Galton's fallacy and economic convergence

Friedman (1992) argues that regressing cross-country incomechanges on their final levels can be informative about -convergence(the tendency for the dispersion of income levels to narrow)whereas a similar regression on initial levels of income cannotbe. In this note we show that Bliss's (1999) dismissal of thisargument is in error.     

THE BLACK-SCHOLES EQUATION REVISITED: ASYMPTOTIC EXPANSIONS AND SINGULAR PERTURBATIONS

In this paper, novel singular perturbation techniques are applied to price European, American, and barrier options. Employment of these methods leads to a significant simplification of the problem in all cases, by reducing the number of parameters. For American options, the valuation problem is reduced to a procedure that may be performed on a rudimentary handheld calculator. The method also sheds light on the evolution of option prices for all of the cases considered, the results being particularly illuminating for American and barrier options.     

An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options

This paper considers in detail a realistic mortgage valuation model (including the potential for early prepayment and the risk of default), based on stochastic house-price and interest-rate models. As well as the development of a highly accurate numerical scheme to tackle the resulting partial differential equations, this paper also exploits singular perturbation theory (a mathematically rigorous procedure, based on the idea of the smallness of the volatilities), whereby mortgage valuation can be accurately approximated by very simple closed-form solutions. Determination of equilibrium contract rates, previously requiring many computational hours is reduced to just a few seconds, rendering this a highly useful portfolio management tool; these approximations compare favorably with the full numerical solutions. The method is of wide applicability in US or other mortgage markets and is demonstrated for UK fixed-rate mortgages, including insurance and coinsurance.     

Extending quadrature methods to value multi-asset and complex path dependent options

The exposition of the quadrature (QUAD) method (Andricopoulos, Widdicks, Duck, and Newton, 2003. Universal option valuation using quadrature methods. Journal of Financial Economics 67, 447–471 (see also Corrigendum, Journal of Financial Economics 73, 603 (2004)) is significantly extended to cover notably more complex and difficult problems in option valuations involving one or more underlyings. Trials comparing several techniques in the literature, adapted from standard lattice, grid and Monte Carlo methods to tackle particular types of problem, show that QUAD offers far greater flexibility, superior convergence, and hence, increased accuracy and considerably reduced computational times. The speed advantage of QUAD means that, even under the curse of dimensionality, it is not necessary to resort to Monte Carlo methods (certainly for options involving up to five underlying assets). Given the universality and flexibility of the method, it should be the method of choice for pricing options involving multiple underlying assets, in the presence of many features, such as early exercise or path dependency.     

A Tournament Model of Fund Management

Abstract:  We develop a tournament model of portfolio management and test it on UK investment trusts. Our model extends the literature by analysing middle-ranking funds who aim to beat a benchmark; spanning two periods; focusing on 'extreme' portfolios; and using a signal-extraction framework. We predict that 'losing' managers will adopt extreme portfolios, and increasingly so, the further behind the fund is and the nearer the ranking date. Losing managers will choose high/low market exposure depending both on anticipated market movements and on whether they have sufficient assets to take advantage of a rising market. Our empirical tests support these predictions.     

On the enhanced convergence of standard lattice methods for option pricing

For derivative securities that must be valued by numerical techniques, the trade‐off between accuracy and computation time can be a severe limitation. For standard lattice methods, improvements are achievable by modifying the underlying structure of these lattices; however, convergence usually remains non‐monotonic. In an alternative approach of general application, it is shown how to use standard methods, such as Cox, Ross, and Rubinstein (CRR), trinomial trees, or finite differences, to produce uniformly converging numerical results suitable for straightforward extrapolation. The concept of Λ, a normalized distance between the strike price and the node above, is introduced, which has wide ranging significance. Accuracy is improved enormously with computation times reduced, often by orders of magnitude. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:315–338, 2002     

Unanticipated monetary growth,output and the price level: U.K. 1946–1977

This paper develops and estimates using annual data from 1946–1977 a three-equation model of the U.K. economy, in which output is affected only by unanticipated monetary growth whereas the price level is influenced by both anticipated and unanticipated changes in money supply. Expectations of monetary growth are assumed to be Muth-rational. The model was estimated using efficient procedures, and tests of the over-identifying restrictions were generally favourable to model specification. Some features of the price equation are unsatisfactory and the results in this section must be considered tentative.