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Arbitrage opportunities in options - how options are priced, explained in layman's terms - without resorting to the BS pricing model

Arbitrage opportunities in options - how options are priced, explained in layman's terms - without resorting to the BS pricing model
Alright retards, I've been laid off at work due to beervirus and I've been eyeing and toying with the idea to get back into options trading. I'm writing this post to raise the bar for discussion on this sub, I'm tired of seeing just memes. We'll never match WSB unless there is a healthy mix of dankass memes and geniass discussions.
Now, when it comes to options, I am completely self-taught (completely from first principles, back in 2008, before you autists came up with the idea of watching videos on youtube). Since I am completely self-taught, my perspective will be different from the people who learnt this stuff while studying MBA/finance courses/NSE accredited investing courses. So if what I'm saying is different from what you've heard from the dude who swindled you of 20K for two days of options education or your gay BF's live-in partner, remember when it comes to maths, there are many ways of approaching a problem, ultimately, all are the same - profit means account balance goes up, loss means a loss post on ISB goes up.
Now, I'm assuming that you understand how options work. If not, I suggest heading to Zerodha's Varsity to read up on options. If you're too lazy for this, get your micro-dick outta options, this is a man's game, surprise butt-sex awaits amateurs.
I'm also assuming that you've come to realise that the sustainable way to make money in options is to write options. Unless you've got Trump or Ambani on speed dial to get access to news before it becomes news, YOLOing whatever rent money you have on buying options will blow up your account, eventually.
Writing options also means the possibility of account balance going tits up is a real possibility. You gotta, gotta, gotta measure and manage your risk. You can do this only when you understand options as well as your dick.
Towards this, I intend to put up a bunch of posts (depending on many of you shit heads are still reading at this point) that comment about little things that are more of 'wisdom' than 'education'.
The example below talks about currency derivatives. Why currency? Read below:
  • Lower margin needed. I can short a CE/PE contract with only Rs.2000, unlike the >Rs. 70,000 for index contracts. You get to learn, play and wisen up with an order of magnitude less money than with Nifty or Banknifty contracts.
  • More stable underlying. When you're shorting contracts, the last thing you want is the underlying asset going crazy like a broncho during rodeo.
  • Less autistic crowd in the currency market. While banknifty options attract retards like flies to poop, currency derivatives attract a more educated crowd.
  • Sooner or later, you end up acquiring a more balanced education on economics as a whole, rather than the shit fest that goes on in the local circles.
  • The more contracts you can short, the more strategies you can pursue
  • Decent hedging is possible without throwing away all of your potential profits
  • Lesser stress (anybody else going through premature hairloss or is it just me?) because of points outlined above.
Alright, today, I'm going point how the put-call parity works and by extension, show proof for 'efficient markets' by pointing out how opportunities for arbitrage is pretty much non existent, so you guys can cool it with the whole 'market manipulators' knee jerk reaction.
Alright, to start off, here's the current spot rate of the USD-INR pair:
https://preview.redd.it/qup28ay567j51.jpg?width=452&format=pjpg&auto=webp&s=b79ef1a3480e5cbafa42547143c651397ec57f13
Here's today's USD-INR futures closing rate for Sep expiry:
https://preview.redd.it/krghirc677j51.jpg?width=511&format=pjpg&auto=webp&s=60d52b785baa8a1cd240d0df7949a48c8391ba2d
The difference between spot and futures rates is due to differences in what is construed as 'risk-free' interest rates in the US and in India. Check out this video if you want to understand why the Sep futures is trading at a premium of 27 paisa to the spot rate.
Alright, so the deal is, if you buy 1 futures contract @ 74.49, unless the USDINR exchange rate rises by 27 paisa at the end of Sep (i.e. a spot rate of 74.49) you won't make a profit (ignoring brokerage and stuff). If the exchange rate were to remain the same without any change, you stand to lose (0.27 * 1000, currency derivatives have a lot size of 1000) Rs. 270 per lot. Even worse if the rupee were to appreciate (i.e. exchange spot rate goes down).
Now bear with me if the next few paras are exceedingly boorish, I need to spoon feed people who aren't used to currency derivatives. My strategies are mostly aimed at playing a more risk balanced play, something that yields consistent returns which can be compounded. 10% profit compounded monthly gives 314% growth per year, 3.5% profit compounded weekly gives ~600% growth per year.
Given how the USDINR rate is crashing, one way to profit would be to short a futures contract (duh!).
The orange line indicates the current USDINR exchange rate
As indicated above, if the exchange rate does nothing and remains as is till end of Sep, each lot of USDINR futures shorted yields about Rs. 250 in profit (for something that takes up Rs.3000 in margin, that's a >8% profit in return). Things look even better if the exchange rate were to fall further.
The problem is that things heat up quickly if the exchange rate were to go up. Ideally we would want to hedge against it (which also reduces the margin needed drastically). One way to hedge it would be to buy a at-the-money call (74.25CE @ rate of Rs. 0.555 -> Rs. 555 per lot (i.e 0.555*1000)).
https://preview.redd.it/ze16kyphv7j51.jpg?width=588&format=pjpg&auto=webp&s=a3c2bba9fb314beff309671f03a013e69e08f4e0
Having purchased a call option, the P/L curve now looks like:
The max loss is now limited to Rs. 315
The keen-eyed among you will recognise the above P/L curve as one that matches that of a put option. By shorting a futures contract and buying a call option (both with same expiry), we have created a synthetic put option that would have costed us Rs. 315 (0.315*1000) for one lot.
Now, why go through all of this hassle if we can get the same returns by just buying a put option? Makes sense, as long as we can purchase the 74.25 strike put option at a price lesser than Rs. 0.315 (see above).
Let's see what the put options are going for:
Well, how about that...
The market price of 74.25 puts are exactly the same price as our synthetic put. While the synthetic put came in at Rs. 0.315, the put costs another 0.005 extra to avoid the trouble of shorting a futures contract and buying a call at the same time. This is not by chance, big trading desks have algos (trading bots for the virgins here) that keep an eye out for price disparities. In this case, if someone were to be willing to pay more, the algos would compete amongst themselves to sell the puts at any price above 0.32. And if someone were to be willing to sell a put for less than 0.315, the algos would immediately buy.
The price of the puts move in sync with the prices of the futures and call contracts. Conversely, we can create a synthetic call, and you will notice that the price of the synthetic call works out to be the same as the market price for the 74.25 strike call. We can also create a synthetic futures contract the same way.
The prices of derivatives aren't decided willy-nilly. They are precisely calculated at all times, which forms the basis for the best bid/ask prices. There is no room left for someone to come in and make free money via arbitraging using synthetic contracts.
If you found this insightful, and would like more of this sort of posts, let me know.
Options when used properly, can be used to generate risk adjusted returns that are commensurate with the amount of risk you are taking. If you are YOLO-ing, sure, you can double or triple your money, because you can also lose 100% of your margin. Conversely, you can aim for small, steady returns and compound the crap out of them. Play the long game, don't be penny wise and pound foolish.
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