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Back to the Future

其他書名	Comparing Forward and Backward Differentiation for Forward Sensitivities in Monte-Carlo Simulations
出版	SSRN, 2018
URL	http://books.google.com.hk/books?id=tu_6zgEACAAJ&hl=&source=gbs_api

註釋We derive representations for forward sensitivities (also known as future sensitivities) in a Monte-Carlo simulation suitable for backward and forward differentiation. We compare the performance of the two approaches.The calculation of all forward sensitivities of a Monte-Carlo simulation with n paths, m time-steps and r risk factors requires in forward mode r valuations ad r×m conditional expectation (given that the value process is Markovian), and in backward mode 1 valuation and m conditional expectation.There is no additional scaling in the number of path n.