-mozgást feltételeznek. A cikk ezt a feltevést veszi górcső alá a reálopciókra történő alkalmazás szempontjából, és megmutatja, hogy habár önkényesnek tűnhet, valójában nem pusztán egy matematikai szempontból kényelmes megoldás, hanem pénzügyileg is elfogadható feltétel. _______ Real options represent the fl exibility of decision-making, and are thus part of the everyday work of corporate executives, often having great value. Valuing them with the use of traditional Discounted Cash Flow models has limited relevance, therefore arises the alternative methodology of fi nancial option pricing, the traditional versions of which assume that the price of the underlying asset follows Geometric Brownian Motion. The paper examines this assumption from the aspect of real option valuation and shows that although it might seem arbitrary, it is not only a mathematically convenient choice, but also a fi nancially acceptable one.

A villamos erőművek szén-dioxid-kibocsátásának modellezése reálopciók segítségével = Modelling of the carbon dioxide emissions of a power plant, using real options

A szerző egy, a szennyezőanyag-kibocsátás európai kereskedelmi rendszerében megfelelésre kötelezett gázturbinás erőmű szén-dioxid-kibocsátását modellezi négy termékre (völgy- és csúcsidőszaki áramár, gázár, kibocsátási kvóta) vonatkozó reálopciós modell segítségével. A profitmaximalizáló erőmű csak abban az esetben termel és szennyez, ha a megtermelt áramon realizálható fedezete pozitív. A jövőbeli időszak összesített szén-dioxid-kibocsátása megfeleltethető európai típusú bináris különbözetopciók összegének. A modell keretein belül a szén-dioxid-kibocsátás várható értékét és sűrűségfüggvényét becsülhetjük, az utóbbi segítségével a szén-dioxid-kibocsátási pozíció kockáztatott értékét határozhatjuk meg, amely az erőmű számára előírt megfelelési kötelezettség teljesítésének adott konfidenciaszint melletti költségét jelenti. A sztochasztikus modellben az alaptermékek geometriai Ornstein-Uhlenbeck-folyamatot követnek. Ezt illesztette a szerző a német energiatőzsdéről származó publikus piaci adatokra. A szimulációs modellre támaszkodva megvizsgálta, hogy a különböző technológiai és piaci tényezők ceteris paribus megváltozása milyen hatással van a megfelelés költségére, a kockáztatott értékére. ______ The carbon-dioxide emissions of an EU Emissions Trading System participant, gas-fuelled power generator are modelled by using real options for four underlying instruments (peak and off-peak electricity, gas, emission quota). This profit-maximizing power plant operates and emits pollution only if its profit (spread) on energy produced is positive. The future emissions can be estimated by a sum of European binary-spread options. Based on the real-option model, the expected value of emissions and its probability-density function can be deducted. Also calculable is the Value at Risk of emission quota position, which gives the cost of compliance at a given confidence level. To model the prices of the four underlying instruments, the geometric Ornstein-Uhlenbeck process is supposed and matched to public available price data from EEX. Based on the simulation model, the effects of various technological and market factors are analysed for the emissions level and the cost of compliance.

"It's so little money you could make as much at home" - options for work in an impoverished rural region of high unemployment.

Hungary has a higher unemployment rate than the member states of the European Union and even most former socialist countries. This rate for 15-64 year-olds has been around 56% since 1999, as against 66% in the European Union (OECD Employment Database). There is also a high degree of regional unevenness within the country. The situation is worst in North Hungary, an area of multiple economic and social deprivations. Several pieces of research have analysed the causes of long-term unemployment and have highlighted the main social, geographical and institutional factors behind it. People of low educational attainment who live in small villages and members of the Roma minority are particularly likely to have been without jobs for a long time.

Health beliefs and health care options of disparate black communities in the United States

According to the 1999 U.S. Census, there were approximately thirty-three million African Americans and approximately 1.8 million non-Hispanic black immigrants in the United States. The 1997 U.S. Census estimated that there were as many as 554,000 foreign-born Haitians and 505,000 foreign-born Jamaicans living in the United States, mainly residing in Florida and New York. The U.S. Census claims that blacks are one of the largest emerging ethnic groups in America constituting at least twelve percent of this country's population. Because of this increase, their specific health beliefs and health care options are increasingly nationally significant. ^ In the present intra-black and inter-ethnic study, two hundred seventy African Americans, Haitian immigrants, and Jamaican immigrants residing in South Florida were quantitatively and qualitatively surveyed in order to investigate their health beliefs and health care options. According to the reviewed literature, the three black ethnic groups researched in this study have not been compared or contrasted before in relation to these beliefs and health care choices. ^ As was discovered by the present research, differing health beliefs and health care options were the cultural products of the ethnic differences of the researched communities. It was expected that differing health beliefs among the researched black groups might indicate disparate patterns of health care utilization of either western or non-western models. Additionally, it was projected that by investigating the health beliefs and the health care options of these emerging black ethnic groups, western health care providers in the United States could become better versed in medically servicing growing ethnically-disparate black populations. The study yielded results about the researched groups that supported major findings in the reviewed literature. The data were reported and examined, and theoretical generalizations from the data were discussed. The most important of these findings was that, within a race, health beliefs and health care options were determined by specific ethno-cultural variables dependent on national origins. ^

Two parallel, pragmatic, UK multicentre, randomised controlled trials comparing surgical options for upper compartment (vault or uterine) pelvic organ prolapse (the VUE Study) : study protocol for a randomised controlled trial

The VUE study is funded by the National Institute for Health Research Health Technology Assessment programme (project number 11/129/183).

