Exact Price Research Articles

Exact Forward in Monte-Carlo

We look at how to reproduce a nearly exact forward price in Monte-Carlo with a term structure of interest rates or a term structure of dividends, in the case of the Black-Scholes model, as well as the local volatility and stochastic volatility models.

CEV: Constant Lévylasticity of Variance

We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential Levy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity as well as a locally-dependent Levy measure. Using techniques from regular perturbation theory and Fourier analysis, we derive a series expansion for the price of a European-style option. We also provide precise conditions under which this series expansion converges to the exact price. Additionally, for a certain subclass of assets in our modeling framework, we derive an expansion for the implied volatility induced by our option pricing formula. The implied volatility expansion is exact within its radius of convergence. As an example of our framework, we propose a class of CEV-like Levy-type models. Within this class, approximate option prices can be computed by a single Fourier integral and approximate implied volatilities are explicit (i.e., no integration is required). Furthermore, the class of CEV-like Levy-type models is shown to provide a tight fit to the implied volatility surface of S{&}P500 index options.

Fast Swaption Pricing in Gaussian Term Structure Model

We propose a fast and accurate numerical method to price European swaptions in a multi-factor Gaussian term structure model that can speed up the calibration to the volatility surface. Pricing an interest rate option in such a multi-factor term structure model involves evaluating a multi-dimensional integration of the underlying claim's payoff on a domain where the payoff is positive. In our method, we approximate the exercise boundary of the state variables as a hyperplane tangent to the maximum probability point on the boundary and simplify the multi-dimensional integration into an analytic form. The maximum probability point can be found using the gradient descent method. We show that the quality of our method is superior to the result of previous studies by directly comparing them to the exact price obtained from the numerical integration.

The Smile of Certain Lévy-Type Models

We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential Lévy-type process subject to default. The class of processes we consider features locally dependent drift, diffusion, and default intensity as well as a locally dependent Lévy measure. Using techniques from regular perturbation theory and Fourier analysis, we derive a series expansion for the price of a European-style option. We also provide precise conditions under which this series expansion converges to the exact price. Additionally, for a certain subclass of assets in our modeling framework, we derive an expansion for the implied volatility induced by our option pricing formula. The implied volatility expansion is exact within its radius of convergence. As an example of our framework, we propose a class of CEV-like Lévy-type models. Within this class, approximate option prices can be computed by a single Fourier integral and approximate implied volatilities are explicit (i.e., no integration is required). Furthermore, the class of CEV-like Lévy-type models is shown to provide a tight fit to the implied volatility surface of S&P500 index options.

Cost allocation for outside sources replacing service departments

The validity of the linear algebra model to solve the reciprocal service department cost allocation problem has been widely recognized since Kaplan’s seminal paper in The Accounting Review in 1973 [2]. In a manufacturing company, certain departments can be characterized as production departments and others as service departments. Examples of service departments are purchasing, computing services, repair and maintenance, security, food services etc. The costs of such service departments must be allocated to the production departments, which in turn will allocate them to the product. We shall determine the exact price that should be paid to external suppliers of the same services currently supplied by the service departments. We shall also prove that once the costs of services allocated to each production department is obtained, then they will stay the same even if some of the service departments are replaced by outside sources.

A moment approach to bounding exotic options under regime switching

The switching of market regimes has a significant impact on derivative pricing that exposes investors to an additional level of risk. However, deriving the exact price of exotic options under regime switching is still at the early stages of development. In this article, we consider deriving tight upper and lower bounds for the price of a wide class of exotic options under regime switching. We show that the additional complexity introduced by the regime-switching dynamics can be greatly reduced by exploiting the additive structure of the infinitesimal generator of the regime-switching process. As a result, the problem of bounding the option price under regime switching can be reformulated as a semidefinite programming problem, which can be solved efficiently in practice. The effectiveness of our approach is illustrated through numerical examples.

