Anthony Neuberger

Option Prices, Implied Price Processes, and Stochastic Volatility

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.

Robust Bounds for Forward Start Options

We consider the problem of finding a model‐free upper bound on the price of a forward start straddle with payoff . The bound depends on the prices of vanilla call and put options with maturities and , but does not rely on any modeling assumptions concerning the dynamics of the underlying. The bound can be enforced by a super‐replicating strategy involving puts, calls, and a forward transaction. We find an upper bound, and a model which is consistent with and vanilla option prices for which the model‐based price of the straddle is equal to the upper bound. This proves that the bound is best possible. For lognormal marginals we show that the upper bound is at most 30% higher than the Black–Scholes price. The problem can be recast as finding the solution to a Skorokhod embedding problem with nontrivial initial law so as to maximize .

Improved Inference in Regression with Overlapping Observations

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 it performs 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 three empirical applications.

An empirical examination of market maker profits on the London stock exchange

This article uses transaction data to analyze the impact of asymmetric information and market marker risk aversion on the size of market maker profits. The observed bid-ask spread across the 14 stocks in the sample lies in the range of 1–5%. In the absence of asymmetric information and risk aversion, market makers would expect to receive half the spread on average as profit. In fact, their profit is less than half of this for all shares in the sample, and in half the stocks it is actually negative. A methodology is developed to identify separately the impact of information effects and risk aversion, but the results are inconclusive.

Improved inference and estimation in regression with overlapping observations

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 it performs 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 three empirical applications.

Arbitrage pricing with incomplete markets

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 options 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 options 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.

How Large are the Benefits from Using Options

The paper explores the economic value of being able to span market outcomes through the use of options. We model an economy with a single risky asset. Consumption takes place at one date, corresponding to the horizon of all investors. Options on the consumption good are not redundant securities in the economy because volatility is uncertain. The model enables us to examine the benefits to investors of using options to optimize their investments. Within this model, the gains from the use of options appear to be relatively minor.

Model uncertainty and the pricing of American options

The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when we do not impose a model, but rather consider the class of all models which are consistent with a family of European call prices. The bound is enforced by a hedging strategy involving these call options which is robust to model error.

Gold Coins in a Fiat Currency

We investigate the feasibility of minting gold coins with a face value in excess of their bullion value, to circulate as currency alongside paper money. The problem is modelled in a partial equilibrium setting where individuals hold money because they face unpredictable liquidity shocks. Gold coins have a positive expected return. They are less costly to hold than money and are used to meet large, infrequent shocks. An issue of gold coins increases total money demand. Depending on the nature of the liquidity shocks, the seignorage gains to Government from the increase in money holdings may exceed the cost of the gold used in the coins.

The Skewness of the Stock Market at Long Horizons

Higher moments of long-horizon returns are important for asset pricing but are hard to measure accurately using standard techniques. We provide theory showing that short-horizon (e.g. daily) returns can be used to construct precise estimates of long- horizon (e.g. annual) moments without making strong assumptions about the data generating process. Skewness comprises two components: skewness of short- horizon returns and a leverage effect, i.e. covariance between variance and lagged returns. We provide similar results for kurtosis. An application to US stock-index returns shows that skew is large and negative and attenuates only slowly as one moves from monthly to multi-year horizons.