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In the world of increasing price volatility, it is more important than ever to understand how to manage the price risk. The paper deals with the price risk management issues associated with commoditie...
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatilit...
We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first cent...
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Mo...
We answer this question bycomparing te risk-neutral densityestimated in complete markets from cross-section of S&P 500 option prices to the risk-neutral densityinferred from the time series densityof ...

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