"DumbPut" trading at a huge premium over "Fair Put".
New invention for the derivatives market - How to profit of it?
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"DumbPut" trading at a huge premium over "Fair Put".
Hehehe....
The FairPut can't have a price of 11.92 (same as the ordinary put) because for every stock price below the strike at expiration, it pays out more than the ordinary put. Otherwise you'd have an arb -- buy the fairput, sell the ordinary put and you'd never lose. Integrating the payout times the termianal [lognormal] distribution centered around 100 (the ATM[F]), gives a fair price of your FairPut with the inputs above of $17.75. That is about 50% higher than the ordinary put price of $11.92. Your pricer appears to be way off. And that $17.75 is under the lognormal assumption. In the real world, where there is a small but non-zero chance of the stock going to $0, the expectation (fair price) is infinity $. This is because the payoff at stock price = $0 is $infinity, and that swamps everything else.
Delta is not a number you just make up, it is the derivative of the option price with respect to the stock price. The delta (by finite differences) of the FairPut with inputs above is about -0.74. As was pointed out by several posters, the FairPut is impossible to replicate or fully hedge due to the lottery-like payouts in the left tail (and the payout convex in terminal stock price adds to the difficulty). But at least with accurate greeks you could try dynamically hedging it.
You really need to stop here and learn the very basics of ootions.
@Kevin Schmit, thx for the analysis, I'll respond later after testing your objection in practice.
But just a minor correction: I meant: since FairPut is based on CALL, the FairPut premium is always the same as that of CALL. The Greeks are of course the inverse of CALL Greeks, for example FairPut.Delta = Call.Delta - 1, similar for the MyDelta (aka FairDelta), and some of the other Greeks are different than that of CALL, as well.
Update:
How does your arb-analysis change if vanilla PUT is removed from the list?
I mean: if there are just CALL and FairPUT possible to trade?
Update2:
I did a quick analysis of your arb-objection: the result is 0, so there is no arb, IMO:
For example for expiring at spot 120:
long FairPut: Payout=0.0 Profit=-11.923538(-100.00%)
short Put: Payout=0.0 (ie. the initial credit 11.923538 - 0.0 = 11.923538) Profit=11.923538(100.00%)
But in sum it's just zero-sum, ie. no arbitrage.
But just a minor correction: I meant: since FairPut is based on CALL, the FairPut premium is always the same as that of CALL. The Greeks are of course the inverse of CALL Greeks, for example FairPut.Delta = Call.Delta - 1, similar for the MyDelta (aka FairDelta), and some of the other Greeks are different than that of CALL, as well.
Update:
How does your arb-analysis change if vanilla PUT is removed from the list?
I mean: if there are just CALL and FairPUT possible to trade?
Update2:
I did a quick analysis of your arb-objection: the result is 0, so there is no arb, IMO:
For example for expiring at spot 120:
long FairPut: Payout=0.0 Profit=-11.923538(-100.00%)
short Put: Payout=0.0 (ie. the initial credit 11.923538 - 0.0 = 11.923538) Profit=11.923538(100.00%)
But in sum it's just zero-sum, ie. no arbitrage.
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Update3:
when testing the above scenario for spot < K at expiration (for example spot 83.333333), then arb seems indeed possible:
A long FairPut plus a short Put creates arbitrage when spot later becomes < K (actually even at < S0),
So, then the conclusion is: FairPut cannot be used with Put, ie. it works only if the market allows only CALL and FairPUT, but not PUT.
So, the vanilla PUT has to go to hell where it deservedly belongs to!
After all, FairPut was created in the first place because of the shortcomings of Put... Put must be banned from the markets!
when testing the above scenario for spot < K at expiration (for example spot 83.333333), then arb seems indeed possible:
A long FairPut plus a short Put creates arbitrage when spot later becomes < K (actually even at < S0),
So, then the conclusion is: FairPut cannot be used with Put, ie. it works only if the market allows only CALL and FairPUT, but not PUT.
So, the vanilla PUT has to go to hell where it deservedly belongs to!
After all, FairPut was created in the first place because of the shortcomings of Put... Put must be banned from the markets!
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Let's see it this way:
Say the CALL and PUT as we know and use today, exists since about 1973 when Black & Scholes published their paper.
For 47 years since then, the whole world is using the wrong PUT pricing!!!
IMO a shame for the collective human intellect!
It took a non-academic poor outsider guy (me! me!) to find that big flaw in the PUT pricing, and even find a replacement for it (FairPut).
These are the cruel facts, folks!
Say the CALL and PUT as we know and use today, exists since about 1973 when Black & Scholes published their paper.
For 47 years since then, the whole world is using the wrong PUT pricing!!!
IMO a shame for the collective human intellect!
It took a non-academic poor outsider guy (me! me!
) to find that big flaw in the PUT pricing, and even find a replacement for it (FairPut). These are the cruel facts, folks!
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Awaiting Dest's reply....Let's see it this way:
Say the CALL and PUT as we know and use today, exists since about 1973 when Black & Scholes published their paper.
For 47 years since then, the whole world is using the wrong PUT pricing!!!
IMO a shame for the collective human intellect!
It took a non-academic poor outsider guy (me! me!
These are the cruel facts, folks!