Timeline for Equal prices for call and put options with symmetric strikes around contemporaneous price?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2020 at 9:07 | vote | accept | elemenope | ||
| Apr 29, 2020 at 6:58 | comment | added | Kermittfrog | The distribution is not symmetrical as it is lognormal. You may just want to give it a try and see that these statements can only be approximately true. | |
| Apr 28, 2020 at 15:29 | comment | added | elemenope | So if I use the forward price as "center" with strike F(1+x) for calls and F/(1+x) for puts, shouldn't they be priced equally? I get your point of more upward potential for calls. But I don't get how Bates gets to this result? If I calculate F as S_t * exp(r * (T-t)) I still get a higher value for calls, as you suggested. It would make sense if Bates was referring to equal option prices at expiry, but he is referring to prices at t. | |
| Apr 28, 2020 at 15:23 | comment | added | elemenope | Thanks for your answer, really intuitive and helpful! I did some research and found the paper "The Crash of '87: Was It Expected" by Bates (1991). He writes: "If the strike prices of the put and call are spaced symmetrically around the forward price, the symmetry or asymmetry of the risk-neutral distribution will be directly reflected in the relative prices of these out-of-the-money calls and puts. Symmetric risk-neutral distributions imply equal prices for OTM European calls and puts; skewed distributions create systematic divergences." | |
| Apr 28, 2020 at 8:03 | history | edited | Kermittfrog | CC BY-SA 4.0 |
added 31 characters in body
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| Apr 28, 2020 at 7:30 | history | answered | Kermittfrog | CC BY-SA 4.0 |