Pricing options with Green's functions when volatility,interest rate and barriers depend on time

We derive the Green's function for the Black–Scholes partial differential equation with time-varying coefficients and time-dependent boundary conditions. We provide a thorough discussion of its implementation within a pricing algorithm that also accommodates American style options. Greeks can be computed as derivatives of the Green's function. Generic handling of arbitrary time-dependent boundary conditions suggests our approach to be used with the pricing of (American) barrier options, although options without barriers can be priced equally well. Numerical results indicate that knowledge of the structure of the Green's function together with the well-developed tools of numerical integration make our approach fast and numerically stable.     

Upward and downward complementarity: the meso core of evolutionary growth theory

We propose that the concept of complementarity can take two distinct meanings in evolutionary economics: one referring to Adam Smith’s notion of increasing specialization and the division of labour, which we denote ‘downward complementarity’ (wholes into new parts); and a second type that refers to the discovery of emergent complementarity between extant or new components and products, which we call ‘upward complementarity’ (parts into new wholes). We outline this new conception and explore some of its analytic and theoretic implications.     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.     

The comparative performance of chartered accountancy students in South Africa: The impact of historical legacies

African students continue to underperform in South Africa's schools and universities. This paper investigates the comparative performance of African chartered accountancy students from school to post-university level. The paper employed a mixed-method approach to analyse a series of cross-sectional datasets. The results showed that African students have underperformed at school, university and at post-university level, although the performance gap appears to be narrowing in the first professional chartered accountancy examination. The differential performance of these students was explained by poorer marks in mathematics and English that can be traced back to historical legacies in the education sector. South African universities, moreover, perpetuate this disadvantage because they have retained Eurocentric teaching approaches. In order to remove these barriers, tuition at school and university must be complemented by cross-cultural teaching practices and bridging programmes.