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2014•Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its ApplicationsOpen access

Discrete Stochastic Calculus and Its Application to Pricing a Certain Type of Lookback Options

Takahiko Fujita, Mizuki Suga

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Abstract

In this paper, first as a basic formula for the discrete stochastic calculus , we give the multidimensional version of the discrete Itˆo formula. Then we price a certain type of lookback options in the discrete Black Sholes Model and find the discrete hedging strategy of these exotic options. We note that these results are concrete example of discrete Kennedy martingales.

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In this paper, first as a basic formula for the discrete stochastic calculus , we give the multidimensional version of the discrete Itˆo formula. Then we price a certain type of lookback options in the discrete Black Sholes Model and find the discrete hedging strategy of these exotic options. We note that these results are concrete example of discrete Kennedy martingales.

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In this paper, first as a basic formula for the discrete stochastic calculus , we give the multidimensional version of the discrete Itˆo formula. Then we price a certain type of lookback options in the discrete Black Sholes Model and find the discrete hedging strategy of these exotic options. We note that these results are concrete example of discrete Kennedy martingales.

Key concepts: Type (biology), Discrete time and continuous time, Mathematics, Applied mathematics, Mathematical economics, Calculus (dental), Discrete modelling, Discrete-time stochastic process

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