Utility Indifference Valuation

An agent's optimization problem of the expected terminal wealth utility in a trinomial tree economy is solved. At each transaction date, the agent can trade in a riskless asset, a primitive asset subject to constant proportional transaction costs, and a contingent claim characterized by some parameter kappa whose bid and ask price is defined by allowing for different equivalent martingale measures. In addition to the classical portfolio choice problem, the characteristic of the contingent claim κ is determined endogenously in the optimization problem. Under suitable conditions, it is proved that the optimal demand of the agent in the primitive risky asset is zero independently of the choice of the terminal wealth utility function: the agent prefers not to trade in the asset subject to transaction costs, which prevents the market from being complete, rather than trading in both assets. Next, the optimal choice of the contingent claim is characterized and the results are applied to European call and put options with fixed maturity and varying exercise price κ.

We consider an incomplete market with two information structures, complete and partial information and , respectively. The dynamics of the market are given by a risky asset driven by a m-dimensional Brownian motion W = (W1, …, Wm)′ as well as an integer-valued random measure μ(du, dy). To study the values with respect to the different information filtrations, we introduce the concept of dynamic < ![CDATA[exp]] >-utility indifference value (UIV) of with respect to denoted by Ct and the concept of dynamic < ![CDATA[exp]] >-UIV of the contingent claim H denoted by Ct(H), and we describe the dynamics of Ct and Ct(H) by BSDEs.

Liquidity Stress Testing in Asset Management - Part 2. Modeling the Asset Liquidity Risk

Where Experience Matters: Asset Allocation and Asset Pricing with Opaque and Illiquid Assets

Boyle and Vorst work in the framework of the binomial model and derive self-financing strategies perfectly replicating the final payoffs to long and short positions in call and put options, assuming proportional transactions costs on trades in the stock and no transactions costs on trades in the bond. Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Bensaid et al. gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalized by Stettner, Rutkowski and Palmer to the case of asymmetric transaction costs. In this paper, we first determine the number of replicating portfolios and then compute the least cost super replicating portfolio for any contingent claim in a one-period binomial model. By using the fundamental theorem of linear programming, we show that there are only finitely many possibilities for a least cost super replicating portfolio for any contingent claim in a two-period binomial model. As an application of our results, we give an example in which we compute the least cost super replicating portfolio for a butterfly spread in a two-period model.

The transaction cost (TC) escalation is the pervasive problem in the construction industry, which is continuously a threat to maintaining the life cycle cost of projects. Researchers have described the reality of risk for economic transactions. This study has taken the risk as a phenomenon to explore its influence on ex-post TC in construction projects. A questionnaire survey was undertaken from industry professionals to assess the risk of ex-post TC escalation in public-sector construction projects. In total, 475 surveys were conducted in Pakistan and used in the analysis. The data were analyzed using structural equation modeling (SEM) and the measurement and structural model was validated to determine the influence of risk on ex-post TC. The final SEM results show that internal and external risk, including sub hypothesized risks, positively influence TC. The weight of relative importance shows technical risk (23.82%) and environmental risk (22.88%) as significant sub-contributors from internal and external sources, respectively. This study recommends substantial investment in human capacity development to reduce the deficiencies in the ex-ante phase of the projects that help to reduce the risk of ex-post TC escalation. It also suggests the adoption of strict policies on contingency claims, and recommends nontraditional ways of monitoring to overcome the risk of ex-post TC. This study’s results provide valuable information for industry professionals and practitioners to maintain life cycle costs as a contribution to sustainable construction.

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price‐taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid‐ask price pair for this claim is said to be consistent if it is a bid‐ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.

We consider, using the geometric description, a sequence of models of multi-asset financial markets with proportional transaction costs vanishing in the limit. We assume that the price processes are He-type multinomial approximations of a process whose components are correlated geometric Brownian motions. For a given vector-valued contingent claim, defined as a continuous function of the price trajectories, we consider for each model the hedging set, that is, the set of all vector-valued initial endowments permitting to superreplicate the contingent claim by the final position of a self-financing portfolio. We calculate the limit of the hedging sets in the closed topology, obtaining in this way a set-valued version of the Kusuoka limit theorem.

It is noted that pricing derivative securities in a market where risky and riskless assets can be traded is a problem which has been solved for complete markets and general functions of the underlying securities. If an investor pays transaction costs for trading in the risky securities the market is not complete and the investor's preferences must be taken into account in the pricing of such contingent claims. In the paper, this problem is transformed into a stochastic optimal control problem, which is solved by the method of dynamic programming. Computational results are obtained for the writing price, when the writer's risk aversion factor is wealth independent. The pricing of a European call option is determined by the proposed algorithm. >

Fixed rate endowment mortgages differ from fixed rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We use a contingent claims framework for valuing the embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). We assume a mean-reverting interest rate and a lognormal house price diffusion process to arrive at a partial differential equation as the basis of the contingent claims and include conventional mortgage terms such as arrangement fees and prepayment penalties. This methodology provides a template for the borrower, lender and insurer to compare mortgage terms, including the fairness of contract rates, fees and any MIG premiums required, when borrowing more than 75% of the house value at origination. Given the conventional terms and the diffusion processes, we assume the parties have common expectations for some diffusion parameters, including expected future rate and price volatilities. Also we assume that borrowers are 'economic actors' regarding default and prepayment options, and that factors such as mobility, divorce, unemployment, and transaction costs are deterministic and can be ignored in this model, along with moral hazard problems between the insurer and the lender. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results. We provide graphical representations (and interpretations) of each mortgage component as a function of house prices and interest rate levels. After empirical studies on the input parameters, each mortgage component may be compared with 'market values'. This model may also be useful as a 'mark-to-value' proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining 'value added accounting', appropriate reserves, and indeed for setting premiums and business decisions. Finally, we compare endowment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatility.

