The Journal of Finance

Transition Densities for Interest Rate and Other Nonlinear Diffusions

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.00149

Yacine Aït‐Sahalia

This paper applies to interest rate models the theoretical method developed in Aït‐Sahalia (1998) to generate accurate closed‐form approximations to the transition function of an arbitrary diffusion. While the main focus of this paper is on the maximum‐likelihood estimation of interest rate models with otherwise unknown transition functions, applications to the valuation of derivative securities are also briefly discussed.

Telling from Discrete Data Whether the Underlying Continuous‐Time Model Is a Diffusion

Published: 12/17/2002   |   DOI: 10.1111/1540-6261.00489

Yacine Aït‐Sahalia

Can discretely sampled financial data help us decide which continuous‐time models are sensible? Diffusion processes are characterized by the continuity of their sample paths. This cannot be verified from the discrete sample path: Even if the underlying path were continuous, data sampled at discrete times will always appear as a succession of jumps. Instead, I rely on the transition density to determine whether the discontinuities observed are the result of the discreteness of sampling, or rather evidence of genuine jump dynamics for the underlying continuous‐time process. I then focus on the implications of this approach for option pricing models.

Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.215228

Yacine Aït‐Sahalia, Andrew W. Lo

Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state‐price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage‐free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset‐pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility “smiles” for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.

Luxury Goods and the Equity Premium

Published: 11/27/2005   |   DOI: 10.1111/j.1540-6261.2004.00721.x

YACINE AÏT‐SAHALIA, JONATHAN A. PARKER, MOTOHIRO YOGO

This paper evaluates the equity premium using novel data on the consumption of luxury goods. Specifying utility as a nonhomothetic function of both luxury and basic consumption goods, we derive pricing equations and evaluate the risk of holding equity. Household survey and national accounts data mostly reflect basic consumption, and therefore overstate the risk aversion necessary to match the observed equity premium. The risk aversion implied by the consumption of luxury goods is more than an order of magnitude less than that implied by national accounts data. For the very rich, the equity premium is much less of a puzzle.