Valuation Problem Research Articles

An Analytical Method for Multi-Asset Option Pricing Based on a Single-Factor Model

Securities with payoffs determined by multiple correlated stochastic factors present some of the hardest valuation problems in derivatives. Except for rare cases in which a closed-form solution is available, the “curse of dimensionality” causes serious problems for Monte Carlo simulation and other numerical methods as the number of assets, N , grows. This article presents an approach that can simplify such problems enormously with relatively little lost in terms of accuracy for common cases. The idea is quite simple: Model each variable’s risk as being composed of exposure to a single common factor (e.g., the market portfolio) plus an independent idiosyncratic shock. With this assumption, the distribution of the payoff then becomes a realization of the single common factor, which can be easily simulated numerically, plus a draw from the composite density for the sum of the independent idiosyncratic shocks. The article illustrates the approach for pricing rainbow options and the n th-best-of- N contract. The result is highly accurate and almost instantaneous.

Comonotonic Monte Carlo Simulation and Its Applications in Option Pricing and Quantification of Risk

For many kinds of derivative valuation problems, especially those that try for greater realism using return processes that are more consistent with empirical evidence, Monte Carlo simulation is the only feasible solution technique. Among the well-known strategies to improve its efficiency, the use of a well-chosen control variate is often very effective. But a good selection can make a lot of difference. This article explains how the mathematical concept of comonotonicity can be applied as a new way to create a control variate. A remarkable improvement in performance can be achieved using the comonotonic upper bound as the control variate. The article illustrates the power of Comonotonic Monte Carlo simulation in estimating tail value at risk and pricing arithmetic Asian options.

Top-down restructuring of markets and institutions: the Nordic banking crises

This paper explores the lessons that can be learned for the future resolvability and successful reorganization of problem banks from the experience of successful resolutions in Denmark, Finland, Iceland, Norway and Sweden over the last 25 years. The Nordic countries used all of the new tools that will be available following the passing of the Bank Recovery and Resolution Directive. There were difficulties with them, which will provide valuable experience, but it is likely that they will work well in the future. Experience with bailing in is limited but suggested problems of valuation in writing down and larger writedowns than might be anticipated. While the current drive to ensure that only private sector money is used, the predilection for the continuation operation of most banks other than smallest and the extent to which public funds were committed, suggest that the taxpayer is likely to be involved in strategic cases in the future. In particular, the guarantee funds available were insufficient and had to be topped up by the state. Hence, the new resolution funds in the EU may similarly need augmenting in a crisis. However, almost all the main banks involved in the Nordic resolutions were primarily national and retail. Where they involved cross-border operations, as in Iceland, the results were very messy. While many were national SIFIs they only became regional SIFIs as a result of the reorganization after the resolutions. Whether the resolutions could be performed so smoothly for these new larger international banks is not readily verifiable from the Nordic experience.

Network Valuation in Financial Systems

We introduce a network valuation model (hereafter NEVA) for the ex-ante valuation of claims among financial institutions connected in a network of liabilities. Similar to previous work, the new framework allows to endogenously determine the recovery rate on all claims upon the default of some institutions. In addition, it also allows to account for ex-ante uncertainty on the asset values, in particular the one arising when the valuation is carried out at some time before the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution.

On Pricing Asian Options under Stochastic Volatility

American exercise presents difficulties for option valuation. For an in-the-money option, it becomes necessary at each point in time to consider whether to exercise or to hold on, based on expectations about the stock price at option expiration and also about the optionality value of potential exercise on every date when exercise will be possible in the future. An “Asian” option payoff presents its own valuation problems because the payoff is based on the arithmetic average of correlated lognormal prices, which is not lognormal. Adding stochastic volatility makes both of these problems much harder. But in this article, Russo and Staino are able to develop a lattice technique that deals with all three of these difficulties. The stochastic variable that the tree is built around is the variance, while both the current asset price and the running average of past prices to be included in calculating the payoff at expiration are carried along as auxiliary variables, in the form of sets of values at each node that span the range of possible values along all of the paths that lead to that node. Although there are several approximations in the procedure, accuracy is excellent, and execution is relatively fast.

