How do we know that the instantaneous rate of return on this option, $\gamma$ is negative?

I am self-studying models for financial economics and encountered the following problem:

I don't see how the author can conclude that $\gamma = -0.62$. Let's rearrange the second to last equation: $$\gamma - r = -4(0.19 - r)$$ as

$$r = \frac{\gamma + 0.76}{5}.$$

If $\gamma = 0.62$, then $r = 0.276.$

If $\gamma = -0.62$, then $r = 0.028$, as the author states.

So I don't see how the author can conclude $\gamma = -0.62$ when letting $\gamma = 0.62$ does not contradict that $r \geq 0$.

jeremy909

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asked Nov 15, 2016 at 15:00

user2521987

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$\begingroup$ $ 4*0.19 = 0.76 \neq 0.71$, and what is $\gamma$ ? $\endgroup$
– M. Jeunesse
Nov 16, 2016 at 9:36
$\begingroup$ You're correct. I edited the original post to reflect that. However, it still allows for $\gamma$ to be positive or negative. $\gamma$ is the instantaneous rate of return on the put option. $\endgroup$
– user2521987
Nov 16, 2016 at 14:21
1

$\begingroup$ It is very odd. I would have thought the condition should have been $r<\alpha$ i.e. $r<0.19$ not $r\ge 0$. In words: "the expected excess return on the stock is positive". $\endgroup$
– nbbo2
Nov 16, 2016 at 14:32
$\begingroup$ Can you provide the source of this problem? $\endgroup$
– Stefan Voigt
Nov 25, 2016 at 10:55
$\begingroup$ Sure, it's from "Financial Economics" by Abraham Weishaus (It's a study manual for the actuarial exam "Models for Financial Economics") $\endgroup$
– user2521987
Nov 25, 2016 at 16:16

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