In [[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 $\Large d$ and and and upside potential $\Large u$. There is a certain chance $\Large p$ that the stock will go up with percentage $\Large u$ and a chance of $\Large 1-p$ that the stock will go down with percentage $\Large d$. This gives:

$\Large \text {Expected Return}$ = $\Large p \cdot u + (1-p) \cdot d = r$

This gives the general probability of rise of the stock:

$\Large p$ = $\LARGE \frac{(1 + r) -d}{u - d}$

Valuing a call this way gives ($\Large k$ is the exercise price):

$\Large \text{Expected value of a call}$ = $\LARGE \frac{p \cdot max(Su-k,0) + (1 - p) \cdot max(Sd-k,0)}{1 + r}$

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

$\Large p$ = $\LARGE \frac{(0.025) - (-0.25)}{0.33 - (- 0.25)}$ = $\Large .471$

$\Large \text{Expected value of a call}$ = $\LARGE \frac{0.471 \cdot max(106.67 - 80,0) + (1 - 0.471) \cdot max(60-80,0)}{1 + r}$ = $\Large 12.26$

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finance_public
created
Sat, 14 Jan 2012 20:50:10 GMT
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dirkjan
modified
Sat, 14 Jan 2012 20:50:10 GMT
modifier
dirkjan
tags
M12
Principles of Corporate Finance
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creator
dirkjan