Mean square error for the Leland–Lott hedging strategy: convex pay-offs

Leland’s approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim V _T using the classical Black–Scholes formula with a suitably enlarged volatility. The formal mathematical framework is a scheme of series, i.e., a sequence of models with transaction cost coefficients k _n =k ₀ n ^−α , where α∈[0,1/2] and n is the number of portfolio revision dates. The enlarged volatility [^(s)]_n\widehat{\sigma}_{n} in general depends on n except for the case which was investigated in detail by Lott, to whom belongs the first rigorous result on convergence of the approximating portfolio value Vⁿ_TV^{n}_{T} to the pay-off V _T . In this paper, we consider only the Lott case α=1/2. We prove first, for an arbitrary pay-off V _T =G(S _T ) where G is a convex piecewise smooth function, that the mean square approximation error converges to zero with rate n ^−1/2 in L ² and find the first order term of the asymptotics. We are working in a setting with non-uniform revision intervals and establish the asymptotic expansion when the revision dates are t_iⁿ=g(i/n)t_{i}^{n}=g(i/n), where the strictly increasing scale function g:[0,1]→[0,1] and its inverse f are continuous with their first and second derivatives on the whole interval, or g(t)=1−(1−t) ^β , β≥1. We show that the sequence n^1/2(V_Tⁿ-V_T)n^{1/2}(V_{T}^{n}-V_{T}) converges in law to a random variable which is the terminal value of a component of a two-dimensional Markov diffusion process and calculate the limit. Our central result is a functional limit theorem for the discrepancy process.     

Integrated Management of Land Use Systems under Systemic Risks and Security Targets: A Stochastic Global Biosphere Management Model

Interdependencies among land use systems resemble a complex network connected through demand–supply relationships. Disruption of this network may catalyse systemic risks affecting food, energy, water and environmental security (FEWES) worldwide. We describe the conceptual development, expansion and practical application of a stochastic version of the Global Biosphere Management Model (GLOBIOM), used to assess competition for land use between agriculture, bioenergy and forestry at regional and global scales. In the stochastic version of the model, systemic risks of various kinds are explicitly covered and can be analysed and mitigated in all their interactions. While traditional deterministic scenario analysis produces sets of scenario‐dependent outcomes, stochastic GLOBIOM explicitly derives robust outcomes that leave the systems better‐off, independently of which scenario applies. Stochastic GLOBIOM is formulated as a stochastic optimisation model that is critical for evaluating portfolios of robust interdependent decisions: ex‐ante strategic decisions (production allocation, storage capacities) and ex‐post adaptive (demand, trading, storage control) decisions. As an example, the model is applied to the question of optimal storage facilities, as buffers for production shortfalls, to meet regional and global FEWES requirements when extreme events occur. Expected shortfalls and storage capacities have a close relationship with Value‐at‐Risk (VaR) and Conditional Value‐at‐Risk (CVaR) risk measures. A Value of Stochastic Solutions is calculated to illustrate the benefits of the stochastic over the deterministic model approach.     

Preemptive Bidding in Takeover Auctions: An Experimental Study

This paper presents the results of an experimental study on jump bidding in takeover auctions with entry costs. It provides support for signaling hypothesis behind jump bidding and analyzes how the size of the entry costs affects the bidders' behavior and their expected profits. It also shows that jump bidding allows the reallocation of the surplus from the seller to the first bidder but has little effect on the social surplus and the profits of the second bidder. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of urban transportation system change on land prices in the setting of owner-occupied residence

The purpose of this study is to analyze the impact of transportation improvement on the land development process and land price structure in an owner-occupied residence setting. A dynamic model of household and landowner in which the role of land as an asset is explicitly considered is presented, and the process of land development and land price change after the announcement of transportation improvement is investigated. During the period between the announcement and the completion of urban transportation improvement, it is observed that the price of the land that is presently used for agriculture but will be developed in the future is higher than the agricultural land price.     

TRADE,NON‐SCALE GROWTH AND UNEVEN DEVELOPMENT

This paper investigates the relationship between trade and economic development using a two‐country, non‐scale growth model. Depending on the share of the expenditure for manufactured goods, we obtain two different results with regard to long‐run production patterns. Whether or not the follower country can catch up with the leader country in the long run depends on two factors: (1) the patterns of production in both countries and (2) the measure of economic welfare that is used, i.e. per capita income or per capita consumption.     

Preemptive bidding in takeover auctions with affiliated values

This paper extends Fishman's (1988) model of preemptive bidding in takeover auctions to auctions with affiliated values. It shows that preemptive bidding transfers wealth from the seller to the first bidder without affecting the profit of the second bidder and social welfare. It also shows that higher correlation between bidders’ values leads to higher preemption rates but has an ambiguous effect on the size of the opening bid. Finally, it shows that in auctions with affiliated values, even infinitesimal entry costs may lead to a preemptive jump bidding that allows the reallocation of the entire surplus from the seller to the first bidder.     

Unfunded pension liabilities and stock returns

This paper investigates whether the market rationally anticipates the value implications of unrecognized pension obligations, using a large sample of Japanese firms where pension obligations are substantially underfunded. If a firm's unrecognized pension obligation is not incorporated into its share price, its stock returns will be lower than those of other firms, because its deficit will affect the firm's income statement in the coming years. We find that firms with large unrecognized obligations earn lower risk-adjusted returns. This evidence suggests that the market does not efficiently incorporate information in the pension items.     

Integrating Real Options with Managerial Cash Flow Estimates

This article presents a real options model that fits managerial cash flow estimates (optimistic, likely, and pessimistic projections) to a continuous geometric Brownian motion (GBM) cash flow process with changing growth and volatility parameters. The cash flows and the value of a project are correlated to a traded asset, so the real option is priced under the risk-neutral measure with a closed-form solution. The analysis is extended to a sequential compound call option for investments over multiple periods. If the project is correlated to the market, then some of the risk may be mitigated by a delta-hedging strategy. A numerical example shows that the effect of the correlated asset on the real option value is significant, and the relationship between the volatility of the project and the real option value is not analogous to the typical relationship found in financial option pricing. Integrating the expertise and industry knowledge of management, this approach makes possible a more rigorous estimation of model inputs for real option pricing.     

PERFECT AND PARTIAL HEDGING FOR SWING GAME OPTIONS IN DISCRETE TIME

The paper introduces and studies hedging for game (Israeli) style extension of swing options considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions, we derive a formula for valuation of multiple exercise options via classical hedging arguments. Introducing the notion of the shortfall risk for such options we study also partial hedging which leads to minimization of this risk.