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Characterization of optimal stopping regions of American Asian and lookback options
 Mathematical Finance
, 2006
"... A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and ..."
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Cited by 9 (2 self)
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A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian options, we deduce the corresponding nesting relations between the exercise regions of these American options. We illustrate how some properties of the exercise regions of the American Asian options can be inferred from those of the American lookback options.
American Fractional Lookback Options: Valuation and Premium Decomposition
, 2007
"... This paper deals with valuation and premium decomposition of American floatingstrike lookback options written on dividendpaying assets, for which exact formulas are unknown except for the perpetual case. Via a PDE approach, we derive Laplace transforms of the values of lookback call and put options ..."
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This paper deals with valuation and premium decomposition of American floatingstrike lookback options written on dividendpaying assets, for which exact formulas are unknown except for the perpetual case. Via a PDE approach, we derive Laplace transforms of the values of lookback call and put options, which can be decomposed as the associated European values plus the early exercise premiums. Using Abelian theorems of Laplace transforms, we characterize asymptotic behaviors of the early exercise boundaries at a time to close to expiration and at infinite time to expiration. Based on the GaverStehfest inversion method combined with the Newton method, we develop a fast and accurate algorithm for computing both the option value and the early exercise boundary.
Right Type Departmental Bulletin Paper
"... Lookback options are pathdependent options whose payoff at (or prior to) expiry depends on the realized extremum of the underlying asset price attained over the options ’ lifetimes. Lookback options can be classified into two types: fixed strike and floating $st $ rike. Let $(S_{t})_{t\geq 0} $ be ..."
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Lookback options are pathdependent options whose payoff at (or prior to) expiry depends on the realized extremum of the underlying asset price attained over the options ’ lifetimes. Lookback options can be classified into two types: fixed strike and floating $st $ rike. Let $(S_{t})_{t\geq 0} $ be the price process of the underlying asset, and let $m_{t} = \min_{0\leq u\leq t}S_{u} $ and $M_{t} = \max_{0\leq u\leq t}S_{u} $. Assume that