This paper introduces a method for constructing option hedging strategies in the presence of transaction costs. the approach begins with the prescription of a large, but tractable class of strategies. A variational problem is constructed in which the expected square replication error is minimized subject to a fixed initial portfolio value from among the class of strategies. the solution of this variational problem results in a replicating strategy which simulations show outperforms strategies previously considered. We illustrate this method in a particular class of strategies which contains Leland's discrete time replication scheme. We show that a strategy which uses varying time intervals between hedging can significantly reduce replication error for a given initial wealth. We will also construct and assess strategies obtained by optimizing a mean-variance criterion. This methodology extends to other optimization problems involving initial portfolio value and expected square replication error, as well as to other classes of strategies. Copyright 1996 Blackwell Publishers.

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We develop a probabilistic framework for joint simulation of short-term electricity generation from renewable assets. In this paper we describe a method for producing hourly day-ahead scenarios of generated power at grid-scale across hundreds of assets. These scenarios are conditional on specified forecasts and yield a full uncertainty quantification both at the marginal asset-level and across asset collections. Our simulation pipeline first applies asset calibration to normalize hourly, daily and seasonal generation profiles, and to Gaussianize the forecast-actuals distribution. We then develop a novel clustering approach to stably estimate the covariance matrix across assets; clustering is done hierarchically to achieve scalability. An extended case study using an ERCOT-like system with over 500 solar and wind farms is used for illustration.