We introduce a new class of strategies for hedging derivative securities taking into account transaction costs, assuming lognormal continuous-time prices for the underlying asset. We do not assume that the payoff is convex as in Leland (J of Finance, 1985), or that the transaction costs are...

We present an algorithm for hedging option portfolios and custom-tailored derivative securities which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non-linear partial differential equation to evaluate worst-case volatility...

We construct a sequence of trinomial trees in which an asset's price becomes lognormally distributed with given drift mu and a volatility between given sigma_min and sigma_max as the time between trades approaches zero. In this simple model of an incomplete market, we show that, as the time...

Sufficient conditions for existence and a closed form probabilistic representation are obtained for solutions of nonlinear parabolic equations with gauge function term. In particular, the result applies to the generalized Leland equationwhere BSn is the n-dimensional Black-Scholes operator, Ai...

A framework for calibrating a pricing model to a prescribed set of options prices quoted in the market is presented. Our algorithm yields an arbitrage-free diffusion process that minimizes the Kullback-Leibler relative entropy distance to a prior diffusion. It consists in solving a constrained...

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Bid and ask sizes at the top of the order book provide information on short-term price moves. Drawing from classical descriptions of the order book in terms of queues and order-arrival rates (Smith et al., 2003), we consider a diffusion model for the evolution of the best bid/ask queues. We...