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songshu


Total Posts: 5
Joined: Apr 2020
 
Posted: 2020-04-23 15:00
I was told that a long Synthetic (long a call and short a put with the same stike in the same month) is equal to a future with 100 delta and zero other greek. If I am in a situation wherer the call IV is quite different from put IV, eg. call IV at 20/put IV at 30 for the same strike in the same month. Can I still consider a long Synthetic a 'future' contract? If I calculate the greek with IV of each option contract, I have got >100 Delta, -Gamma, -Vega and +theta. Which delta shall I use in the real life? Thanks!

kloc


Total Posts: 34
Joined: May 2017
 
Posted: 2020-04-23 15:29
Mid IVs should be the same, but that's not what's traded. I'm guessing what you're observing is due to bid/ask spread i.e. you're selling a call @20 and buying a put @30 to generate a short synthetic forward position. "Real IV" is 25, but bid/ask spread is +/- 5 vol points. For deep OTM/ITM options, that will be more pronounced so start with ATM strike.

It's bid/ask price spread that's causing the IV spread. IVs are just prices, at the end of the day.


Baltazar


Total Posts: 1775
Joined: Jul 2004
 
Posted: 2020-04-23 22:36
Or you are looking at american option and you have early exercise premium that your pricing formula doesn't account for properly.
Then inverting that formula gives a different implied vol for call and puts.
10 points of vol between the bid and ask is very large for anything liquid.

If the underlying is not liquid and has high short stock fees, that also may be a reason.

Qui fait le malin tombe dans le ravin

Baltazar


Total Posts: 1775
Joined: Jul 2004
 
Posted: 2020-04-23 22:36
dbl post, sorry

Qui fait le malin tombe dans le ravin

songshu


Total Posts: 5
Joined: Apr 2020
 
Posted: 2020-04-24 03:15
I think you got the point. The underlying is not liquid and I am in a market with very high short fee. I don't think it is an ask/bid spread, at least for most part of IV difference. The wired thing is even with illiquid and high short stock fee, the IV difference between call and put was fine before. Just recently after the stock market rebound, a large difference emerged.

So, shall I use the ATM IV, rather than the OTM IV to calculate the greek?

kloc


Total Posts: 34
Joined: May 2017
 
Posted: 2020-04-24 04:50
Baltazar has a good point - american-style options can do that, but the diff is still very extreme.

You can't really use ATM implied vols for greeks - it will affect all the greeks significantly. Just to understand better the source of the discrepancy:
(1) Do you have both sides (bid/ask) for call and put you mentioned previously?
(2) How high is the short borrow fee? Has it changed significantly recently?
(3) What are the moneyness and maturity of the strike you are looking at?

songshu


Total Posts: 5
Joined: Apr 2020
 
Posted: 2020-04-26 10:58
Kloc,

Thanks for your further reply!

It is actually a european-style option and the underlined is a broad-band stock index.

(1) Yes, I have both sides bid/ask for call and put.
(2) Roughly 6-8% for short borrow rate in thero, which was consistent, w/o change recently.
(3) The large differences betwee Call IV and put IV exist regardless of moneyness and maturity. The ATM seems to be the smallest for the same maturity. The far-month ones are lower than the near-month for the same strike.

It seems to me ... I should input seperate call IV and put IV into greeks calculation and each call/put IV should not be the ATM IV or contract IV which is impacted by a instable skew , but the kind of weighted average OTM IV.

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-26 12:47
another reason for the difference:

missing/mispriced dividends or any not accounted cash (e.g. defaults for OTC) may disturb put-call parity (equality for european style, inequality for american style options), hence, implied vols can be different.

Strange


Total Posts: 1651
Joined: Jun 2004
 
Posted: 2020-04-26 19:02
It actually more complex than you think, even once you eliminate the usual stuff like dividends and borrow rates. If the markets are wide, you might simply be seeing call closer to bid-side and put closer to offer-side.

First, there are funding complexities, i.e. funding/carry might be different for long and short underlying or funding might be different for option premium and underlying. It might be a toxic stock of some sort that no risk manager wants on their balance sheet, so people proxy the stock in calls etc.

Then, depending on the market, it might be structural. Ability to unlock profits after delisting might differ between shares and option. Also, in case of corporate actions, the adjustment/process might favor call owners or put owners.

PS. just read the last post, it sounds like some sort market access effect, e.g. local access to leverage for market participants is limited. Is this a Chinese index?

