Dynamic option delta hedge (FRM T4-14)

[my xls is here trtl.bz/2X8LpoV] To dynamically delta hedge is to rebalance the hedged position when the stock price moves (and therefore its delta moves, also). In this example, we rebalance once per week. We assume you are the market maker who writes (that is, sells) 100,000 call options where each option has a delta of 0.522. The initial position delta is therefore -100,000 * 0.522 = -52,000; as naked options you will lose 52,000 for each +$1.00 increase in the stock price. To delta hedge (aka, neutralize delta), you purchase 52,000. Then next week, you buy/sell shares to maintain delta neutrality, hence the "dynamic" aspect. If the realized volatility equals the implied volatility, then the cost of the hedge will approximately equal the option premium!
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[@arvindmathur5556]

This is such a clear explanation and illustration! Superbly explained!

[@ripon729]

A million thanks for such great content free of cost :D

[@joshjung5083]

Thank you so much for the useful content!!!!! Exactly what I needed to understand dynamic hedging

[@savagemp5]

Thanks, great content and knowledge shared, I couldn't find any1 nor any blog on this

[@mztech1925]

This is amazing. And thanks for the excel model.

[@ExcelTutorials1]

Awesome video as always!!!

[@crentistDaDentist]

Extremely helpful !!

[@Erays_Adventures]

Thank you!

[@tinwav]

thank you so much, i was so confuseeedddddddd

[@cristag.a3457]

Honestly, best content for the FRM. Thanks so so much!!!! :D

[@UnculturedGaming]

how do you calculate the interest cost ?

[@AcademaxPaperHelp]

Hi From what distribution do you draw the share price in each period (49, 48.12 etc. )? What are its parameters? And how does the standard deviation (20%)coincide? Thank you

[@narwhals7820]

idk

[@SuperDangerousMouse]

Can you offer ideas on optimal delta-hedging? For example, above, Hull decides that we are going to hedge every fixed amount of time (1 week) until expiration? Should we hedge every week? every 1 dollar? or every 1% change in delta? In theory, it should average out in the long run, right? What do people do in practice? When we're short options, how do we minimize negative-scalping? Say for example, I decided to hedge every 1% change in delta... I start off flat (delta-neutral). Now my position is long .0.25% delta... I do nothing. Later, I'm long 0.50%, should I sell a unit? or wait until I reach 1.00%. Do people lean toward short delta in equities and positive in commodities? Thanks, and all your videos (that I've seen) are great.

[@danielmateoriveraortiz6234]

When number of rehedging increase, (delta t) or you hedge more frequently the PnL at the end is less probable to gain or loss, it means to be closer to 0. In the BSM it is supposed that you can trade continuously, so in the formula you are perfectly hedged. In practice this not happens, the hedging is tried to be optimized taking into account transaction costs, so the frequency of hedge will depend on that.

[@arvindmathur5556]

@@danielmateoriveraortiz6234 plus even if you are delta hedged, gamma risk can still kill the option writer due to negative convexity of the call writer's payoff diagram

[@mangao4334]

Do market makers rebalance their book every week or everyday? many thanks

[@giggt6701]

Can you please share the sheet? The link says it was deleted. I’m unable to reproduce certain Inputs

[@jaythizzle1969]

Hedge on new implied vol (after the move) or original implied vol at the time of the initiation of the trade? Say vol was at 20, stock goes down big, now the new implied vol is 50. Better to hedge on the 20 or the 50?

[@bionicturtle]

The hedge illustrated is dynamic for purposes of neutralizing the position delta. Implied volatility enters as a factor only because the initial calls (in this case) are sold for $240,000 and this premium collected associates with an implied volatility of 20.0% (ie, implied volatility is a function of price). Then this will match the cumulative hedging cost (adjusting for TVM) if the realized volatility happens to be 20%.

[@olivermohr417]

Is it OK to keep purchased volatility constant when calculating delta hedge, if I use a different volatility for the underlying asset random walk?

