Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Factor Proportions and the Growth of World Trade

Most of the expansion of global trade during the last three decades has been of the North-South kind - between capital-abundant developed and labour-abundant developing countries. Based on this observation, I argue that the recent growth of world trade is best understood from a factor-proportions perspective. I present novel evidence documenting that differences in capital-labour ratios across countries have increased in the wake of two shocks to the global economy: i) the opening up of China and ii) financial globalisation and the resulting upstream capital flows towards capital-abundant regions. I analyse their impact on specialisation and the volume of trade in a dynamic model which combines factor-proportions trade in goods with international trade in financial assets. Calibrating this model, I find that it can account for 60% of world trade growth between 1980 and 2007. It is also capable of predicting international investment patterns which are consistent with the data

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)