Arbitrage-free market models for option prices: the multi-strike case

This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for constructing such models, we introduce the new concepts of local implied volatilities and price level. We show that these new quantities provide a natural and simple parametrization of all option price models satisfying the natural static arbitrage bounds across strikes. We next characterize absence of dynamic arbitrage for such models in terms of drift restrictions on the model coefficients. For the resulting infinite system of SDEs for the price level and all local implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We give explicit examples of volatility coefficients satisfying the required assumptions, and hence of arbitrage-free multi-strike market models of option prices.      

On the duality principle in option pricing: semimartingale setting

The purpose of this paper is to describe the appropriate mathematical framework for the study of the duality principle in option pricing. We consider models where prices evolve as general exponential semimartingales and provide a complete characterization of the dual process under the dual measure. Particular cases of these models are the ones driven by Brownian motions and by Lévy processes, which have been considered in several papers. Generally speaking, the duality principle states that the calculation of the price of a call option for a model with price process S=e ^H (with respect to the measure P) is equivalent to the calculation of the price of a put option for a suitable dual model S′=e ^H′ (with respect to the dual measure P′). More sophisticated duality results are derived for a broad spectrum of exotic options. The second named author acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG, Eb 66/9-2). This research was carried out while the third named author was supported by the Alexander von Humboldt foundation.     

Prediction of Individual Bond Prices via a Dynamic Bond Pricing Model: Application to Japanese Government Bond Price Data

In this paper, we propose a dynamic bond pricing model and report the usefulness of our bond pricing model based on analysis of Japanese Government bond price data. We extend the concept of the time dependent Markov (TDM) model proposed by Kariya and Tsuda (Financial Engineering and the Japanese Markets, Kluwer Academic Publishers, Dordrecht, The Netherlands, Vol. 1, pp. 1–20) to a dynamic model, which can obtain information for future bond prices. A main feature of the extended model is that the whole stochastic process of the random cash-flow discount functions of each individual bond has a time series structure. We express the dynamic structure for the models by using a Bayesian state space representation. The state space approach integrates cross-sectional and time series aspects of individual bond prices. From the empirical results, we find useful evidence that our model performs well for the prediction of the patterns of the term structure of the individual bond returns.     

Convexity theory for the term structure equation

We study the convexity and model parameter monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide sharp conditions on the model parameters under which the convexity of the price in the short rate is guaranteed. Under these conditions, the price is decreasing in the drift and increasing in the volatility of the short rate. We also study the convexity properties of the logarithm of the price and find simple conditions on the coefficients that guarantee that the price is log-convex or log-concave.      

Efficiency in Turkish banking: post-restructuring evidence

Turkish banking sector went through a significant restructuring process in the aftermath of the country's financial crisis of 2000–2001. In this paper, we analyze the evolution of banking performance using a novel approach due to Ray [(2007). “Shadow Profit Maximization and a Measure of Overall Inefficiency.” Journal of Productivity Analysis 27, 231–236]. We derive ‘shadow unrealized profit scores’ as well as ‘shadow input–output prices’ for each year and bank in the sector from 2002 to 2011. We argue these scores operationalize the Hicksian concept of ‘monopolistic quiet life’. We provide some evidence the sector came closer to the ‘zero profit condition’ as well as displaying a closer approximation to the ‘law of one price’ over time. We show the variability of these ‘shadow prices’ essentially coincides with that of corresponding actual prices. We utilize shadow price information to show that business models and competitive choices of banks differ across ownership types with foreign banks competing on the broadest front compared to state-owned and privately owned Turkish banks.     

The effect of framing and negotiation partner’s objective on judgments about negotiated transfer prices

A common approach to set transfer prices is via intra-firm negotiation. However, Luft and Libby [Luft, J. L., & Libby, R. (1997). Profit comparisons, market prices and managers’ judgments about negotiated transfer prices. The Accounting Review, 72(2), 217–229] found that because of the existence of self-serving biases, negotiating managers have different expectations regarding what constitutes a ‘fair’ transfer price, leading to a less efficient negotiation process. In this study, we examine two factors that are expected to affect managers’ transfer price negotiation judgments, namely, framing as a gain or as a loss and the negotiation partner’s objective (whether the partner’s objective involves high or low concern-for-others). We propose that these two factors affect managers’ perceptions of the negotiation context, and thus the way they interpret the economic and social consequences of accounting information. Our results show that a loss frame (compared to a gain frame) exacerbates managers’ self-serving biases and increases the ‘transfer price expectation gap’ between buyers and sellers. Further, in our experiment where market price is higher than equal-profit price, we find that managers’ transfer price expectations are lower (and deviate more from the prevailing market price) when they are negotiating with a partner with high concern-for-others than with a partner with low concern-for-others. We discuss the broader implications of these results for the design of management accounting systems.     

On the Welfare Gains of Price Dispersion

Can price dispersion be associated with higher levels of welfare? To answer we compare two economies that differ only in the way prices are formed. In the first, sellers post a unique price–quantity pair, with no price dispersion. In the second, sellers post a quantity only and let prices be determined ex post by realized demand, resulting in price dispersion. We show that while agents trade lower quantities when prices are dispersed (an intensive margin effect), they also trade more often (an extensive margin effect). At low inflation, the extensive margin dominates making agents better off with price dispersion.     

Dilution,anti-dilution and corporate positions in options on the company's own stocks

Abstract

In this paper, we analyse options that are bought or sold by the company on whose stocks these options are written, leading to dilution and anti-dilution effects. We provide valuation equations for the European versions of such options, and discuss conditions for existence and uniqueness of their prices. Option prices to be paid or received for these options by the company are shown to be different from those that apply for standard options (which are bought and sold by outside investors). Since the options become part of the company's assets/liabilities, the stochastic process followed by the stock price changes. We demonstrate how the new stock price process can be derived, and discuss economic implications of our results. Numerical examples illustrate our findings.     

Oligopolistic markets with sequential search and production cost uncertainty

This article analyzes a sequential search model where firms face identical but stochastic production costs, the realizations of which are unknown to consumers. We characterize a perfect Bayesian equilibrium satisfying a reservation price property and provide a sufficient condition for such an equilibrium to exist. We show that (i) firms set on average higher prices and make larger profits compared to the scenario where consumers observe production costs, (ii) expected prices and consumer welfare can be non‐monotonic in the number of firms, and (iii) the impact of production cost uncertainty vanishes as the number of firms becomes very large.     

An empirical model of search with vertically differentiated products

This article provides a framework for studying price dispersion in markets with product differentiation and search frictions. We show under which assumptions we can obtain an equilibrium in which vertically differentiated firms mix prices over different supports. The model can explain the frequently changing prices reported in several empirical studies, but also why some firms have persistently higher prices than others. We show how to estimate the model by maximum likelihood using only prices. Estimates for grocery items in the United Kingdom reveal that most of the observed price variation is explained by supermarket heterogeneity rather than search frictions, whereas the estimated amount of search is low.