[@lucaspalladino4452]

🐐🐐🐐🐐

[@tutumumu8428]

Assuming you sell a call(short) and at the same time you delta hedge it with stock. if the stock price drop say significantly, do you keep the premium at expiration or will the hedge offset the premium and you end up with 0 impact ?

[@gaving9463]

You end up with theta

[@nononnomonohjghdgdshrsrhsjgd]

and what is the point in selling a call option at all? If the premium is appr. as much as the costs of hedging, what is the point to make a delta hedge with short call?

[@bmwman5]

Ok so looking at this it doesn’t make sense to Delta hedge bcos am taking in $240,000 (when I wrote the options) and it’s costing me $263,000 (at end of week 20), so loss of $23,000. Correct? Delta hedge not worth it??

[@jayavigneshr8460]

no as per BSM the value is 240000 and it is not exactly the option price charged. Added to that the gamma is not hedged in the example.Generally market makers will have a margin for doing all these in the option price they charge

[@kaiwang2924]

Yes teach me like I'm a dummy!

[@matts6165]

I have had to watch this video more than once to grasp what is actually happening. This works well for European options, but how to deal with American style options because if it is in the money, you might find yourself having sold a call option at 50 strike and now the spot is trading much higher and you incur a loss. I know American options trade much higher because of these early exercise benefit. But my question to you is how would a market maker hedge out their risk with an American style option? Thanks! and great video

[@themomentcollector5402]

But you bought also shares, so in case of assignment you deliver the shares, and you incur no additional cost, your portfolio delta is 0. The only issue is gamma risk, which occurs from abrupt changes in the price, might leave you temporarily unhedged that way.

[@RobertJewkes]

Does The pv of 263 work out to be 240 using risk free rate of 5% ?

[@bionicturtle]

Not exactly, but only because this example re-balances weekly instead of continuously. The important assumption to the equality--i.e., between PV(cumulative cost) and BSM Price (by definition, a PV)--is that the REALIZED volatility equals the implied volatility inherent to the BSM PV. If the realized volatility equals the implied volatility AND the rebalancing is continuous, then they should be equal. As Hull writes, "If the hedging worked perfectly, the cost of hedging would, after discounting, be exactly equal to the Black-Scholes-Merton price for every simulated stock price path. The reason for the variation in the hedging cost is that the hedge is rebalanced only once a week. As rebalancing takes place more frequently, the variation in the hedging cost is reduced. "

[@RobertJewkes]

Bionic Turtle thanks. Love what you guys are doing :)

[@bionicturtle]

Thank you, much appreciated!

[@steveengst6554]

@@bionicturtle First, thoroughly enjoy your videos! As for the simulation, I don't think the math works out when discounting the cost of the dynamic hedge. Specifically, Hull discounts at 10% per annum, not 5% for 20 weeks. Why did Hull use 10% per annum? Thanks!

[@giggt6701]

Also last step in confused, you are long the call, that’s in the money. You collect 57.50-50= 7.25 M. You have a cost of 5,263,000. Then how do I arrive at 263,000? And I can’t find how you discounted 263,000 to get 240,000 at 5 percent

[@bpradel]

How did we obtain the cumulative cost of $263,000?

[@JohnSikes73]

At the end of maturity (20 weeks), the market maker owns 100,000 stocks (net value 5,725,000) and has sold 100,000 options. Since the options are in the money, the buyer will exercise them. Per option payoff will be 7.25. So the market maker has to pay a net of 725,000 to the option bearers. Hence the market makers portfolio has a net value of 5,000,000. But then the market maker has incurred 5,263,000 in order to hedge the portfolio, so overall 263,000 has been spent in hedging the portfolio. But then he has also received 240,000 by selling the options initially. So you can think of this amount as being used in financing the hedge.

[@St0iCiSm]

@@JohnSikes73 So at the end of maturity, even if the price of the stock went up, the market maker doesn't bear any loss ?

