Approximate option pricing
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 nperiod option on a stock is the expected timediscounted value of the future cash flow on an nperiod stock price path. Pathdependent 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 pathdependent option is {number_sign}P hard. They show that certain types f pathdependent options can be valued exactly in polynomial time. Asian options are pathdependent options that are particularly hard to price, and for these they design deterministic polynomialtime 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 nperiod 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 largedeviation results for random walks that may be of independent interest.
Year of publication: 
20091110


Authors:  Chalasani, P. ; Saias, I. ; Jha, S. 
Subject:  mathematics, computers, information science, management, law, miscellaneous  INVESTMENT  PRICES  INDUSTRY  MARKET  FORECASTING  CAPITAL  TRADE  GLOBAL ASPECTS  RESOURCES 
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