Editing Black–Scholes model (section)

====Derivations====
{{See also|Martingale pricing}}
A standard derivation for solving the Black–Scholes PDE is given in the article [[Black–Scholes equation]].

The [[Feynman–Kac formula]] says that the solution to this type of PDE, when discounted appropriately, is actually a [[martingale (probability theory)|martingale]]. Thus the option price is the expected value of the discounted payoff of the option. Computing the option price via this expectation is the [[risk neutrality]] approach and can be done without knowledge of PDEs.<ref name="Nielsen">{{cite web |first= Lars Tyge |last= Nielsen | year=1993 | url= http://www.ltnielsen.com/wp-content/uploads/Understanding.pdf | title = Understanding ''N''(''d''<sub>1</sub>) and ''N''(''d''<sub>2</sub>): Risk-Adjusted Probabilities in the Black–Scholes Model |website=LT Nielsen}}</ref> Note the [[expected value|expectation]] of the option payoff is not done under the real world [[probability measure]], but an artificial [[risk-neutral measure]], which differs from the real world measure. For the underlying logic see section [[Rational pricing#Risk neutral valuation|"risk neutral valuation"]] under [[Rational pricing]] as well as section [[Mathematical finance#Derivatives pricing: the Q world|"Derivatives pricing: the Q world]]" under [[Mathematical finance]]; for details, once again, see [[John C. Hull (economist)|Hull]].<ref name="Hull">{{Cite book|last=Hull |first=John C. |year=2008| edition=7th |title=Options, Futures and Other Derivatives |publisher=[[Prentice Hall]] |isbn=978-0-13-505283-9}}</ref>{{rp|307–309}}