
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
37th Annual Symposium on Foundations of Computer Science (FOCS '96)
Approximate option pricing
Burlington, VT
October 14October 16
ISBN: 0818675942
ASCII Text  x  
P. Chalasani, S. Jha, I. Saias, "Approximate option pricing," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 244, 37th Annual Symposium on Foundations of Computer Science (FOCS '96), 1996.  
BibTex  x  
@article{ 10.1109/SFCS.1996.548483, author = {P. Chalasani and S. Jha and I. Saias}, title = {Approximate option pricing}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1996}, isbn = {0818675942}, pages = {244}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1996.548483}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Approximate option pricing SN  0818675942 SP EP A1  P. Chalasani, A1  S. Jha, A1  I. Saias, PY  1996 KW  Monte Carlo methods; approximate option pricing; world financial markets; computational problem; binomial pricing model; stock price; random walk; pathdependent options; #P hard; polynomial time; deterministic polynomialtime approximate algorithms; perpetual American put option; Monte Carlo methods; error bounds; error analysis; random walks VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
As increasingly large volumes of sophisticated options 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 we show that pricing an arbitrary pathdependent option is #P hard. We show that certain types of pathdependent options can be valued exactly in polynomial time. Asian options are pathdependent options that are particularly hard to price, and for these we design deterministic polynomialtime approximate algorithms. We 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, our algorithms have guaranteed error bounds that are polynomially small (and in some cases exponentially small) in the maturity n. For the error analysis we derive largedeviation results for random walks that may be of independent interest.
Index Terms:
Monte Carlo methods; approximate option pricing; world financial markets; computational problem; binomial pricing model; stock price; random walk; pathdependent options; #P hard; polynomial time; deterministic polynomialtime approximate algorithms; perpetual American put option; Monte Carlo methods; error bounds; error analysis; random walks
Citation:
P. Chalasani, S. Jha, I. Saias, "Approximate option pricing," focs, pp.244, 37th Annual Symposium on Foundations of Computer Science (FOCS '96), 1996
Usage of this product signifies your acceptance of the Terms of Use.