A novel method for coevolving PS-optimizing negotiation strategies using improved diversity controlling EDAs

In agent-mediated negotiation systems, the majority of the research focused on finding negotiation strategies for optimizing price only. However, in negotiation systems with time constraints (e.g., resource negotiations for Grid and Cloud computing), it is crucial to optimize either or both price and negotiation speed based on preferences of participants for improving efficiency and increasing utilization. To this end, this work presents the design and implementation of negotiation agents that can optimize both price and negotiation speed (for the given preference settings of these parameters) under a negotiation setting of complete information. Then, to support negotiations with incomplete information, this work deals with the problem of finding effective negotiation strategies of agents by using coevolutionary learning, which results in optimal negotiation outcomes. In the coevolutionary learning method used here, two types of estimation of distribution algorithms (EDAs) such as conventional EDAs (S-EDAs) and novel improved dynamic diversity controlling EDAs (ID2C-EDAs) were adopted for comparative studies. A series of experiments were conducted to evaluate the performance for coevolving effective negotiation strategies using the EDAs. In the experiments, each agent adopts three representative preference criteria: (1) placing more emphasis on optimizing more price, (2) placing equal emphasis on optimizing exact price and speed and (3) placing more emphasis on optimizing more speed. Experimental results demonstrate the effectiveness of the coevolutionary learning adopting ID2C-EDAs because it generally coevolved effective converged negotiation strategies (close to the optimum) while the coevolutionary learning adopting S-EDAs often failed to coevolve such strategies within a reasonable number of generations.

The exact import price and its implications for the US external imbalance

This article calculates the Feenstra's (1994) ‘exact price index’ for each category of US-imported goods and aggregates them to analyse the US import demand equation for assessing the seriousness of the external imbalance. What distinguishes Feenstra's exact price index is that it incorporates new product varieties. The exact import price index thus calculated suggests that US conventional import prices are biased upwards. The consequent downward adjustment in import prices causes appreciation in the real exchange rate and lowers the excessive portion of imports (the difference between actual and theoretical amounts of imports obtained from the import demand equation). Since the early 2000s, however, the role that new product varieties play in lowering the excessive portion of imports has declined because the impact of new products on import prices has been outweighed by the impact of the spike in primary commodity prices, which has resulted in a substantial depreciation of the real exchange rate. It is possible that this depreciation combined with relatively large excessive imports has caused the subsequent US current account deficit to stop expansion from the late 2000s onwards.

Exact and hybrid methods for the multiperiod field service routing problem

This article deals with a particular class of routing problem, consisting of the planning and routing of technicians in the field. This problem has been identified as a multiperiod, multidepot uncapacitated vehicle routing problem with specific constraints that we call the multiperiod field service routing problem (MPFSRP). We propose a set covering formulation of the problem for the column generation technique and we develop an exact branch and price solution method for small-sized instances. We also propose several heuristic versions for larger instances. We present the results of experiments on realistic data adapted from an industrial application.

Matching Sensitivities to Discrete Dividends: A New Approach for Pricing Vanillas

The incorporation of a dividend yield in the classical Black-Scholes framework results in a minor modification of the well-known formula, since the lognormality of the underlying asset is preserved. However, market-makers prefer to work with cash dividends with fixed value instead of a dividend yield. Since there is no closed-form solution for the price of a European call in this case, many approximations have been proposed in the literature. Here, we present a new approach based on an exact analytical formula for the sensitivity to dividends of a European option. We use this result to elaborate a price proxy having the same Taylor expansion as the exact price with respect to the dividends. The resulting proxy has no computational complexity (the same as for the usual Black-Scholes formula), and numerical tests show the excellent accuracy of the method for all practical cases. Copyright © 2011 Wilmott Magazine Ltd.

