International Journal of Theoretical and Applied Finance

It is generally argued that with lifting of barriers to the flow of capital across countries by respective governments, the capital markets have come closer and are now more integrated. This paper examines the existence (or absence) of integration among stock indices of 11 developed and emerging stock markets from three continents: Asia, Europe and America. Using synchronous weekly closing index values from November, 1990 through December, 2001, the study found that all the 11 stock markets are cointegrated. The cointegration analysis was carried out using an error correction vector autoregression (VECM) model. The study goes further to test whether there are any causal relationships among the indices and has used a hitherto empirically untested methodology to explore the causal relationships. Results show that capital market indices from European countries and the USA are not Granger caused by any index. On the other hand, causality effects are much pronounced in Asian capital markets. The capital market in Hong Kong "leads" the other markets in Asia. This learning would help fund managers in managing their exposure in Asian capital markets. The regulators may use the causality results to identify the markets driving movements in a country's capital market and take corrective measures.

Based on a Reinforced Urn Process introduced by Muliere et al. [11], we propose a stochastic model for the probability of credit default for debt issuers belonging to the same Moody's rated class. The model predicts how a default probability belonging to a given term structure evolves in time as information about credit defaults of debt issuers with the same Moody's rating becomes available. Connections between implied credit default probabilities and credit spreads will be exploited.

We present a detailed description of storage options valuation using a multilevel tree methodology which takes into account both the stochastic evolution of the energy commodity price underlying the storage contract or asset, as well as the storage facility operational constraints. We derive also a quasi-analytical solution for the storage value as a strip of calendar spread options, which is applicable when the storage constraints are ignored. The two valuation methodologies are applied within the framework of a one-factor and a two-factor diffusion model for the commodity price. As an interesting example of a path-dependent option with American exercise style, we take a look at the storage option injection and withdrawal exercise price boundaries and examine how these exercise decision boundaries are influenced by variations in the model's input parameters. We provide numerical results illustrating the dependence of the storage option value on the price model parameters, and interpret the observed parameter dependence using the calendar spreads formula as a useful analysis tool. We analyze and present numerical results regarding the dependence of the option value on the storage operational parameters.

A new approach to the problem of computing risk sensitivities of Bermuda swaptions in a lattice, or PDE, framework is presented. The algorithms developed perform the task much faster and more accurately that the traditional approach in which the Greeks are computed numerically by shocking the appropriate inputs and revaluing the instrument. The time needed to execute the tradition scheme grows linearly with the number of Greeks required, whereas our approach computes any number of Greeks for a Bermuda swaption in nearly constant time. The new method explores symmetries in the structure of Bermuda swaptions to derive recursive relations between different Greeks, and is essentially model-independent. These recursive relations allow us to represent risk sensitivities in a number of ways, in particular as integrals over the "survival" density. The survival density is obtained as a solution to a forward Kolmogorov equation. This representation is the basis for practical applications of our approach.

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified broadly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the trend of a world index. It turns out that it can be directly observed since the expected increments of the index equal four times those of the quadratic variation of its square root. Using a world stock index as approximation of the discounted GOP it is shown that, in reality, the trend of the discounted GOP does not vary greatly in the long term. This leads for a diversified world index to a natural model, where the index is a transformed square root process of dimension four. The squared index volatility appears then as the inverse of the square root process. This feature explains most of the properties of an index and its volatility.