Approximate option pricing

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As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on ... continued below

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18 p.

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Chalasani, P.; Saias, I. & Jha, S. April 8, 1996.

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Description

As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.

Physical Description

18 p.

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OSTI as TI96011264

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  • 37. annual symposium on foundations of computer science, Burlington, VT (United States), 13-16 Oct 1996

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  • Other: TI96011264
  • Report No.: LA-UR--96-1554
  • Report No.: CONF-961004--1
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/373883 | External Link
  • Office of Scientific & Technical Information Report Number: 373883
  • Archival Resource Key: ark:/67531/metadc687277

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Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • April 8, 1996

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • Feb. 25, 2016, 1:24 p.m.

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Chalasani, P.; Saias, I. & Jha, S. Approximate option pricing, report, April 8, 1996; New Mexico. (digital.library.unt.edu/ark:/67531/metadc687277/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.