Geodesic
Lower and upper bounds for prices of Asian-type options
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 234-241.

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In the context of dealing with financial risk management problems, it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and lower bounds for Asian-type options is proposed in this paper. The bounds obtained are applicable to the continuous- and discrete-time frameworks for the case of time-dependent interest rates. Numerical examples are provided to illustrate the accuracy of the bounds. 
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A. A. Novikov; N. E. Kordzahia. Lower and upper bounds for prices of Asian-type options. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 234-241. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a12/

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