Editing Binomial options pricing model (section)

{{short description|Numerical method for the valuation of financial options}}
In [[finance]], the '''binomial options pricing model''' ('''BOPM''') provides a generalizable [[Numerical analysis|numerical method]] for the valuation of [[Option (finance)|options]]. Essentially, the model uses a "discrete-time" ([[Lattice model (finance)|lattice based]]) model of the varying price over time of the [[underlying]] financial instrument, addressing cases where the [[Closed-form expression|closed-form]] [[Black–Scholes formula]] is wanting, which in general does not exist for the '''BOPM'''.<ref>{{Cite journal |last=Georgiadis |first=Evangelos |title=Binomial options pricing has no closed-form solution |journal=Algorithmic Finance |date=2011 |volume=1 |issue=1 |pages=11–18 |doi=10.3233/AF-2011-003 |publisher=IOS Press}}</ref>

The binomial model was first proposed by [[William F. Sharpe|William Sharpe]] in the 1978 edition of ''Investments'' ({{ISBN|013504605X}}),<ref>[https://www.nobelprize.org/prizes/economic-sciences/1990/sharpe/biographical/ William F. Sharpe, Biographical], nobelprize.org</ref> and formalized by [[John Carrington Cox|Cox]], [[Stephen Ross (economist)|Ross]] and [[Mark Rubinstein|Rubinstein]] in 1979<ref>{{Cite journal |last1=Cox |first1=J. C. |authorlink1=John Carrington Cox |last2=Ross |first2=S. A. |authorlink2=Stephen Ross (economist)|last3=Rubinstein |first3=M. |authorlink3=Mark Rubinstein|doi=10.1016/0304-405X(79)90015-1 |title=Option pricing: A simplified approach |journal=[[Journal of Financial Economics]]|volume=7 |issue=3 |page=229 |year=1979|citeseerx=10.1.1.379.7582 }}</ref> and by Rendleman and Bartter in that same year.<ref>Richard J. Rendleman, Jr. and Brit J. Bartter. 1979. "Two-State Option Pricing". ''[[Journal of Finance]]'' 24: 1093-1110.  {{doi|10.2307/2327237}}</ref>

For binomial trees as applied to [[fixed income]] and [[interest rate derivatives]] see {{section link|Lattice model (finance) #Interest rate derivatives}}.