Let’s say I don’t care about what’s happening in world politics, economy and other things. But I do know the numbers. Now I’ll try to come up with a strategy that will make a profit (well I’m 95% confident)

The idea is simple.

- I consolidate RBI reference rate of USD-INR for everyday for two years. It’s public data. you can fetch it yourself from here. It’ll look something like this,
- Next I’m going to group them for same month. Now you’ll ask me why grouping is required, we can easily analyse continuous data. The reason is, we are not exactly grouping according to month. Rather we’re grouping them by expiry of derivative series. Most importantly the expiry of Options. Because we will not be trading in spot market. The strategy is executed wholly inside derivative segment of USD-INR.

This table demonstrate the reference rate of USD-INR pair for the last 7 months. Here we define another parameter i.e. spread. Spread is the difference of maximum and minimum rate in that month. For the moment do not ask why we need this, just remember we’ll need this later. - At this point I’ll talk briefly about some Unicorn called Options. But this will be just an overview. If you want to know more you should read this (I know this is a big read, but that’s how it is. No shortcut). Screw definition, lets understand by an example. Consider USD-INR current spot price (RBI exchange rate) 64.1438 . I go to derivative market and I buy some magical unicorn called USDINR 64 CE. The name itself is complex. So lets simplify this thing. It simply means at the end of current month (Series Expiry) no matter what is the rate of USD-INR, I’ll have an option to buy 1USD at the rate of 64INR. Consider this like as a kind of insurance. Normally you pay a premium. If something happens (rate goes abobe 64) the insurance company pays you back. But the basic funda is, majority of the insurance holder will not claim. That’s how insurance works. In derivative market also, 95% of options expires worthless.
- Now say at the end of month USD-INR reference rate is 66 (just assume). But I’ve bought an option to buy it at 64. Great! so the guy who sold the option (mainly Investment banks) will pay you the difference of 2 INR (SPOT – STRIKE i.e. 66-64 = 2)
- Consider the opposite case, at the end of month the rate is 62. So obviously I won’t be willing to buy USD at 64. So the option seller will keep the premium you paid.

That’s all you need to know about options, for now atleast. But before closing, lets clarify one thing. If the spot price (reference rate) never crosses my strike rate (64INR in case of USD-INR 64 CE), I stand a chance to make profit. So if I sell options (insurance) that has very less probability of happening, I’ll make profit (might be small profit, but profit statistically more likely than loss)

- Now it’s time to understand why you calculated spread. To find the maximum movement in a month. So that we can estimate what is the likelihood, that the strike, at which I sold the option never crosses. You can download the whole spreadsheet from here. But I’ll note down some important observation.
- Only thrice (3 times) in last 2 years (24 months) the price movement was more than 2.
- Mean change in a month is 1.1
- We can make the calculation more lenient, by considering how likely it is for us to take position at worst possible condition. But this will do for us now.

- Here is the maximum change in a month for last 24 months. Now if we calculate the mean, it comes around 1.0977. The standard deviation for this series is 0.6912. From basic statics we know that the chance of a random observation, falling under the range of (mean – 2* standard deviation) and (mean + 2* standard deviation) is roughly 95% So we can say under a time-frame of a month the probability that the magnitude of this movement greater than 2.34 is less than 5%. So we can say with 95% confidence that if sell options at a strike price more than 2.34, we can be 95% sure that the option will expire worthless i.e. the price will not cross our strike price e.g. say the current USD-INR pair is trading at 64, if we buy USD-INR CALL option with strike more than 66.34 ( e.g. USD-INR 66.5 CE), our probability of making money (maybe a bit low amount) is 95%
- This is the strategy, we sell options with strike beyond 2.34 of the current price. Wait till the month end. We make money with 95% probability. Here we need to consider two points,
- The change in currency price in a day should follow Normal distribution. If you want to check if that’s true, go on plot the changes. But remember if we plot the changes as I provided, it’ll never come in normal distribution, because I’ve ignored sign of the change (took only magnitude for calculation). Now you should ask why I ignored the sign then? Well, the reason is we’ll make the strategy more general than selling just call option. And even if I do so it’ll increase our margin of error, not decrease it.
- We ignored liquidity factor associated with that strike. In simple words, we ignored the check if someone is really ready to buy at that strike (Because I can sell only when somebody is ready to buy).
**Volatility**in market should give you higher liquidity in high strike prices.

- This generalization a bit advanced. You should read this, if you don’t have any ideas about options, before reading this section. If you think about this (paragraph no. 6.1) a bit, you’ll find out the strategy is statistically valid for PUT options also. So we’ll generalize the strategy more to say,

**The probability of an OTM (Out-OF-The-Money) option, with STRIKE PRICE more or less 2.34, expiring ITM (In-The-Money) is less than 5%.** - That’t it, we found a statistically probable strategy. It’s simple,has lower cost than spot market and as it’s selling options, the margin required can be given by pledging equity shares in your DEMAT account.

**Sell OTM options with strikes 2.34 away from current reference rate, you’ll make profit 95% of the time.**

In reality we need to slightly modify the strategy considering real situation. If the geo-politacal situation is extremely stable we can trade with even lower strike. Even a strike 1SD away is not crossed in 63% cases (we can earn higher premium, by taking a bit more risk).We also need to consider liquidity factor for the strike.

Credits: I borrowed a image from Zerodha Versity. Thay have some excellent educational resource for free. You should of course read that if you want to start trading seriously.