Global equality of resources and the problem of valuation

The principle that every individual on the planet has a claim to an equal share of Earth’s natural resources has an intuitive attraction. Yet the Principle of Natural Resource Equality is not without its problems. This article focuses on the problem of valuation. Unless and until its adherents are able to develop an adequate theoretical mechanism for determining the comparative value of two or more bundles of natural resources the principle lacks applicability and persuasive force. Three adequacy constraints on such a mechanism are presented and then applied to a theorisation of the Principle of Natural Resource Equality that I have already expounded elsewhere: Global Equality of Resources. In each case I try to argue that Global Equality of Resources could satisfy the adequacy constraint, provided that both this theory and the relevant constraint are properly understood.

A geometric Levy model for [formula omitted]-fold compound option pricing in a fuzzy framework

In this paper, we study the problem of n-fold compound option valuation using the martingale method and the theory of fuzzy sets. We adopt a geometric Levy process for modeling the underlying asset price dynamics. The log-price is the sum of a Brownian motion with drift and a Poisson process describing jumps in the price. To obtain the pricing formula for n-fold compound option, we use the Esscher transformed martingale measure as the equivalent martingale measure. The major challenge in deriving the closed-form analytic expression for n-fold compound options is to calculate complex multivariate normal integrals; the complexity is due to the sophisticated structure of the options. In order to overcome this difficulty, we prove a mathematical expectation related to multivariate normal variables. To the best of our knowledge, this report describes the first time that such an approach has been adopted, and it is highly useful in the pricing of n-fold compound options and many other financial derivatives. Because the uncertainty in financial markets simultaneously involves randomness and fuzziness, we assume that the underlying asset price follows a fuzzy stochastic process. Under this assumption, the α-cut of the fuzzy price of n-fold compound call options is derived. Considering a decision maker’s subjective judgment, the permissible range of the expected prices of n-fold compound call options with uncertainty is given. Finally, numerical examples are presented to illustrate and analyze the theoretical results.

Partially observable stochastic optimal control problems for an energy storage

In this paper we study the valuation of an energy storage facility in the presence of stochastic energy prices as it arises in the case of a hydro-electric pump station. The valuation problem is related to the problem of determining the optimal charging/discharging strategy that maximizes the expected value of the resulting discounted cash flows over the lifetime of the storage. Adding to the literature we use a regime switching model for the energy price which allows for a changing economic environment described by a non-observable Markov chain. We formulate the problem as a stochastic control problem under partial information in continuous time. Applying filtering theory we find an alternative state process containing the filter of the Markov chain, which is adapted to the observable filtration. For this alternative control problem we derive the associated Hamilton-Jacobi-Bellman (HJB) equation which is not strictly elliptic. Therefore we study the HJB equation using regularization arguments. Finally, we solve the optimization problem numerically.

Approximation to Default Swaptions in Reduced-Form Framework: Calibration and Comparison of Intensity Dynamics

We develop an approximation to pricing default swaptions in general intensity models which yields a fast and accurate analytic/semi-analytic solution to the valuation problem. We consider several dynamics for intensity and derive 'extended transforms' for inverse Gaussian- and tempered stable Ornstein-Uhlenbeck processes. Having convenient pricing formulae, we are able to provide the first account of calibration of intensity models to credit options. Further, we extend the model by adding a shift, thus resulting in a tractable model that keeps the intensity positive, matches closely implied volatilities of default swaptions, and fits exactly the CDS spreads.

Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value

We consider the problem of valuing inputs in a production environment in which input supply is uncertain. Inputs can be workers in a firm, risk factors for a disease, securities in a financial market, or nodes in a networked economy. Each input takes its values from a finite set, and uncertainty is modeled as a probability distribution over this set. First, we provide an axiomatic solution to our valuation problem, defining three intuitive axioms which we use to uniquely characterize a valuation scheme that we call the a priori Shapley value.Second, we solve the problem of valuing inputs a posteriori - that is, after observing output. This leads to the Bayesian Shapley value.Third, we consider the problem of rationalizing uncertainty when the inputs are rational workers supplying labor in a non-cooperative production game in which payoffs are given by the Shapley wage function. We find that probability distributions over labor supply that can be supported as mixed strategy Nash equilibria always exist. We also provide an intuitive condition under which we prove the existence of a pure strategy Nash equilibrium. We present several applications of our theory to real-life situations.

К вопросу об оценке стоимости объектов интеллектуальной собственности

Рассматриваются вопросы совершенствования практических методик оценки стоимости объектов интеллектуальной собственности в современных условиях хозяйствования и процедуры интеграции оценок на основе затратного, доходного и сравнительного (рыночного) подходов как меры развития экономического и финансового состояния производственного предприятия в настоящем и будущем.

A Study on High Valuation of Industrial Capital Investment <br/>—Based on the Viewpoint of Strategic Benefit

Different from the pure financial investors, investors of established company not only take financial returns into account, but also strategic benefits. The existence of strategic benefits distorts the behavior of industrial capital for investment. And high valuation is one of its manifestations. This paper constructs a model to illustrate the high valuation of industrial capital investment. If a complementary relationship exists between invested projects and industrial capital investor’s core business (i.e. strategic benefit is positive), then the industrial capital investment will result in high valuation; besides, if a substitute relationship exists between the invested projects and industrial capital investor’ score business (i.e. strategic benefit is negative), high valuation problem also appears. This paper highlights the origin of high valuation problem, and puts forward corresponding proposals to solve this problem.

Development of the methodology for the evaluation of a hydro-pumped storage power plant: Swiss case study

During the last two decades, an evolving market structure is recognised starting from the spot market and its derivatives, resulting to several other markets such as the Intraday Market (IM), the Balancing Market (BM) and the Reserve Capacity Market (RCM). The participation in these markets has changed significantly the operation policy of the plants and, consequently, their value in the market. The current paper deals with the problem of the long-term valuation of a Hydroelectric Pump Storage (HPS) plant participating in the DAM and IM. For this purpose, an appropriate methodology has been developed while it is demonstrated on a real case study concerning the operation of a Swiss based HPS plant that participates in the DAM and IM of the German electricity market, for a horizon of thirty-five (35) years.

Dividend maximization in a hidden Markov switching model

Abstract In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.

Contextual semantics in quantum mechanics from a categorical point of view

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

Gas storage valuation with regime switching

In this paper we treat a gas storage valuation problem as a Markov Decision Process. As opposed to existing literature we model the gas price process as a regime-switching model. Such a model has shown to fit market data quite well in Chen and Forsyth (2010). Before we apply a numerical algorithm to solve the problem, we first identify the structure of the optimal injection and withdraw policy. This part extends results in Secomandi (2010). Knowing the structure reduces the complexity of the involved recursion in the algorithms by one variable. We explain the usage and implementation of two algorithms: A Multinomial-Tree Algorithm and a Least-Square Monte Carlo Algorithm. Both algorithms are shown to work for the regime-switching extension. In a numerical study we compare these two algorithms.

The development of the concept of ecosystem services: A review of foreign Publications

