Black-Scholes Option Pricing - Revision history

Dirkjan at 19:23, 27 August 2020

2020-08-27T19:23:30Z

Dirkjan: Replaced content with "Black-Scholes Option Pricing Category:finance Category:M13 Category:Term"

2020-08-27T18:38:34Z

Replaced content with "Black-Scholes Option Pricing Category:finance Category:M13 Category:Term"

Dirkjan: Created page with "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..."

2020-08-25T07:39:15Z

Created page with "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..."

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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.

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]]

[[Category:M13]]

[[Category:Term]]

← Older revision		Revision as of 18:38, 27 August 2020
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]]		[[Category:finance]]

← Older revision		Revision as of 19:23, 27 August 2020
Line 1:		Line 1:
−	~~Black~~-~~Scholes~~ Option ~~Pricing~~	+	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.
		+
		+	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]]		[[Category:finance]]