Measuring the welfare effects of reducing a subsidy on a commodity using micro-models: An application to Kuwait's residential demand for electricity

This paper provides a conceptual and empirical approach for evaluating the direct benefits and costs that are associated with reforming the price of a subsidized commodity using a micro-model. The welfare analysis is based on two alternative scenarios, a hypothetical percentage increase in the price of the commodity and a hypothetical percentage decrease in the amount of subsidy. The latter is considered to be a simultaneous problem in which the exact price of the commodity that reduces consumption, and subsequently the subsidy to the specific target level needs to be determined first. As a case study, the paper utilizes the most recent Household Expenditure Survey in the State of Kuwait to estimate residential electricity demand for different household groups (i.e., low-, middle-, and high-income), and employs a partial equilibrium model to measure the welfare implications that may result from a reduction in the electricity subsidy rates. The empirical findings show that a small increase in the price of electricity would reduce annual consumption by 4741millionkWh and annual subsidy by US$734 million. The results also show that the loss in consumers’ welfare is approximately US$145 million, while the financial and environmental benefits to the society ranges between US$658 million and US$889 million. The magnitude of these welfare gains suggests that electricity price reforms combined with a rebate scheme to compensate households for their welfare loss, offsetting any political resistance to reform, is a win-win situation.

Minimum return guarantees with fund switching rights—An optimal stopping problem

Recently, there is a growing trend to offer guaranteed products where the investor is allowed to shift her account/investment value between multiple funds. The switching right is granted a finite number of times per year, i.e. it is American style with multiple exercise possibilities. In consequence, the pricing and the risk management is based on the switching strategy which maximizes the value of the guarantee put-option. We analyze the optimal stopping problem in the case of one switching right within different model classes and compare the exact price with the lower price bound implied by the optimal deterministic switching time. We show that, within the class of log-price processes with independent increments, the stopping problem is solved by a deterministic stopping time if (and only if) the price process is in addition continuous. Thus, in a sense, the Black and Scholes model is the only (meaningful) pricing model where the lower price bound gives the exact price. It turns out that even moderate deviations from the Black and Scholes model assumptions give a lower price bound which is really below the exact price. This is illustrated by means of a stylized stochastic volatility model setup.

Coordination mechanisms with hybrid local policies

We study coordination mechanisms for scheduling n jobs on m parallel machines where agents representing the jobs interact to generate a schedule. Each agent acts selfishly to minimize the completion time of his/her own job, without considering the overall system performance that is measured by a central objective. The performance deterioration due to the lack of a central coordination, the so-called price of anarchy, is determined by the maximum ratio of the central objective function value of an equilibrium schedule divided by the optimal value. In the first part of the paper, we consider a mixed local policy with some machines using the SPT rule and other machines using the LPT rule. We obtain the exact price of anarchy for the problem of minimizing the makespan and some bounds for the problem of minimizing the total completion time. In the second part of the paper, we consider parallel machine scheduling subject to eligibility constraints. We devise new local policies based on the flexibilities and the processing times of the jobs. We show that the newly devised local policies outperform both the SPT and the LPT rules.

Photoinhibition: molecular mechanisms and physiological significance

Photoinhibition: molecular mechanisms and physiological significance

Exact Price of Anarchy for Polynomial Congestion Games

We show exact values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients. The given values also hold for weighted and unweighted network congestion games.

Matching the Sensitivities to Discrete Dividends: A New Approach for Pricing Vanillas

The incorporation of a dividend yield in the classical option pricing model of Black-Scholes results in a minor modification of the Black-Scholes formula, since the lognormal dynamic of the underlying asset is preserved. However, market makers prefer to work with cash dividends with fixed value instead of a dividend yield. Since there is no closed-form solution for the price of a European Call in this case, many methods have been proposed in the literature to approximate it. Here, we present a new approach. We derive an exact analytic formula for the sensitivity to dividends of an European option. We use this result to elaborate a proxy which possesses the same Taylor expansion around 0 with respect to the dividends as the exact price. The obtained approximation is very fast to compute (the same complexity than the usual Black-Scholes formula) and numerical tests show the extreme accuracy of the method for all practical cases.