[@albertrovirafarre8383]

I think there is a better way to neutralize the delta from minute 0 of entering the market. It is having the same deltas with options. 100k shares - 200k options. (Deltas actions 1- Deltas options 1) And rebalancing is direct. You just have to adjust delta of the options and compensate the costs of the contracts until expiration. sorr for my english.

[@johnpalma7265]

It sounds too me like the market maker is simply loaning out the options and hedging in an attempt to keep the premium when the options expire,wether they expire in ITM or OUT, am i on the right track or of base? Thanks

[@canyoubudget]

Can someone please show me the discounting from the 263k to 240k in 20 weeks at 5%? I'm struggling to get down to 240k in that timeframe and cannot find the Hull textbook.

[@canyoubudget]

I understand the inability to continuously re-balance is causing some noise, but I'm having a hard time coming close to 240k.

[@calripson]

It's gamma risk that takes pros out on a stretcher.

[@mina-xm1pc]

Actually I would to ask about the profit of writer of the call options who did all of this, what actually they gain by doing all this process? I can understand that probably they gain from the premium but at the end they have 263,000 cumulative costs?

[@AcademaxPaperHelp]

That's only one scenario, that it's not likely to happen ( the option writer should be experienced)

[@arvindmathur5556]

@@AcademaxPaperHelp Even experienced option writers are getting killed by gamma risk as illustrated by Gamestop.

[@nononnomonohjghdgdshrsrhsjgd]

@@arvindmathur5556 so what is the delta hedge of short call used for in the practice? In expected value the cost of hedging should be equal to the premium. Let assume that it is only the delta that changes, is the sense of the whole delta hedging maybe that the loss as well as the gain are most probably not severe. when is this strategy worthy?

[@arvindmathur5556]

Dear Bionic Turtle, Please make a video on the effect on hedge funds of the recent volatility of Gamestop and the related gamma risk which is killing the shorts.

[@SC-bi6my]

I think you are missing of the compounding effect of interest rate ..in cost and interest

[@bionicturtle]

No, I don't think it is missing, see column L (Interest Cost): each week's interest cost is the Rf rate (5%) divided by 52 multiplied by the CUMULATIVE Cost Incl Interest. Link to XLS in description

[@daviddalton9350]

WTF? Where are you going to get a 5% risk free rate in February 2019?

[@olvinfuentes7514]

lmao 1:50 wtf? you start by saying you've written 100k options then 1k & then you start the example with 100 options...

[@bionicturtle]

maybe substitute "listening" for lmoa and you'll hear what I said: writing 100,000 options (which is the example) is writing 1,000 contracts because each contract is for 100 options; i.e., in case your multiplication is as good as your attitude: 100 * 1,000 = 100,000. But thanks for lmao wtf its sweet of you to stop by #sarcasm

[@olvinfuentes7514]

@@bionicturtle "you have written that is to say you have sold 100,000 call options." you're all over the place.

[@bionicturtle]

@@olvinfuentes7514 sell = write = short. There is not a single inconsistency, it's just you. I often clarify the synonyms, in this case some viewers might not know that "writing" options is selling/shorting them.

[@olvinfuentes7514]

@@bionicturtle you're getting so mad bc I pointed out a technical mistake? The 2nd part is correct: 1000 contracts × 100 options = 100k. But you're not selling "100,000 call options." You're selling 1000 call options.

[@bionicturtle]

​ @Olvin Fuentes I never get emotional about YT noise. I don't see the mistake: to write (aka, sell) 100,000 options is, by definition of exchange specifications, to write 1,000 (call option) contracts. Here's Hull on the example, "Tables 19.2 and 19.3 provide two examples of the operation of delta hedging for the example in Section 19.1, *where 100,000 call options are sold* " (same as my yellow highlight). What exactly is the mistake, or for that matter ANY MISTAKE, such that I am "all over the place" ?