This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani~1994!, Dupire~1994, 1997!, and Rubinstein~1994!, who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adjusted to fit current option prices exactly, just as interest rate processes can be adjusted to fit bond prices exactly. The procedure works with many volatility models, is fast to calibrate, and can price exotic options efficiently using familiar lattice techniques.
This paper presents an exact finite-sample statistical procedure for testing hypotheses about the weights of mean-variance efficient portfolios. The estimation and inference procedures on efficient portfolio weights are performed in the same way as for the coefficients in an OLS regression. OLS t-and F-statistics can be used for tests on efficient weights, and when returns are multivariate normal, these statistics have exact t and F distributions in a finite sample. Using 20 years of data on 11 country stock indexes, we find that the sampling error in estimates of the weights of a global efficient portfolio is large.
This paper presents a new arbitrage-free approach to the pricing of derivatives, when the price process of the underlying security does not conform to the standard assumptions. In comparision to the Black-Scholes price process we relax the requirements of i) continuity; ii) constant volatility; and iii) infinite trading possibilities. We retain the assumption that the average volatility of price changes over the option's life is known, and we require that price jumps not be greater than some specified size. With only these assumptions we show that the no-arbitrage bound on a European call option's value approaches the Black-Scholes price as the maximum jump size approaches zero. We present a simple numerical method for the calculation of option pricing bounds for any specified maximum jump size, and discuss implications of our model for hedging, and the estimation of volatility.derivatives, arbitrage, price jumps,
We present an improved method for inference in linear regressions with overlapping observations. By aggregating the matrix of explanatory variables in a simple way, our method transforms the original regression into an equivalent representation in which the dependent variables are non-overlapping. This transformation removes that part of the autocorrelation in the error terms which is induced by the overlapping scheme.Our method can easily be applied within standard software packages since conventional inference procedures (OLS-, White-, Newey-West-standard errors) are asymptotically valid when applied to the transformed regression. Through Monte Carlo analysis we show that they perform better in finite samples than the methods applied to the original regression that are in common usage. We illustrate the significance of our method with two empirical applications.JEL classification: C20, G12
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