Timeline for Calculating the annual return on an option using a replicating porfolio
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 17, 2016 at 0:45 | history | bounty awarded | user2521987 | ||
| Sep 17, 2016 at 0:45 | vote | accept | user2521987 | ||
| Sep 16, 2016 at 15:17 | comment | added | LocalVolatility | You are right - my mistake. But at least now I finally spotted what went wrong in the first place. You have the correct formula for $\beta$ but forget to apply discounting when computing the value - i.e. you don't take into account the $e^{-r h}$ term. | |
| Sep 16, 2016 at 15:09 | comment | added | user2521987 | Using the two equations, I derived the formula for $\beta$ myself and arrived at exactly what the author has. The original post has been updated with my derivation. | |
| Sep 16, 2016 at 7:58 | comment | added | LocalVolatility | So now that you have two equations in two unkown, why don't YOU solve for $\beta$ yourself? If you do that you'll find that the formula that the textbook gives is wrong. | |
| Sep 16, 2016 at 7:38 | history | edited | LocalVolatility | CC BY-SA 3.0 | There was a bracket missing in the formula for beta. Added the dividend yield. |
| Sep 16, 2016 at 0:56 | comment | added | user2521987 | I'm certain it applies here because it follows the same "chain of reasoning" as your solution. This is just an explicit formula for $\beta$ that's NOT in terms of $\Delta$, as your formula is. | |
| Sep 16, 2016 at 0:47 | comment | added | user2521987 | The value of the replicating formula at time $h$, with stock price $S_h$, is $\Delta S_h + e^{rh}\beta$. At the prices $S_h = S_d$ and $S_h = S_u$, a replicating portfolio must satisfy: $\Delta \cdot S_d \cdot e^{\delta h} + (\beta \cdot e^{rh}) = P_d$ and $\Delta \cdot S_u \cdot e^{\delta h} + (\beta \cdot e^{rh}) = P_u$. The two unknowns $\Delta$ and $\beta$ allow us to solve for $$\beta = e^{-rh} \cdot \frac{u P_d - d P_u}{u - d}.$$ | |
| Sep 15, 2016 at 16:38 | comment | added | LocalVolatility | Do you understand how the textbook derived it? Is it in a different context / sure it applies here? Don't just take "formulas from the textbook" for granted. | |
| Sep 15, 2016 at 15:00 | comment | added | LocalVolatility | I showed you how to obtain the correct expression for $\beta$ and your formula for it looks different. So the question is not really why your formula doesn't apply but rather how you obtained it since it seems wrong. | |
| Sep 15, 2016 at 14:58 | comment | added | user2521987 | I understand your solution and why it provides the correct $\beta$. One thing that I still don't understand is why my formula, $$\beta = \frac{uP_d - dP_u}{u - d}e^{-rh}$$ does not apply here and give the same $\beta$ that you calculated. That formula is what the textbook provided. | |
| Sep 13, 2016 at 22:56 | history | answered | LocalVolatility | CC BY-SA 3.0 |