Smooth convergence in the binomial model

In this article, we consider a general class of binomial models with an additional parameter λ. We show that in the case of a European call option the binomial price converges to the Black–Scholes price at the rate 1/n and, more importantly, give a formula for the coefficient of 1/n in the expansion of the error. This enables us, by making special choices for λ, to prove that convergence is smooth in Tian’s flexible binomial model and also in a new center binomial model which we propose. Ken Palmer was supported by NSC grant 93-2118-M-002-002.     

Duality theory for robust utility maximisation

In this paper, we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real line. Our results are inspired by – and can be seen as the robust analogues of – the seminal work of Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999). Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.

     

No-arbitrage criteria for financial markets with transaction costs and incomplete information

This note deals with criteria of absence of arbitrage opportunities for an investor acting in a market with frictions and having a limited access to the information flow. We develop a mathematical scheme covering major models of financial markets with transaction costs and prove several results including a criterion for the robust no-arbitrage property and a hedging theorem.      

A binomial approximation for two-state Markovian HJM models

This article develops a lattice algorithm for pricing interest rate derivatives under the Heath et al. (Econometrica 60:77–105, 1992) paradigm when the volatility structure of forward rates obeys the Ritchken and Sankarasubramanian (Math Financ 5:55–72) condition. In such a framework, the entire term structure of the interest rate may be represented using a two-dimensional Markov process, where one state variable is the spot rate and the other is an accrued variance statistic. Unlike in the usual approach based on the Nelson-Ramaswamy (Rev Financ Stud 3:393–430) transformation, we directly discretize the heteroskedastic spot rate process by a recombining binomial tree. Further, we reduce the computational cost of the pricing problem by associating with each node of the lattice a fixed number of accrued variance values computed on a subset of paths reaching that node. A backward induction scheme coupled with linear interpolation is used to evaluate interest rate contingent claims.     

An adjusted binomial model for pricing Asian options

We propose a model for pricing both European and American Asian options based on the arithmetic average of the underlying asset prices. Our approach relies on a binomial tree describing the underlying asset evolution. At each node of the tree we associate a set of representative averages chosen among all the effective averages realized at that node. Then, we use backward recursion and linear interpolation to compute the option price.     

Prediction markets for foresight

To navigate turbulent business environments, organizations have to develop foresight capacities that enable them to anticipate probable futures, respond rapidly to emerging changes, and support future oriented action. However, there are remaining barriers that impede a wider implementation of foresight. In particular, the necessities to deal with the future, anticipate change, enhance participation and reduce costs and complexity call for new methods to improve current foresight activities. In this paper, we introduce prediction markets to the field of foresight. Prediction markets are a structured approach to collect and aggregate information from groups and have recently gained attention in forecasting. Prediction markets go beyond simple forecasting and can contribute to foresight by providing advantages in terms of continuous and real-time information aggregation, motivation of participation and information revelation as well as cost-efficiency and scalability. We suggest four promising fields of application for prediction markets to enhance foresight: (1) continuous forecasting and environmental scanning, (2) combining with deliberative approaches, (3) continuous idea generation and (4) expert identification. We conclude by considering prediction markets as a nascent and promising method for foresight and advocate for further research.     

Are the China-related stock markets segmented with both world and regional stock markets?

Implementing the Capital Asset Pricing Model framework, this study investigates the integration of three China-related stock markets, namely, the A-, B- and H-share markets, with both the Hong Kong stock market and the world market. An analysis of market segmentation versus integration using the Jorion and Schwartz model suggests that the A-share market was a segmented market during the period 1995–2004. However, evidence of a higher-level integration between the A- and B-share markets, and the A-share and Hong Kong stock markets is found in the sub-period tests. The hypothesis that the B- and H-share markets are becoming increasingly integrated with the world stock market is not supported.     

Large sample validity of the binomial distribution for lives with unequal mortality rates

Abstract

Let us consider a group of n lives which are observed during some time or age interval. Suppose that the following conditions are satisfied: 1. The probability of death within the interval considered has the same value q for each person of the group.

2. These lives represent statistically independent observations (with respect to mortality).

     

Duality for pathwise superhedging in continuous time

Finance and Stochastics - We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of $d$  risky assets with continuous price...     

International diversification with frontier markets

We provide an analysis of frontier market equities with respect to world market integration and diversification. Principal component results reveal that frontier markets exhibit low levels of integration. In contrast with developed and emerging markets, frontier markets offer no indication of increasing integration through time. Furthermore, individual frontier market countries do not exhibit consistent rates of changing integration. Structural break tests identify breakpoints in integration, as well as integration dynamics across countries. We show that frontier markets have low integration with the world market and thereby offer significant diversification benefits.     

On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case.Received: March 2004, Mathematics Subject Classification (2000): 62P05JEL Classification: G11, G13The authors are grateful to an anonymous referee for numerous helpful comments and to Yulia Romaniuk for final corrections. The paper was partially supported by grant NSERC 264186.     

The interrelatedness of global equity markets, money markets, and foreign exchange markets

This article investigates different aspects of global financial markets, specifically relationships among equity markets, money markets, and foreign exchange markets across countries. To represent the three major financial markets of the world, Japan is the proxy for Asia, Germany is the proxy for Europe, and the United States is the proxy for North America. Strong evidence exists that international money markets and international equity markets are becoming increasingly integrated over time. This article incorporates foreign exchange values as partial determinants of equity returns and money market returns and investigates the interactions among these three asset markets from a global perspective.     

Nontraded asset valuation with portfolio constraints: a binomial approach

We provide a simple binomial framework to value American-stylederivatives subject to trading restrictions. The optimal investmentof liquid wealth is solved simultaneously with the early exercisedecision of the nontraded derivative. No-short-sales constraintson the underlying asset manifest themselves in the form of animplicit dividend yield in the risk-neutralized process forthe underlying asset. One consequence is that American calloptions may be optimally exercised prior to maturity even whenthe underlying asset pays no dividends. Applications to executivestock options (ESO) are presented: it is shown that the valueof an ESO could be substantially lower than that computed usingthe Black-Scholes model. We also analyze nontraded payoffs basedon a price that is imperfectly correlated with the price ofa traded asset.     

Mortality data and the binomial probability law

Introduction.

Critics of the custom that bases actuarial theory on the probability calculus whilst admitting that probability theory may be applicable, have denied that mortality data satisfy the requirements of independence and equi-probability demanded by ‘simple’ theory. We believe that the proper answer to these polemics is that ‘equi-probability’ and ‘independence’ are technical phrases introduced as part of a theory which is purely conceptual. To seek to deny the applicability of the theory on the grounds of the lack of one-to-one correspondence of these words with their counterparts in the everyday world is precipitate. The evaluation of the theory must be decided by the correctness of the results it forecasts. Few of the critics mentioned have produced statistics which support their case: some have even misapplied the theory they so earnestly criticise.