PPS. the fact that the differences increase OTM is a tell-tell sign that you got some forward or carry asymmetry issues, IMHO. You can either vary borrow borrow and rebates to get to put call parity or you can delta-weight the put/call to quickly get approximate right vol.

'Progress just means bad things happen faster.’

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-26 20:46
From put/call make synthetic forward. Watch out bid/ask for long call/short put. If you plot it and see linear dependence on strike making price=0 at ATM, then you got everything correct and I can assure you, these volatilities will match.

Just remember, for European-style, at maturity:
call - put = max(Fwd-K,0) - min(K-Fwd,0) , which is Fwd-K

Then apply expectation operator and you will see that under ANY modeling assumption you obtain the wanted relationship.

For american the reasoning is a bit more complicated, but ok. Think it through a bit.

I did same trick for eq, fx, ir (swaptions) and even bitcoins - everywhere it worked.

songshu


Total Posts: 5
Joined: Apr 2020
 
Posted: 2020-04-28 06:45
You are right it is a Chinese index. I am from China and working with the local stock index option.

I also want to get the delta-weighted average;however, I have to choose an IV to calculate the greek. The trading software is using the 30-day realized vol (close to close) , which is way off. In such a case, which IV shall I use to come out of greek? The options include the local version of VIX(free of the model), each contract IV, ATM IV seperately for call and put, or 'delta-weighted average IV seperately for call and put (perhaps inaccurate because of IV input)

Thanks!

kloc


Total Posts: 34
Joined: May 2017
 
Posted: 2020-04-28 18:21
@songshu: as I mentioned previously, IV is just another way to represent option price. Price of a call (or a put) option with some strike K and time to maturity T is a function of (1) forward price F, (2) discount factor DF, and (3) implied volatility IV. You can ignore (2) at the moment and assume that it's equal to 1. Assuming the forward is well-defined and known, have you tried to compute IVs yourself instead of getting it from your broker? Note, however (as others mentioned), that already getting forwards can be complicated sometimes (lending fees, funding...), but what I described should help you start.

There's no "correct IV for greeks" - there is only "correct IV for option price". Figure out the correct IV (and forward) to compute the option price and greeks will follow.

mtsm


Total Posts: 252
Joined: Dec 2010
 
Posted: 2020-04-29 01:48
Not sure how relevant this is going to be as I can't be bothered to read this thread more than diagonally. But basically put call parity maybe a model independent relationship, but it's a rather weak constraint. It will only hold if actually enforcable by careful arbitrage. People tend to pay too much attention to it, including some agencies who offer valuation services for various options markets.

In my mind it's only really weighty in an option market in which there isn't any price discovery for ITM options. Then it is customary to invoke it and model the skew on OTM options only. That is the case in OTC option markets such as european interest rate swaptions.

If there is certain degree of price discovery possible on ITM options, forget about it. The use of separate vol surfaces for call and put options is customary in such a case.

The reason this topic is interesting is that throughout the Covid-19 turmoil lots and lots of deviations from put call parity have been observed among various optoin markets. It completely has no reason to hold at all. Just think of calls, puts and the underlying as independent products.

Forget put call parity, it's textbook stuff, unless there is a real liquid market for the underlying, the calls and the puts, then things can be arbed into put call parity.

One thing that is always bad is to make some process overly reliant on certain idealized realtionships that have every reason to hold in a textbook, but can easily be broken in markets. Examples for this abound...

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-29 02:02
It's a joke, right?

Violation of put-call parity for european is free lunch (minus costs). I see no reason for such orthodoxy.

mtsm


Total Posts: 252
Joined: Dec 2010
 
Posted: 2020-04-29 02:17
Maybe it's a textbook free lunch for you if you like to eat paper.

No it's not a joke. As I was saying that sort of violation is often present in some markets under fairly mild conditions and is so for good reasons. Moreover under illiquid conditions like we have had them recently it cropped up in markets in which it is normally absent.

It's a pretty weak constraint. It's completely meaningless to talk about free lunch unless you can actually collect your lunchbox.

There are many other examples in finance where this is the case. Think for example interest parity in a maturity sector in which FX forwards and the corresponding cross-currency basis overlap. Or even something like products trading on exchanges and in a quasi-fungible manner in over the counter markets. There are free lunches everywhere, in principle. In practice it's different.

