International Journal of Theoretical and Applied Finance

This paper presents alternative approach to foreign exchange market trading decisions. The model is equally applicable to the arbitrage practices of international banks, to the hedging decisions of multinational corporations, to the investment decisions of currency fund managers and to the uncovered positions of currency speculators. By using a network model to represent these situations complex problems can be modeled and the optimization problem required to maximize profit or eliminate risk can be accurately formulated.

Twenty-one significant bubbles followed by large crashes or severe corrections in Latin-American and Asian stock markets are identified. We find that, with very few exceptions, these speculative bubbles can be quantitatively described by a rational expectation model of bubbles predicting a specific power law acceleration as well as so-called log-periodic geometric patterns. This model considerably extends the applicability of the rational expectation model of bubbles followed by crashes or severe corrections previously proposed for the major financial markets in the world, i.e. the USA and the foreign exchange markets. A comparison of the model predictions using the price and the logarithm of the price, respectively, furthermore indicates according to our model that such large downward movements in the markets are nothing but depletions of the preceding bubble thus bringing the market back towards equilibrium. In addition, a set of secondary stock markets are also shown to exhibit well-correlated "anti-bubbles" triggered by a rash of crises on emerging markets in early 1994. This suggests that smaller stock markets can weakly synchronize not only because of the over-arching influence of the US market, but also independent of the US market due to external factors such as the Asian crisis of 1994.

Credit contagion means that the credit deterioration of an entity causes the credit deterioration of other entities. In this paper, we build and test a continuous-time model for defaultable securities using a diffusive process for risk-free interest rate, and a finite-state continuous-time Markov process for the correlation of credit. The credit contagion, in particular, is established by relating transition rates of various credit states. Examples of derivative pricing with calibrated credit contagion model are provided. Initial empirical results with the benchmarks of Brady bonds show that our model is a viable new technique for the pricing and risk-managing of credit derivatives.

Index tracking is a very common and popular approach in portfolio management. When there is neither (nonconvex) transaction costs nor minimal transaction unit constraints, the problem can be formulated as a convex least square problem, so that it can be solved by standard methods. However, when the transaction cost is nonconvex and not negligible, or if there is a minimal unit constraint on the amount of transaction, the problem becomes a nonconvex minimization problem with discrete variables. In this paper, we will propose a branch and bound algorithm for solving this class of problems and show that it can solve an index tracking problem of practical size in a reasonable amount of computation time.