Timeline for Why discounted derivative price is a martingale?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2017 at 0:38 | comment | added | Mark Joshi | i have clarified. | |
| Jun 17, 2017 at 0:37 | history | edited | Mark Joshi | CC BY-SA 3.0 |
deleted 23 characters in body
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| Jun 16, 2017 at 10:28 | comment | added | JejeBelfort | @DaneelOlivaw Thanks, but it seems not everyone agrees as my edit to the post was reverted... | |
| Jun 16, 2017 at 10:02 | comment | added | Daneel Olivaw | I do agree with @JejeBelfort, the first part of the answer is misleading, specially because just below it is mathematically explained why the derivative price process is a martingale. | |
| Jun 16, 2017 at 9:35 | comment | added | JejeBelfort | @Mark Joshi Agreed with the answer. However, you state that $D_t$ is a martingale by decree and the line below you say that $D_t$ is a martingale by the tower law. It is either one or the other, not both. | |
| Jun 16, 2017 at 2:50 | comment | added | Alex C | Suppose prices are equal to expectation under some measure: $P_{t0}=E_{t0}[g(S_T)]$, $P_{t1}=E_{t1}[g(S_T)]$, etc. What can we say about the evolution of prices in this setup? Let us compute $E_{t0}[P_{t1}]=E_{t0}[E_{t1}[g(S_T)]]=E_{t0}[g(S_T)]=P_{t0}$ which shows that P is a Martingale. QED. Tedious perhaps but explicitly shows how the Tower Property of Expectation is used (to eliminate nested exectations). | |
| S Jun 16, 2017 at 0:22 | history | rollback | Mark Joshi |
Rollback to Revision 1 - Edit approval overridden by post owner or moderator
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| Jun 15, 2017 at 12:34 | history | suggested | JejeBelfort | CC BY-SA 3.0 |
This is the definition of the martingale, and this does not come from the tower law.
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| Jun 15, 2017 at 9:11 | review | Suggested edits | |||
| S Jun 16, 2017 at 0:22 | |||||
| Jun 15, 2017 at 0:25 | history | answered | Mark Joshi | CC BY-SA 3.0 |