Timeline for Effect of correlation on a best-of rainbow option
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2020 at 15:16 | comment | added | Oscar | Let us continue this discussion in chat. | |
| Jul 4, 2020 at 13:11 | comment | added | Oscar | Ah, I see. I think the formatting might've gotten screwed up looking at it on my phone, thank you. | |
| Jul 4, 2020 at 12:58 | comment | added | ir7 | X-K (it can be negative) is less than (X-K)^+, that's why it appears in the lower bound. Basically, you have to go through all cases (depending on the middle max choice): Y-K>X-K>0, Y-K>0>X-K, etc | |
| Jul 4, 2020 at 12:54 | comment | added | Oscar | Indeed, thank you I will give you a shout once I'm further along. Could you also give your first "sandwich" equation for best-of another look over? The left hand side and right hand side are the same apart from missing parenthesis, is that a typo? And should there be a + sign to indicate max(x-k,0) pay offs, or should it just be (X_T-K) like you wrote (so a forward contract payoff)? | |
| Jul 4, 2020 at 12:50 | comment | added | ir7 | In the end, you compare (for various inputs, like correlation): target product MC, proxy product MC and proxy product non-MC. | |
| Jul 4, 2020 at 12:49 | comment | added | Oscar | And here I thought I was gonna relax this weekend. You are pretty much right on the mark, I do have both Black Schooled and vanilla Monte Carlo functions with segregated payoff classes. The vanilla MC class gives the same price as the black schooles class, as does the rainbow class function for the best-of call in the case where there is only 1 asset (as it should). I have also checked that the normal variates I create for the simulation do indeed have the expected correlations from the covariance matrix, so I've ruled out some structural issues. I will implement outperformance and see. | |
| Jul 4, 2020 at 12:42 | comment | added | ir7 | Yes. Any related payoff for which you know the prices under a non-MC method is worth putting in to make sure there is no structural problem with your framework. If you used object oriented design, you might already have the payoff class already segregated from the actual simulation. Once you are confident the framework works well for payoffs I used, you can then move confidently to subtler ones. | |
| Jul 4, 2020 at 12:37 | comment | added | Oscar | Hey, thank you. In what I'm trying to model the worst-of option would pay the smallest increase rather than highest decline so I think your example is different from mine there. For your debugging advice, to clarify, you advice I price and compare: (vanilla call + outperformance_X-Y) ; (best-of call) ; (vanilla call + outperformance_Y-X) and compare for both analytical and MC valuations? Is that right? | |
| Jul 4, 2020 at 12:16 | comment | added | ir7 | @Oscar Added one more edit. Might help with your debugging. | |
| Jul 4, 2020 at 12:15 | history | edited | ir7 | CC BY-SA 4.0 |
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| Jul 4, 2020 at 12:02 | comment | added | ir7 | @Oscar Btw, you might want to inquire (maybe here on SE) if there is an analytic formula (even if just approximation) to implement and compare against your MC implementation (of course with standard assumptions like flat vols etc.). | |
| Jul 4, 2020 at 11:47 | history | edited | ir7 | CC BY-SA 4.0 |
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| Jul 4, 2020 at 11:47 | comment | added | ir7 | @Oscar I subtracted a strike everywhere to allow for negative payoffs. In the worst of option contract the investor receives the highest decline (as opposed to increase). In both cases they should benefit from low correlation. In practice, they use percentage returns (against respective original stock prices) in the payoffs. I made some edits. | |
| Jul 4, 2020 at 11:39 | history | edited | ir7 | CC BY-SA 4.0 |
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| Jul 4, 2020 at 6:19 | comment | added | Oscar | Is there a typo in your equation? The LHS and RHS are the same. I think I do see the intuition for the bets-of option still, but what about the worst-of? If you have 2 assets currently at-the-money and a correlation of -1, then wouldn't that mean your option will never have a positive payoff (since if one goes up the other goes down). Same situation for best-of will obviously be very much in your favor however since you're guaranteed a payoff, so how can both of them be sensitive to correlation in the same way? | |
| Jul 3, 2020 at 23:06 | history | answered | ir7 | CC BY-SA 4.0 |