Options arbitrage in imperfect markets

Article Abstract:

Option valuation models are based on an arbitrage strategy - hedging the option against the underlying asset and rebalancing continuously until expiration - that is only possible in a frictionless market. This paper simulates the impact of market imperfections and other problems with the "standard" arbitrage trade, including uncertain volatility, transactions costs, indivisibilities, and rebalancing only at discrete intervals. We find that, in an actual market such as that for stock index options, the standard arbitrage is exposed to such large risk and transaction costs that it can only establish very wide bounds on equilibrium options prices. This has important implication for price determinations in options markets, as well as for testing of valuation models. (Reprinted by permission of the publisher.)

Hedging (Finance), Arbitrage

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Corrections for trading frictions in multivariate returns

Article Abstract:

When observed stock returns are obtained from trades subject to friction, it is known that an individual stock's beta and covariance are measured with error. Univariate models of additive error adjustment are available and are often applied simultaneously to more than one stock. Unfortunately, these multivariate adjustments produce non-positive definite covariance and correlation matrices, unless the return sample sizes are very large. To prevent this, restrictions on the adjustment matrix are developed and a correction is proposed, which dominates the uncorrected estimator. The estimators are illustrated with asset opportunity set estimates where daily returns have trading frictions. (Reprinted by permission of the publisher.)

Evaluation, Finance, Stocks, Multivariate analysis, Eigenvalues, Analysis of covariance, Covariance analysis

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Market risk and model risk for a financial institution writing options

Article Abstract:

Derivative valuation and risk management involve heavy use of quantitative models. To develop a quantitative assessment of model risk as it affects the basic option writing strategy that might be followed by a financial institution, we conduct an empirical simulation, with and without hedging, using data from 1976 to 1996. Results indicate that imperfect models and inaccurate volatility forecasts create sizable risk exposure for option writers. We consider to what extent the damage due to model risk can be limited by pricing options using a higher volatility than the best estimate from historical data. (Reprinted by permission of the publisher.)

Financial Services, Finance and Insurance, Models, Economic aspects, Risk (Economics), Financial institutions

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