This paper introduces a new numerical option pricing method by fast recursive projections. The projection step consists in representing the payoff and the state price density with a fast discrete transform based on a simple grid sampling. The recursive step consists in transmitting coefficients of the representation from one date to the previous one by an explicit recursion formula. We characterize the convergence rate of the computed option price. Numerical illustrations with different American and Bermudan payoffs with discrete dividend paying stocks in the Black-Scholes and Heston models show that the method is fast, accurate, and general.
The fact that human economic behaviour has a significant irrational element - one that is simultaneously hard-to-explain and highly predictable - has fascinated economists for decades from Fechner, 1860 to Shiller, 2005 and beyond. In this dissertation, I investigate the field from various perspectives: chapter 1 examines the impact that language describing irrational behaviour in the media has on stock markets; chapter 2 looks at whether musical harmonics can predict what choices participants in money-sharing games will make; and chapter 3 takes an existing theroetical model of stochastic decision-making and changes it to help explain phenomena such as the overweighting of small probabilities, the 'willingness-to-accept'-'willingess-to-pay' (WTA-WTP) disparity, and preference reversals.
We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly cross-sectionally correlated or share at least one unobservable common factor. It only requires computing the largest eigenvalue of the empirical cross-sectional covariance matrix of the residuals of a large unbalanced panel. A general version of this criterion allows us to determine the number of omitted common factors. The panel data model accommodates both time-invariant and time-varying factor structures. The theory applies to random coefficient panel models with interactive fixed effects under large cross-section and time-series dimensions. The empirical analysis runs on monthly and quarterly returns for about ten thousand US stocks from January 1968 to December 2011 for several time-invariant and time-varying specifications. For monthly returns, we can choose either among time-invariant specifications with at least four financial factors, or a scaled three-factor time-varying specification. For quarterly returns, we cannot select macroeconomic models without the market factor.
