Difference between revisions of "Black-Scholes Option Pricing"

Revision as of 18:38, 27 August 2020

Black-Scholes Option Pricing

@@ Line 1: / Line 1: @@
-The Black–Scholes model or Black–Scholes-Merton is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European-style options. The formula led to a boom in options trading and the creation of the Chicago Board Options Exchange. lt is widely used by options market participants.
+Black-Scholes Option Pricing
-The black scholes option pricing model uses the following variables:
-{| class="wikitable"
-!Variable
-!Option
-|-
-|'''<math>X</math>'''
-|Exercise price
-|-
-|<math>S</math>
-|Stock price
-|-
-|<math>t</math>
-|Time to experation
-|-
-|<math>\sigma ^2</math>
-|Variance of returns on stock
-|-
-|<math>r</math>
-|[[Risk free rate of return|Risk free rate of return]]
-|-
-|}
-The value of a call option for a non-dividend paying underlying stock in terms of the Black–Scholes parameters is:
-<math>C(S,t)</math> = <math>N(d_{1})~S-N(d_{2})~K e^{-r(T-t)}\,</math>
-with
-<math>d_{1}</math>=<math>\frac{\ln(\frac{S}{K})+(r+\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}}</math>
-<math>d_{2}</math>=<math>\frac{\ln(\frac{S}{K})+(r-\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}} = d_{1}-\sigma\sqrt{T-t}</math>
 [[Category:finance]]