Continous hedging as a rachet device to lock-in profits

botpro · Mar 8, 2016

ironchef said:
Interesting concepts and thank you for sharing your thoughts. I don't know if you are right but I am going to take a careful look at this.

Questions:

1. How to hedge if you are long instead of short?

Here's an example for long call option:
http://www.quantprinciple.com/inves..._strategies/delta_neutral_hedging_strategies/
"Here we will look at a very simple strategy in which the investor will buy a call option, and short the actual underlying stock [...]"

And here a similar example for long call option:
http://www.optiontradingtips.com/options101/delta-hedging.html

I don't know if they are correct, but would expect so.

2. How do you dynamically hedge against volatility?

Hmm. according to what I read so far, hedging against volatility seems not that easy.
I only played with constant volatility in normal market situations over short periods of 1 to 3 months.
I admit I'm new to hedging; still studying and playing around.
Maybe others can comment about hedging against volatility. I too would be interested in the answer to this.

botpro · Mar 8, 2016

shooter said:
botpro, in your simulation you have to factor in the losses associated with the actual hedging itself. You have to view that as a 'trade' itself, not just a hedge to the short option.

There is still a worm in my q&d framework as it unfortunately not always gives a positive result ;-(.
It indeed could be the effect of what you describe.
As said, hedging is new for me, I just had this crazy idea which I couldn't resist to try out...

botpro · Mar 8, 2016

donnap said:
OP's playing games, but for the sake of discussion.

Yes it will work...sometimes.

As with many trades there are a myriad of possible outcomes.

Scenario 1: Strat works well. You make decent money on options or hedging or both.

Scenario 2: Strat works well enough. You make some money on a difficult trade.

Scenario 3: Strat loses a little, but hedging or option side keep losses small. Again, a difficult trade.

Scenario 4: Large loss. Market moves too fast one way or the other and hedging can't keep up. Or, you are whipsawed to death by hedging operations.

Scenario 5: Disaster. Market makes a very large move on news and you are crushed by losses on one side or the other. You can't even assume that the market always going to be there.

Analysis: Could be used with discretion, but not all of the time. It is possible that it will make money the majority of the time, but potential gains are fairly capped, while the loss potential isn't. A difficult strat. Not a good idea.

Hmm. I was under the impression that hedging per se means protecting against market risks.
But it seems not always to hold. I'am dissatisfied. ;-(
Why do all the much work needed for hedging (and also have the capital for the stock), if there is no guarantee for success? I don't get it... ;-(
I think I made an error somewhere... ;-(

botpro · Mar 8, 2016

botpro said:
Here's an example for long call option:
http://www.quantprinciple.com/inves..._strategies/delta_neutral_hedging_strategies/
"Here we will look at a very simple strategy in which the investor will buy a call option, and short the actual underlying stock [...]"

And here a similar example for long call option:
http://www.optiontradingtips.com/options101/delta-hedging.html

I don't know if they are correct, but would expect so.

In these examples a call option is added into the portfolio and a dynamic delta hedging is applied.
The goal is to keep the initial value of the portfolio (yes, really! ;-) and I don't get it!).

So, one might ask: for what shall this be good if the PnL is 0 ? ;-) Just for the sake of demonstrating hedging?
And nobody of the article authors seems to understand what he is talking about, nor explains the truth behind it.

...Unless there is a well known unspoken secret in the industry... ;-)
My guess based on my friends logic&maths is this: the initial account value shall not represent 100%, but instead a lower percentage, for example 95%
(or is it maybe the other way around: a higher percentage like 105%? Anyway...)
And the difference, here 5%, is the PnL% one calculates in.
Only after this would all that hedging circus would make a sense. Don't you agree?

Hedging with short options is understandable (securing the credit), but with long options not so, IMO...
Hedging seems to be good for freaking-out!... ;-)

ironchef · Mar 9, 2016

botpro, I don't think your hedging scheme works:

According to the analysis of the Goldman study you quoted, the end results of a dynamic hedges were zero P&L if the options were not mispriced. i.e.,

The hedger now follows a Black-Scholes hedging strategy, rehedging at discrete, evenly spaced time intervals as the underlying stock changes. At expiration, the hedger delivers the option payoff to the option holder, and unwinds the hedge. We are interested in understanding the final profit or loss of this strategy:

Final P&L = Value of Black-Scholes hedge at T - Final option payoff.

If the hedger had followed the exact Black-Scholes replication strategy, rehedging continuously as the underlying stock evolved towards its final value at expiration, then, no matter what path the stock took, the final P&L would be exactly zero. This is the essence of the statement that the Black-Scholes formula provides the ‘‘fair’’ value of the option. When the replication strategy deviates from the exact Black-Scholes method, the final P&L may deviate from zero. This deviation is called the replication error.

