We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a...

We study model-driven statistical arbitrage in US equities. Trading signals are generated in two ways: using Principal Component Analysis (PCA) or regressing stock returns on sector Exchange Traded Funds (ETFs). In both cases, the idiosyncratic returns are modelled as mean-reverting processes,...

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 establish new optimal bounds on the Ohmic conductivity tensor of a single-phase polycrystal through a comparison principle which uses a null-Lagrangian. A similar technique is used to obtain a sharp inequality correlating the conductivities of a two-phase composite material and the material...

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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...

Extensions to the Black-Scholes model have been suggested recently that permit one to calculate worst-case prices for a portfolio of vanilla options or for exotic options when no a priori distribution for the forward volatility is known. The Uncertain Volatility Model (UVM) by Avellaneda and...

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...