Let’s focus on expiry trading as this is the easier bit compared to trading them on other days or entering positional (which I'll cover in future posts).
First let me quickly mention what I did last Thursday.
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I started off with Bnf 37800pe-37500pe PRS at 1:4 & Nifty CRS expecting Bnf to make a recovery or atleast outperform Nifty. Bnf didn’t quite behave as expected first half so reduced that ratio to 1:2 and shifted down puts to 37300pe (1:5 with 37800) i.e. changed it to a ladder
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For a PRS let’s see how PnL would’ve behaved over the day.
Fig below shows how price of a PRS evolves with time to expiry. When we enter a credit PRS, the entry price is negative (below the x-axis in the pic) and later on depending on the price being above or below this level +
we are in a profit or a loss on the trade (obviously!)
Let’s say we enter a 1:3 PRS on BNF with the long put at the money (K1) and short puts out of the money (K2). Let’s say overall delta is slightly positive and we collect a credit. How does PnL evolve?
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Refer pic below. Purple lines are profits made with Bnf staying flat or around the level after entry ending up just collecting premium at expiry. Red lines are losses if Bnf moves down much further.
What is driving the Pnl?
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Let’s look at the different components driving the PnL. See pic below (pasting pic to reduce length of this thread)
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Hence, if Bnf remains flat and delta turns slight negative we can add more shorts to make it delta neutral or if Bnf keeps moving up we can book profits on the whole position and shift the PRS up and maintain a delta neutral position (I prefer not to make the new position
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delta positive again as that might be too aggressive). Important to maintain the same “range” as earlier till first half. Range can be reduced as we are closer to expiry.
And what if Bnf keeps moving down? Keep shifting short puts into lower strikes (not all at once) and
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create a ladder(ratios with shorts at multiple strikes). I suggest against shifting the long put down! Why? With market going down and position making a loss prudent to accept the bearish sentiment & make delta slightly negative overall and staying in the long put does that.
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One can adjust delta to neutral if index stabilizes. If index keeps going down one can further defend the position by:
Making position delta negative or turning it into a put spread OR
Make it an asymmetrical fly by buying further away OTM puts (say 100 away from K2)
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Stop-Losses- Can be placed more conservatively compared to what one places on the put leg of a short strangle. This is due to the long option leg present as an “upfront” hedge.
Ok expiry case done!
Finally, the best scenario to trade RS!
See pic below
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In a follow up thread in the future (not anytime soon!!), I’ll discuss trading RS (incl. CRS) on non-expiry days which is a little challenging & very interesting given vol comes into play.
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Let’s try to understand what factors impact ratio spreads and how to trade & risk manage them.
As it’s impossible to fit everything into one thread I’m dividing this into two. I’ll cover factors that affect ratio spreads
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in the first part and then discuss how to trade & risk manage them in the second (which I’ll post tomorrow morning). Finally, I’ll discuss the best case scenario to trade them that has a very good risk reward.
A quick (boring) intro:
Ratio spreads (RS): Short OTM/ATM options
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and go long options that are more in the money than the options shorted. Quantity of options shorted are in multiples of quantity of options bought.
Factors that affect ratio spreads:
(super important)
Delta wrt TTE – As we near expiry, delta of OTM option goes down(see pic)
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Thought of posting a primer on stochastic processes that’ll be useful for any future posts on whether deriving Black’s formula for pricing calls/puts (my next post and should be a quick one) or discussing interpolation of vol surfaces (SVI) etc.
This should also help understanding my VIX derivation post better.
Any let's get started.
Any underlying variable, be it a Nifty/BankNifty, USDINR, crude etc, can be represented as a stochastic process with a drift and a diffusion(random) component.
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Think of a stochastic process as a random variable evolving with time OR a collection of random variables that have been gathered at different times (Usually all stochastic processes, expectations are always defined under some probability measure but I’m not touching on
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#Distribution Below is how an index return distribution can "potentially" evolve with time AS OBSERVED at starting time t=0.
As an example, one can view this as a potential #Nifty return distribution with PDFs given by Nov month end options (t=1), Dec month end options (t=2)..
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and so on (T=1 can be weekly also but I reckon weekly distributions won't look that smooth based on what I observed of option price/IV behavior).
Things to note:
At t=0 nothing is random, everything deterministic and pdf is a dirac-delta function.
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And with time, probability of index moving away from its mean (colored with orange ticks) goes up and so pdf spreads wider and it's peak value keeps coming down in order to assign more weight to returns away from its mean.
Once upon a time (many many many years ago!) one of my friends was asked to implement a forecasting project as the last stage of getting an offer from a prop trading firm in Europe. Below is the problem statement:
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Input data consists of (several hours of) trade and order book data for a listed product.
Order book data consists of time, bid/offer price and size resp. whereas the trade data
consists of time, price and volume.
Objective: Build a quantitative model to trade this instrument.
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My friend was a uni. chicago booth grad but had a lazy arse so I helped him implement it with the help of a common HFT friend. We both knew shit and the project was all implemented through the HFT guy’s guidance. I’m just presenting the report below. Check out.
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The NSE India VIX white paper (link below) only gives the formula and we will derive it in this thread. That'll be the only focus of this thread with more in future threads. www1.nseindia.com/content/indice…
This is going to be mathematical and my post yesterday about expectation and integration should help. But I’ll try to reduce jargon and leave out unnecessary mathematical details. Some topics such as stochastic processes have been touched upon here. Will post more on that later
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Let’s say f(x) is any function of a stock (or any other tradable underlying) ‘x’ and whose 1st & 2nd derivatives exist. Following on from the derivation last time of the PDF of any underlying,
‘x’ has a PDF, φ(k), given in fig below.
(Thread) A basic math primer for people with non-math background (this will also help in understanding my post tomorrow on India VIX).
I’ll be simplifying a lot of math details here.
I’ll mostly talk on "expected value" and a bit on integration.
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Expected value is one of the most important terms in financial markets. When we want to find fair value or “price” of any financial derivative we mathematically try to find its “expected value”. We will define what it is later on. But first let’s talk about random variables.
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Random variables: When we talk of random variables we talk of what values/outcomes a variable can take and what is the probability of each of these outcomes. So, two important terms here: outcomes & their probabilities.
Nifty, BNF (and their vols etc) are all random variables
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