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-29 13:22
ok.
it just goes in contrast with my experience, where I checked this arb for eq, fx, ir (swaptions) and bitcoins - everywhere it works. Short term deviations can be observed due to jumps and which happen of course. But it seems you are talking about long term systemic shifts in liquidity or on-side inventory concentration. Just to make sure: we both discuss portfolio where call, put and forward all have the same maturity, right?

mtsm


Total Posts: 252
Joined: Dec 2010
 
Posted: 2020-04-29 16:26
It's a complicated discussion to be had actually. My main point is to say that there is a certain degree of over-reliance on put call parity and there is some danger to that. It just doesn't have any strong reason to hold.

I don't want to appear as sounding overly confident in what I write. Please feel free to call out the bs.

As to your points: How can you even check it? I mean what is your starting point, prices or vols? Are you on the sell-side, the buy-side, in some third party agency, in academia? Where is your data from?

For ir swaptions which is the market I know best among the 3 you quote, there isn't anything to check really. It will mostly be satisfied trivially, but ultimately it depends what your starting point is. Without going into crazy details, this is a market that is mostly discoverable ATMF only, with some indications of fairly superficial properties of the skew in the interdeale broker market and presumably some counterparty marknig tie our via clearing if that product is cleared yet. There is mostly nothing to check here. The ir skew is mostly bullshit, as in who knows what it should be???

For FX I don't know. I don't know how two sided that market is. It probably depends on curency pairs, maturities, market regimes...

For equities there are known deviations. There is some published work on this. Some stat arb people use information from that as features.

Yes I am talking about something like you say, not necessarily long term.

Yes we are dicussing the case of european or very soft american options at a given expiry date and for options across all strikes and forward agreements across all strikes.

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-29 17:04
Let's say, I am risk practitioner with personal tick to high-frequency

> Where is your data from?

Either real time feed or backtesting of the spread for liquid spot (equity, forex, bitcoin) or many years of markit EOD/EOM many years data on Swaptions, even for Bermudan it works. I saw arbs 10+ ago, which is "ages" since.

In plain vanilla european payoffs at time of maturity are:
max(S-K,0) - max(K-S,0) = S - K

which is put-call parity. No matter, which model you think of. The only thing which is not here is discount and credit (one of legs falls out)


> Please feel free to call out the bs.

well, self-sanity is welcome, otherwise I am becoming a plumber here.

seems you talk in slogans. not good.

mtsm


Total Posts: 252
Joined: Dec 2010
 
Posted: 2020-04-30 01:36
Sorry to disappoint here. What I am saying is not very profound really, I am aware of that.

There is nothing wrong with your statement of the put-call parity relation, all agreed and entirely model independent, but all on paper still only.

I was suggesting in my previous message that it may not be easy to check it systematically in many markets, because you don't have adequate price discovery. And your data source is indeed important. If you get your data from a second hand source that bakes put-call parity into some process then it will hold trivially. For instance I argued that for eurpoean swaptions it's a pointless exercise and it most likely holds trivially. Means nothing. Let's not even discuss Bermudans. Also and a propos, it is actually funny that you bring up that said agency in this context. Lol.

I am only asserting two things I guess. First it's a strong relationship on paper, but it is much weaker in practice depending on market conditions. Secondly, lately there have been deviations from it in various options markets, which in principle have properly liquid markets for the corresponding underlyings. This isn't a statement about arbitrage or anything like it. It's an observation on select trades. It just doesn't hold at times and there is nothing you can do about it, no free lunch, no nothing.

Anyway, that's all I have on this topic...

ronin


Total Posts: 591
Joined: May 2006
 
Posted: 2020-04-30 12:27
> free lunch (minus costs)

@nikol,

It ain't free then, is it?

"Eat as much as you like. It's all free. Except for the costs, of course."

Love it.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1143
Joined: Jun 2005
 
Posted: 2020-04-30 14:52
:))

Indeed, tautology. My sanity filter got spoiled.

songshu


Total Posts: 5
Joined: Apr 2020
 
Posted: 2020-05-20 08:00
Just report back the call/put parity has recently been restored. okay, there are still some difference beween ATM IV of call and out, but been within a reasonable range in my mind. If we look back, does it sound like a 'free lunch' offered by the pre-mature market? During the time of C/P parity coming back, the underlined seems to be quite stable. I still don't quite get why such thing happened in a quiet time.

Thank all of you for your nice feedback to the original question!
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