Goldman Sachs used Monte Carlo to simulate all possible outcomes.

I used the Black Scholes formula, went through a couple of scenarios of 30 day short ATM puts using SPY and delta hedge daily, assumed constant volatility and normal theta decay. My Final P&L was ~$0.0 profit, consistent with Goldman's conclusions. If I include transaction costs, the outcome was negative profit.

Would you be kind enough to share your simulation parameters with me here?

Regards,

botpro · Mar 9, 2016

ironchef said:
botpro, I don't think your hedging scheme works:

According to the analysis of the Goldman study you quoted, the end results of a dynamic hedges were zero P&L if the options were not mispriced. i.e.,

Goldman Sachs used Monte Carlo to simulate all possible outcomes.

I used the Black Scholes formula, went through a couple of scenarios of 30 day short ATM puts using SPY and delta hedge daily, assumed constant volatility and normal theta decay. My Final P&L was ~$0.0 profit, consistent with Goldman's conclusions. If I include transaction costs, the outcome was negative profit.

Would you be kind enough to share your simulation parameters with me here?

Regards,

I tried many variations. Latest params were the following:

Code:

    // define the input params to use in GBM / BSM:
    const double dbDaysInYear       = 252.0;
    const double dbMktSecondsPerDay = 23400.0;  // US regular market hours make up that much (6.5h/day), excluding premarket and aftermarket hours

    const double dbSpot0            = 100.0;    // start with this stock price
    const double dbVolaPct          = 20.0;     // historic volatility

    const size_t uExpDays           = 21;        // 252
    const size_t uHoldDays          = 21;       // uExpDays;

    const double dbEarningsYieldPct = 0.0 ;
    const double dbDividendYieldPct = 0.0;
    const double dbStrike           = 100.0;    // 95.0;

 // const size_t nBarsPerDay        = 780;      // ie. 30-sec bars @ dbMktSecondsPerDay
    const size_t nBarsPerDay        = 390;      // ie. 60-sec bars @ dbMktSecondsPerDay

 // const double dbBarSizeInSec     = dbMktSecondsPerDay / double(nBarsPerDay);     // 60 s, ie. 1 min

    const double dbHedgeEveryNsec   = 300;  // 3600;  // set this

    const size_t uHedgeEveryNbars   = size_t(double(nBarsPerDay) / (dbMktSecondsPerDay / dbHedgeEveryNsec));   // ie. 5 bars

.
But I think I finally grasp the hedging case for long options too. In an other discussion somewhere else someone wrote this:

Code:

"This means that if you hedge dynamically, then you'll/should make a tidy profit.
In fact, if you hedge continuously over the lifespan of the option, you should, theoretically,
make exactly the premium that you paid for the option, assuming BS pricing."

So, in the long option case dynamic hedging should result in a PnL of about the same size like the premium one had paid.
Yes, then it of course would make a big sense!
But the book and paper authors simply neglect to mention this important bit of information, and the poor reader like me just wonders where the logic is in what the book/paper author writes... ;-)

But I've not been able to replicate this yet, ie. to prove it, due to my q&d framework I quickly developed but which still has some bugs; will need more time to fix it.
If shorting is involved, then coding becomes a nightmare, I made this discovery many times... ;-(

botpro · Mar 9, 2016

And here is also a "modern" hedging text especially for the MM types:
http://www.riskencyclopedia.com/articles/dynamic_hedging/

Martinghoul · Mar 9, 2016

Well, I'll be damned... Looky what interesting things you'd find in that article:
"First of all, the portfolio loses money with dynamic hedging because it has negative gamma—something the dynamic hedging cannot change.
...
The fact that the portfolio has negative gamma means that the dealer is going to lose money dynamically hedging it. If the portfolio had positive gamma, the opposite would be true."

botpro · Mar 9, 2016

Martinghoul said:
Well, I'll be damned... Looky what interesting things you'd find in that article:
"First of all, the portfolio loses money with dynamic hedging because it has negative gamma—something the dynamic hedging cannot change.
...
The fact that the portfolio has negative gamma means that the dealer is going to lose money dynamically hedging it. If the portfolio had positive gamma, the opposite would be true."

;-) I admit I didn't read it fully, only upto the mentioning of market makers... and thought it could maybe useful for our market makers here... ;-)

botpro · Mar 9, 2016

Ok, here a preliminary status of this research study:

Since dynamic hedging seems to work, then the claim of mine made here (and in the previous thread)
that a profitable strategy with zero loss is possible, seems indeed to be true and even provable.

So, this then means IMHO much, very much for a consistent successful trading... ;-)

Don't you agree?