New invention for the derivatives market - How to profit of it?

Q: Was (or is) this newly found flaw in the PUT pricing, the reason for many of the market crashes since 1973?
A: YES! Especially those market crashes since 1987.

Q: Would FairPut have prevented the above said market crashes?
A: IMO YES!
 
thecoder said:
lognormal is used for pricing the options (ie. calculating the premium), and normaldist is used for FairPUT computations. This is the correct method, as I first tried hard with the lognormal but failed b/c as soon as you add risk-free-rate and/or dividends then it doesn't work with lognormal... So, I'm convinced this method is the correct method.

And regarding vola smile etc.: they are IMO still there as the pricing is still done by BSM.
But I must admit I hadn't time to test especially this aspect deeper yet, but I'm confident...

And: the goal was to create a mirror image of CALL for the FairPUT. So, since it works, then it has to be correct, IMO :)
More...


First of all, your "FairPut" idea already exists. Traders already use the normal price distribution to price options for instruments that have unlimited downside as well as unlimited upside. Crude oil prices and futures spreads can go negative, and interest rate products (Treasuries, Bund,etc) have theoretically unlimited upside price potential due to negative interest rates. Puts and calls have equal payouts in these products, so your idea is nothing new. This options pricing model, the Bachelier model, has been around for awhile, so your idea is not original. Read about the Bachelier model vs the Black-Scholes model here:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2782719

And therein lies your problem, grasshopper...the biggest flaw to your argument and idea. If you assume a normal price distribution in your pricing model in order to get equal payout for your "Fair put" vs the call, you must assume the potential upside price appreciation equals the potential downside price depreciation for the stock or equity index. In order for the payout of the put and call to be equal, the stock or index must be able to move equally in each direction, i.e. the stock must be able to go down just as much as it can go up. Therefore, it is a well known fact and mathematically proven, that you must assume negative prices for the underlying instrument (stock, index, future, etc.) in order to use the normal price distribution, which you insist on using. Because stock prices have limited downside and cannot go below zero ($0), you cannot, are forbidden, and are completely in the wrong for using the normal price distribution to price your put options, i.e. You are modeling negative stock prices if you use a normal price distribution. Stocks can't go below $0, so you are stuck, and forced to use the lognormal price distribution to price your puts.

$100 Put: Max payout at expiration is $100
$100 Call: Max payout is unlimited

When assuming the lognormal price distribution for the underlying, a 1 standard deviation move higher will always exceed in payout (price terms) the same 1 standard deviation move lower. Therefore your put prices must always be less than the same strike call prices given the same z-score, and standard deviation move in the stock. As someone who writes code, you should at least have some grasp of freshman level statistics 101.
 
Read my lips: You are modeling negative stock prices if you use "normaldist for FairPUT computations."

Result: Your "Fair Puts" are going to be grossly overpriced with excessively high deltas.
 
VolSkewTrader said:
First of all, your "FairPut" idea already exists. Traders already use the normal price distribution to price options for instruments that have unlimited downside as well as unlimited upside. Crude oil prices and futures spreads can go negative, and interest rate products (Treasuries, Bund,etc) have theoretically unlimited upside price potential due to negative interest rates. Puts and calls have equal payouts in these products, so your idea is nothing new. This options pricing model, the Bachelier model, has been around for awhile, so your idea is not original. Read about the Bachelier model vs the Black-Scholes model here:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2782719

And therein lies your problem, grasshopper...the biggest flaw to your argument and idea. If you assume a normal price distribution in your pricing model in order to get equal payout for your "Fair put" vs the call, you must assume the potential upside price appreciation equals the potential downside price depreciation for the stock or equity index. In order for the payout of the put and call to be equal, the stock or index must be able to move equally in each direction, i.e. the stock must be able to go down just as much as it can go up. Therefore, it is a well known fact and mathematically proven, that you must assume negative prices for the underlying instrument (stock, index, future, etc.) in order to use the normal price distribution, which you insist on using. Because stock prices have limited downside and cannot go below zero ($0), you cannot, are forbidden, and are completely in the wrong for using the normal price distribution to price your put options, i.e. You are modeling negative stock prices if you use a normal price distribution. Stocks can't go below $0, so you are stuck, and forced to use the lognormal price distribution to price your puts.

$100 Put: Max payout at expiration is $100
$100 Call: Max payout is unlimited

When assuming the lognormal price distribution for the underlying, a 1 standard deviation move higher will always exceed in payout (price terms) the same 1 standard deviation move lower. Therefore your put prices must always be less than the same strike call prices given the same z-score, and standard deviation move in the stock. As someone who writes code, you should at least have some grasp of freshman level statistics 101.
More...

that’s a lot of words you wrote there, unfortunately it’s all wasted effort.
 
Lognormal distribution: The Black-Scholes-Merton model assumes that stock prices follow a lognormal distribution based on the principle that asset prices cannot take a negative value; they are bounded by zero.
 
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