Foreign publications devoted to the problems of determination and valuation of ecosystem services and their practical application in planning economic activities are under review. This direction of studies is being rapidly developed. It was clearly shaped after the global Millennium Ecosystem Assessment performed in 2005 on the initiative of the United Nations. In the recent decade, this direction has got an official status; specialized journals have been founded; regular conferences and workshops have been conducted. The number of publications in this field has increased considerably. The contribution of soil scientists to the valuation of ecosystem services remains modest. It is argued that the assessment and valuation of the ecosystem services of soils is a promising direction for soil science. Ecosystem services are subdivided into the groups of provisional, regulating, cultural, and supporting services. The latter group is considered the natural basis ensuring the efficient performance of other ecosystem services with their direct or indirect impact on human well-being. The assessment of ecosystem services implies three major directions: ecological, economic (monetary), and social. For each of the groups of ecosystem services, specific methods of their economic valuation are applied. Thus, provisional services are mainly assessed according to their market values. The contribution of provisional services to the total value of ecosystem services is relatively small. Regulating services are often estimated by the avoided cost and replacement cost methods, and cultural services (recreation, inspiration source, aesthetic value, spiritual value) are valued by the travel cost method. The methods of nonmarketable valuation are essentially based on the willingness-to-pay approach. Upon valuation of ecosystem services at the local level, a systems approach should be applied; it is necessary to taken into account cooperation bonus obtained by the particular stakeholders. It should also be noted that the removal of additional pressures from ecosystems in a given place might result in the increase of the anthropogenic loads on ecosystems in other places. The separation, mapping, and valuation of ecosystem services are performed with an ultimate goal to ensure sustainable development of the society and human well-being. The ecological and economic approaches in this field are actually aimed at strengthening of the role of market mechanisms in the environmental protection policy.

Application of Alternative Valuation Formulas for a Company Sale

In this paper, a company owner (valuation subject) is interested in selling a company (valuation object). The potential seller must conduct a business valuation to determine what minimum price he must demand without the transaction proving disadvantageous. The purpose of our paper is to show how alternative valuation formulas solve this valuation problem under realistic imperfect market conditions. As a main conclusion, the business value can usually not be calculated using the future earnings method.

Are costs of capital necessarily constant over time and across states of nature?

Abstract Miller (2009a) opened a debate in this journal on the correct determination of weighted average costs of capital (WACC). So far Bade (2009) , Pierru (2009a) , Lobe (2009) as well as Keef, Khaled, and Roush (2012) have contributed to this debate. Even though they discuss the same, rather simple valuation problem, the dispute cannot be considered resolved. Whilst they agree that Miller erroneously assumed constant leverage ratios, the center of discussion is now placed on the question whether or not cost of capital is constant over time when leverage changes and interest paid is not tax deductible. In particular, Keef et al. (2012) demand time-invariant WACC and criticize Bade (2009) and Pierru (2009a) for allowing WACC to change over time. The aim of this paper is twofold. Firstly, we show that the arguments of Keef et al. (2012) are flawed and their criticism of Bade (2009) and Pierru (2009a) is thus unfounded. Keef et al. (2012) are wrong to ignore that not only financial risk but also operational risk can change over time. Secondly, we provide evidence that cost of capital can also be dependent on the future state of nature. So far this fact has been neglected by all contributors to this debate and becomes obvious only if state-dependent cash flow realizations, not only their expected values, are considered as well.

Accrual accounting in Italian universities: a technical perspective

Purpose– The purpose of this paper is to examine the impact of full accrual accounting on the Italian public universities and, in this context, how some technical-accounting problems typical of public sector (recognition and valuation issues) have been addressed. An additional purpose investigated in this paper is the role of International Public Sector Accounting Standards (IPSASs) in helping to overcome these technical-accounting issues, for the case under examination.Design/methodology/approach– The paper involves studying whether, and to what degree, some of the accounting choices made by the universities complied with the principles of full accrual accounting for several specific accounting registrations characterised by the presence of recognition and valuation issues. During this investigation, the paper also analyses whether the universities followed the accounting rules set out by the IPSAS Board.Findings– The findings highlight that, in general, there is a low degree of compliance with full accrual accounting principles and they also revealed that IPSASs do not provide any detailed guidelines that can help universities in overcoming the recognition and valuation problems typical of the public sector.Originality/value– The analysis presented in the paper confirms the findings of previous literature identifying a low level of compliance to full accrual accounting principles. This research shed light also on the longstanding debate about the role of IPSASs in promoting full accrual accounting in the public sector, revealing the scarce contribution of IPSASs to this process.