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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 |
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| − | <math>\text {Expected Return}</math> = <math>p \cdot u + (1-p) \cdot d = r</math>
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| − | This gives the general probability of rise of the stock:
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| − | <math>p</math> = <math>\frac{(1 + r) -d}{u - d}</math>
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| − | Valuing a call this way gives (<math>k</math> is the exercise price):
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| − | <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>
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| − | Using the same example as in [[Replicating Portfolio|Replicating Portfolio]] we get:
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| − | <math>p</math> = <math>\frac{(0.025) - (-0.25)}{0.33 - (- 0.25)}</math> = <math>.471</math>
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| − | <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>
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| | [[Category:finance]] | | [[Category:finance]] |
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