Risk-Neutral Valuation - Revision history

Dirkjan at 19:25, 27 August 2020

2020-08-27T19:25:53Z

Dirkjan: Replaced content with "Risk-Neutral Valuation Category:finance Category:M12 Category:Principles of Corporate Finance Category:Term"

2020-08-27T18:39:28Z

Replaced content with "Risk-Neutral Valuation Category:finance Category:M12 Category:Principles of Corporate Finance Category:Term"

Dirkjan: Created page with "In Principles of Corporate Finance the risk neutral valuation is calculated by assuming that investors are indifferent to risk and expect r..."

2020-08-25T07:41:26Z

Created page with "In Principles of Corporate Finance the risk neutral valuation is calculated by assuming that investors are indifferent to risk and expect r..."

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In [[Principles of Corporate Finance|Principles of Corporate Finance]] the risk neutral valuation is calculated by assuming that investors are indifferent to risk and expect return on stock to be equal to the risk-free rate of interest. Furthermore it assumed that stock have a certain downside potential <math>d</math> and and and upside potential <math>u</math>. There is a certain chance <math>p</math> that the stock will go up with percentage <math>u</math> and a chance of <math>1-p</math> that the stock will go down with percentage <math>d</math>. This gives:

<math>\text {Expected Return}</math> = <math>p \cdot u + (1-p) \cdot d = r</math>

This gives the general probability of rise of the stock:

<math>p</math> = <math>\frac{(1 + r) -d}{u - d}</math>

Valuing a call this way gives (<math>k</math> is the exercise price):

<math>\text{Expected value of a call}</math> = <math>\frac{p \cdot max(Su-k,0) + (1 - p) \cdot max(Sd-k,0)}{1 + r}</math>

Using the same example as in [[Replicating Portfolio|Replicating Portfolio]] we get:

<math>p</math> = <math>\frac{(0.025) - (-0.25)}{0.33 - (- 0.25)}</math> = <math>.471</math>

<math>\text{Expected value of a call}</math> = <math>\frac{0.471 \cdot max(106.67 - 80,0) + (1 - 0.471) \cdot max(60-80,0)}{1 + r}</math> = <math>12.26</math>

[[Category:finance]]

[[Category:M12]]

[[Category:Principles of Corporate Finance]]

[[Category:Term]]

← Older revision		Revision as of 18:39, 27 August 2020
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−	In [[Principles of Corporate Finance\|Principles of Corporate Finance]] the risk neutral valuation is calculated by assuming that investors are indifferent to risk and expect return on stock to be equal to the risk-free rate of interest. Furthermore it assumed that stock have a certain downside potential <math>d</math> and and and upside potential <math>u</math>. There is a certain chance <math>p</math> that the stock will go up with percentage <math>u</math> and a chance of <math>1-p</math> that the stock will go down with percentage <math>d</math>. This gives:	+	Risk-Neutral Valuation
−
−	~~<math>\text {Expected Return}</math> = <math>p \cdot u + (1-p) \cdot d = r</math>~~
−
−	~~This gives the general probability of rise of the stock:~~
−
−	~~<math>p</math> = <math>\frac{(1 + r) -d}{u - d}</math>~~
−
−	~~Valuing a call this way gives (<math>k</math> is the exercise price):~~
−
−	~~<math>\text{Expected value of a call}</math> = <math>\frac{p \cdot max(Su-k,0) + (1 - p) \cdot max(Sd-k,0)}{1 + r}</math>~~
−
−	~~Using the same example as in [[Replicating Portfolio\|Replicating Portfolio]] we get:~~
−
−	~~<math>p</math> = <math>\frac{(0.025) - (-0.25)}{0.33 - (- 0.25)}</math> = <math>.471</math>~~
−
−	~~<math>\text{Expected value of a call}</math> = <math>\frac{0.471 \cdot max(106.67 - 80,0) + (1 - 0.471) \cdot max(60-80,0)}{1 + r}</math> = <math>12.26</math>~~
−
	[[Category:finance]]		[[Category:finance]]

← Older revision		Revision as of 19:25, 27 August 2020
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−	~~Risk~~-~~Neutral Valuation~~	+	In [[Principles of Corporate Finance\|Principles of Corporate Finance]] the risk neutral valuation is calculated by assuming that investors are indifferent to risk and expect return on stock to be equal to the risk-free rate of interest. Furthermore it assumed that stock have a certain downside potential <math>d</math> and and and upside potential <math>u</math>. There is a certain chance <math>p</math> that the stock will go up with percentage <math>u</math> and a chance of <math>1-p</math> that the stock will go down with percentage <math>d</math>. This gives:
		+
		+	<math>\text {Expected Return}</math> = <math>p \cdot u + (1-p) \cdot d = r</math>
		+
		+	This gives the general probability of rise of the stock:
		+
		+	<math>p</math> = <math>\frac{(1 + r) -d}{u - d}</math>
		+
		+	Valuing a call this way gives (<math>k</math> is the exercise price):
		+
		+	<math>\text{Expected value of a call}</math> = <math>\frac{p \cdot max(Su-k,0) + (1 - p) \cdot max(Sd-k,0)}{1 + r}</math>
		+
		+	Using the same example as in [[Replicating Portfolio\|Replicating Portfolio]] we get:
		+
		+	<math>p</math> = <math>\frac{(0.025) - (-0.25)}{0.33 - (- 0.25)}</math> = <math>.471</math>
		+
		+	<math>\text{Expected value of a call}</math> = <math>\frac{0.471 \cdot max(106.67 - 80,0) + (1 - 0.471) \cdot max(60-80,0)}{1 + r}</math> = <math>12.26</math>
		+
	[[Category:finance]]		[[Category:finance]]