Timeline for How does volatility affect the price of binary options?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 10, 2013 at 1:02 | comment | added | Vince | phew, thanks Brian. as a former eq deriv trader myself, now i see what you mean -- should have interpreted where you were aiming. | |
| May 10, 2013 at 0:35 | comment | added | Brian B | @Veeken: thank you for pointing out the error. By "flat skew in the options-trading sense" I mean that an options trader would perceive option implied vols to be the same across strikes if the option prices were generated by the BS model. In the sense of distributional moments, you are quite correct that the 3rd moment (skew) is negative for this model. It is an unfortunate collision of terminology between traders and mathematicians that the same word is used both ways. | |
| May 10, 2013 at 0:32 | history | edited | Brian B | CC BY-SA 3.0 |
fixed maximum, added picture
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| May 8, 2013 at 20:48 | comment | added | Vince | i don't understand what you mean by 'flat' skew in the BS model. As soon as $\sigma>0$, there is skew in the BS model. Allow me to cast the first integral above into BS terms: BinaryCashCall = $e^{-rT}*N(d_2)$ with $d_1, d_2$ given here:en.wikipedia.org/wiki/…. as $\sigma \to \infty$, $d_1 \to \infty$ while $d_2 \to -\infty$. This makes $N(d_2) \to 0$, and thus makes the binary call price 0. By obvious symmetry, the binary put goes to 1 in the event. All this is in the BS world. Thanks for your time... | |
| May 8, 2013 at 19:10 | comment | added | Brian B | @Veeken: Once can construct models where put payoffs go to 1, but they are not the Black-Scholes model, which has "flat" skew in the options-trading sense. | |
| May 7, 2013 at 20:43 | comment | added | Vince | Brian, isn't it the other way around? as vol goes to $\infinity$ cash binaries with put payoffs go to 1 while those with call payoffs go to 0, for any strike K. this is because of the negative skew, which makes the left side of the distribution far more 'heavy' than the right side as vol goes to $\infinity$. see here: en.wikipedia.org/wiki/File:Some_log-normal_distributions.svg | |
| May 7, 2013 at 13:44 | history | edited | Brian B | CC BY-SA 3.0 |
added 2 characters in body
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| Oct 13, 2011 at 12:43 | history | edited | Brian B | CC BY-SA 3.0 |
center eqns change PDF nad fix increasing to decreasing
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| Oct 7, 2011 at 1:05 | vote | accept | CQM | ||
| Sep 29, 2011 at 13:12 | history | edited | Brian B | CC BY-SA 3.0 |
out of money puts optimal vol
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| Sep 29, 2011 at 12:34 | history | answered | Brian B | CC BY-SA 3.0 |