Options to advance co-ordination and analysis of climate data in Europe

Systematic, high-quality observations of the atmosphere, oceans and terrestrial environments are required to improve understanding of climate characteristics and the consequences of climate change. The overall aim of this report is to carry out a comparative assessment of approaches taken to addressing the state of European observations systems and related data analysis by some leading actors in the field. This research reports on approaches to climate observations and analyses in Ireland, Switzerland, Germany, The Netherlands and Austria and explores options for a more coordinated approach to national responses to climate observations in Europe. The key aspects addressed are: an assessment of approaches to develop GCOS and provision of analysis of GCOS data; an evaluation of how these countries are reporting development of GCOS; highlighting best practice in advancing GCOS implementation including analysis of Essential Climate Variables (ECVs); a comparative summary of the differences and synergies in terms of the reporting of climate observations; an overview of relevant European initiatives and recommendations on how identified gaps might be addressed in the short to medium term.

Health Literacy and Medicare Recipient's Knowledge of Health Insurance Options

Health literacy is a major problem for the aging population (Parker, Ratzan, & Lurie, 2003). The significance of this study was to access the relationship between health literacy and knowledge of Medicare to determine ways in which seniors can effectively navigate their healthcare insurance.

Use of farmer-prioritized vertisol management options for enhanced green gram and tomato production in central Kenya

Green grams (Phaseolus aures L.) and tomato (Solanum lycopersicum L) are widely grown in the vertisols of the Mwea Irrigation Scheme alongside the rice fields. Green grams can fix nitrogen (biological nitrogen fixation) and are grown for its highly nutritious and curative seeds while tomatoes are grown for its fruit rich in fibres, minerals and vitamins. The two can be prepared separately or together in a variety of ways including raw salads and/or cooked/fried. They together form significant delicacies consumed with rice which is the major cash crop grown in the black cotton soils. The crops can grow well in warm conditions but tomato is fairly adaptable except under excessive humidity and temperatures that reduce yields. Socio-economic prioritization by the farming community and on-farm demonstrations of soil management options were instituted to demonstrate enhanced green gram and tomato production in vertisol soils of lower parts of Kirinyaga County (Mwea East and Mwea West districts). Drainage management was recognized by the farming community as the best option although a reduced number of farmers used drainage and furrows/ridges, manure, fertilizer and shifting options with reducing order of importance. Unavailability of labour and/or financial cost for instituting these management options were indicated as major hindrances to adopt the yield enhancing options. Labour force was contributed to mainly by the family alongside hiring (64.2%) although 28% and 5.2% respectively used hired or family labour alone. The female role in farming activities dominated while the male role was minimal especially at weeding. The youth role remained excessively insignificant and altogether absent at marketing. Despite the need for labour at earlier activities (especially when management options needed to be instituted) it was at the marketing stage that this force was directed. Soils were considered infertile by 60% but 40% indicated that their farms had adequate fertility. Analysis showed that ridging and application of farm yard manure and fertilizer improved fertility, crop growth and income considerably. Phosphate and zinc enhancement reduced alkalinity and sodicity. Green gram and tomato yields increased under ridges and farm yard manure application by 17-25% which significantly enhanced household income.

Surgical Options After Fontan Failure

OBJECTIVE: The objective of this European multicenter study was to report surgical outcomes of Fontan takedown, Fontan conversion and heart transplantation (HTX) for failing Fontan patients in terms of all-cause mortality and (re-)HTX. METHODS: A retrospective international study was conducted by the European Congenital Heart Surgeons Association among 22 member centres. Outcome of surgery to address failing Fontan was collected in 225 patients among which were patients with Fontan takedown (n=38; 17%), Fontan conversion (n=137; 61%) or HTX (n=50; 22%). RESULTS: The most prevalent indication for failing Fontan surgery was arrhythmia (43.6%), but indications differed across the surgical groups (p<0.001). Fontan takedown was mostly performed in the early postoperative phase after Fontan completion, while Fontan conversion and HTX were mainly treatment options for late failure. Early (30 days) mortality was high for Fontan takedown (ie, 26%). Median follow-up was 5.9 years (range 0-23.7 years). The combined end point mortality/HTX was reached in 44.7% of the Fontan takedown patients, in 26.3% of the Fontan conversion patients and in 34.0% of the HTX patients, respectively (log rank p=0.08). Survival analysis showed no difference between Fontan conversion and HTX (p=0.13), but their ventricular function differed significantly. In patients who underwent Fontan conversion or HTX ventricular systolic dysfunction appeared to be the strongest predictor of mortality or (re-)HTX. Patients with valveless atriopulmonary connection (APC) take more advantage of Fontan conversion than patients with a valve-containing APC (p=0.04). CONCLUSIONS: Takedown surgery for failing Fontan is mostly performed in the early postoperative phase, with a high risk of mortality. There is no difference in survival after Fontan conversion or HTX.

Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.