Timeline for Notion of risk-less portfolio in derivation of Black-Scholes
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2017 at 16:25 | history | tweeted | twitter.com/StackQuant/status/834438964354416640 | ||
| Feb 21, 2017 at 22:37 | vote | accept | Handschuh | ||
| Feb 21, 2017 at 15:54 | answer | added | Gordon | timeline score: 4 | |
| Feb 21, 2017 at 15:32 | comment | added | Handschuh | @Gordon Many thanks for your comments (much appreciated, though I can not upvote them due to lack of reputation?)! I edited my original post accordingly. Quite an upleasant suprise that there are mistakes in the literature on such a basic topic... Though I'm still wondering why vanishing of the $dW_t$-term equals risk-freeness. | |
| Feb 21, 2017 at 15:15 | history | edited | Handschuh | CC BY-SA 3.0 |
added 552 characters in body
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| Feb 21, 2017 at 14:32 | comment | added | Gordon | Should be $V_t+\Delta S_t= -Ke^{-r(T-t)}N(d_2)$. | |
| Feb 21, 2017 at 14:23 | comment | added | Gordon | @LocalVolatility and Hanschuh, this is a common mis-understanding even in John Hull's book. For a vanilla European call option $V_t + \Delta S_t= Ke^{-r(T-t)}N(d_2)$, which is not risk-free.Yes, locally risk free implies that the dW terms goes to zero. | |
| Feb 21, 2017 at 14:21 | comment | added | Handschuh | @Gordon: In your linked comment the assumption that the portfolio is free of risk seems to imply that the $dW_t$-term in $X_t$ vanishes as well. Isn't that the same kind of argument? Though the self financing aspect indeed seems fishy. Thank you guys for your comments btw! | |
| Feb 21, 2017 at 14:18 | comment | added | Handschuh | @dbluesk: I agree that this equation is deterministic. But if I understand correctly it should be a consequence of the riskfreeness (and the no arbitrage assumption). | |
| Feb 21, 2017 at 14:10 | comment | added | LocalVolatility | @Gordon - While I agree with $P_t$ not being self-financing, it surprises me that you say it is not locally risk-free? | |
| Feb 21, 2017 at 13:46 | comment | added | Gordon | The portfolio $P_t=V_t+\Delta S_t$ is neither self-financing nor (locally) risk free; see discussion here. | |
| Feb 21, 2017 at 12:07 | comment | added | dbluesk | But your integral $dPt=rP_td_t$ is deterministic, there is no Wiener process there. That's why it's risk-free. | |
| Feb 21, 2017 at 12:06 | review | First posts | |||
| Feb 21, 2017 at 12:30 | |||||
| Feb 21, 2017 at 12:01 | history | asked | Handschuh | CC BY-SA 3.0 |