At the international level, treasury issues - and cash management in particular - introduce degrees of complexity beyond those experienced in a single country. While the fundamentals of cash management are the same, environmental factors such as taxation, exchange controls, currency risk, interest rate risk, country risk, and statutory accounting/reporting requirements add new dimensions to the problems. There are also tactical problems such as country differences in collections, time delays and inconsistent accounting standards which make credit risk evaluation difficult and introduce nonuniform contract and legal recourse avenues and significantly higher transaction cost elements. From a multinational company's perspective, clear objectives must be stated by senior management so as to provide the treasury function with a clear set of guidelines. For most corporations, the principal objects of the international treasury activity should be to: protect the corporation's liquid assets, principally cash, until they are required for re-investment in the business operations or for pay-out to the stakeholders in the company; maximize the use of cash and debt commensurate with the company's operating environment. Provide the business operations in each country with sufficient liquidity and credit to deliver on its business objectives; carefully manage all financial risks confronting the company, keeping in mind that all risk is symmetrical. Risk can be positive and negative. Financial risks are additional factors of production which must also be managed and to ignore them is to speculate. The object is to reduce factors of volatility which can prove detrimental to the concern; and consistently provide the lowest after-tax fully-hedged capital available to the company. Take advantage of the corporation's collective international businesses to create economies of scale and to reduce transaction costs. In order to fulfil these goals, the company must provide for professional treasury skills with adequate systems and other resources. The international treasury activity must be in touch with the line operations of the company so as to anticipate issues and communicate actions.

This paper analyzes a simple mean-variance model of an imperfect capital market in which trade in assets involves costs. Fixed transactions costs, which result in investors only partially diversifying their portfolios, are shown to imply equilibrium asset prices substantially different from the Sharpe-Lintner prices. An improvement in the markets, in the form of lowering the trading costs, is shown to result in an increase in the number of assets held by each investor, in lowering equilibrium risk premia, and also in increasing the number of active investors.

On November 14–15, 2008, the Federal Reserve Bank of Cleveland hosted a conference on “Liquidity in frictional asset markets.” In this paper, we review the literature on asset markets with trading frictions in both finance and monetary theory using a simple search‐theoretic model, and we discuss the papers presented at the conference in the context of this literature. We will show the diversity of topics covered in this literature, for example, the dynamics of housing and credit markets, the functioning of payment systems, optimal monetary policy and the cost of inflation, the role of banks, the effect of informational frictions on asset trading.

Purpose of the study. The first goal of the study is a comparative analysis of the models of the accounting system of the stock market operating on the territory of the Russia, in particular, the model of the distributed accounting system and the model of the centralized accounting with the use of the central depository are considered. The second goal is to apply the distributed ledger technology in the development of a new model for the stock market accounting system. The goals are conditioned by the growing interest to the technology and similarity of its internal processes with the system of accounting of digital assets. The needs in optimization of the existing accounting system, bringing the system to the logical centralization are revealed. The application of distributed ledger technology for the purpose of unification of depository accounting systems is proposed. The analysis of efficiency of the given models is carried out and the criteria of efficiency estimation of each model are revealed. Materials and methods. For carrying out the research the works of description of register system genesis of stock market in Russia were applied. Works of Russian and foreign researchers in the field of influence of technology of distributed registers on accounting system and business processes of organizations are studied. The methodology for comparing models was the approach to the development of highly specialized evaluation criteria that meet the needs of the largest number of stock market participants. Results. Evaluation criteria were developed, on the basis of which the comparison of the existing models of the accounting system of stock market and the projected model on the distributed ledger technology was carried out. The needs for optimization of the existing accounting system of Russia, bring the system to the logical centralization of interaction of elements are revealed. Suggestions for the use of distributed ledger technology in order to unite the register systems of obligations have been developed The variety of elements of the accounting system of the Russian stock market was determined a large number of indicators used in comparisons of models, as well as a variety of approaches, both to the construction of the indicators themselves and to the collection of data to ensure their calculation and comparison. Conclusion. According to the results of the research it was determined that the decentralized model of the stock market accounting system on the distributed ledger technology in comparison with the classic model reduces the transaction cost of obligation right accounting operations, optimizes the complexity of the processes of interaction between the elements of the system, such as depositories and registrars, increases the transparency of the stock market, the processes of the transition of assets rights, due to which the liquidity of such assets and the increases investors interest. Decentralized model standardizes the of communication data, which has a positive effect on the indicators of information systems of participants. In comparison with the centralized model, the decentralized model eliminates the central depository transaction commission, eliminates monopolization to choose the direction of stock market depository accounting system development. Finally, the positive influence of the decentralized model on the stock market as a whole was revealed. The resulting form of relations will reduce the main cost indicators of the accounting system elements, such as transaction costs, the cost of support and development of information systems, the number of necessary formats for the application of interaction with counterparties.