Pricing American Options in a Mild Stochastic Environment

The problem of pricing derivative financial products is central to the theory of capital markets. An option is a financial contract conveying its owner the right of buying or selling a financial asset (underlying asset) at a preset strike price K, at a fixed expiration date T (maturity). Unlike European options, which can be exercised only at maturity date, an American option can be exercised at any time t prior to the maturity date. Most of the option pricing methods, starting with the well-known Black-Scholes model (1973), are based on the assumption that the market uncertainty can be modeled by a Wiener process. In this context, while it is possible to obtain convenient analytical option pricing formulae for European options, it is very difficult to obtain exact results for American options. In the present paper, we assume that the market uncertainty is modeled by a more regular stochastic process, which was called, by A. Halanay, a mild stochastic environment. In this context, we are able to obtain precise stopping rules, determining the exact exercise time and the exact price of an American option.

Supply, Demand, and Equilibrium: The Algebra

This technical note refreshes the algebraic representation of linear demand and supply, how to account for shifting curves, and how to include taxes. This is part of the refresher course in Economics at Darden. Excerpt UVA-G-0592 Supply, Demand, and Equilibrium: The Algebra Understanding supply and demand is invaluable for any structured analysis of the real markets where firms compete. So far, to develop intuition we have drawn these markets. We approximated supply and demand with straight lines. In this note, we calculate the exact price and quantity at which goods are bought and sold. To do so, we use algebra and represent supply and demand with an equation instead of a graph. Equation of a Straight Line Figure 1. Straight line. Figure 1 plots a line. It touches both the vertical Y-axis and the horizontal X-axis. With the help of the X-axis and the Y-axis, we can define any point on the graph. A double (X,Y) contains the coordinates of any point. The variables X and Y tell us how far a point lies from the origin, which is the point (0.0) where the X-axis and Y-axis meet. As we see, our line cuts the X-axis and Y-axis respectively at the horizontal and vertical intercept at the points (4,0) and (0.2). . . .

Les hémorragies utérines fonctionnelles

Dysfunctionnal uterine bleeding (DUB) is a significant health problem in premenopausal women. First line therapy is traditionally medical therapy but often ineffective. Hysterectomy is obviously effective in stopping bleeding but is associated with morbidity and is most costly. Endometrial ablation technique is becoming the first conservative line in the management of DUB. In 2007, the Cochrane Data Base, and the NICE published the new guidelines for DUB treatment. Pharmaceutical treatments should be considered in the following order: levonorgestrel-releasing intra uterine system and if hormonal treatment is not acceptable, tranexamic acid can be used. This is the exclusive line of treatment for women who desire to be pregnant, and the first step for the others one. The rapid development of second generation technique of endometrial destruction suggests that these techniques are becoming "the gold standart" for the patients without desire of future pregnancy. These techniques are easier that endometrial resection/ablation by hysteroscopy without major complications. In France, the National Health Insurance must find a codification CCAM for giving an exact price to the procedure. This new tarification could include the device cost and could avoid either inefficient procedure like datation and curetage or morbide procedure like hysterectomy.

Consumer Cognition and Pricing in the Nines in Oligopolistic Markets

The paper fully characterizes the Bertrand equilibria of oligopolistic markets where consumers may ignore the last (i.e., the right‐most) digits of prices. Consumers, in this model, do not do this reflexively or out of irrationality, but only when they expect the time cost of acquiring full cognizance of the exact price to exceed the expected loss caused by the slightly erroneous amounts that are likely to be purchased or the slightly higher price that may be paid by virtue of ignoring the information concerning the last digits of prices. It is shown that in this setting there will always exist firms that set prices that end in nine though there may also be some (nonstrict) equilibria where a non‐nine price ending occurs. It is shown that all firms earn positive profits even in Bertrand equilibria. The model helps us understand in what kinds of markets we are most likely to encounter pricing in the nines.