5 Jun, 13 tweets, 3 min read
Monte-Carlo Simulation 101

One of the most powerful tools in any practitioner's toolbox is MC simulation. Every trader/quant that I knows has some kind of MC sim code ready to use for pricing or analysis.

Why is MC such an important piece in derivatives pricing?
The true beauty about MC sim is that we can use it to price literally any type of product we want : vanilla options, 1st/2nd/Nth order exotics, baskets, etc... . you name it, MC can price it, why? because we simulate future price paths with very few parameters...
define the distribution shape (let's face it, we always default to normal distribution), assume drift/volatility, set horizon, and tell me how many paths you want to simulate and I can generate it in lightspeed...

Sound like a no brainer right? this is where it gets bit tricky..
We all know that the underlying process in derivatives pricing is a stochastic process (Brownian Motion to be exact). In short, stochastic process is a process where increments (log-price) are random and independent of each other (i.i.d). This is the core of Brownian Motion
Why is that so important? because it means that our process has NO memory, which means that the future price path is independent of the past (aka Markov process). This allows us to price/simulate the future price from any starting point along the path. Cool right?
Just think what would have happen if this was not the case... think how hard it would to price options on VIX where you need to use the entire history of VIX data from the big bang until today... not very practical imo...

But there is a flip-side to using such process...
Over last few years more and more studies have shown that price dynamic across different asset do carry some kind of long/short memory, which contradicts the Brownian Motion dynamic (which is in the heart of MC simulation). Many have shown highly positive/negative autocorrelation
of log-price (increments), which we usually call them as trend/mean reversion. So how do we model this kind of dynamic? We turn to Fractional Brownian Motion (fBm)

Although sounding quite intimidating, fBm is simply a general case of the "normal" brownian motion
In BM we assume zero-autocorrelation between increments, so we set the autocorrelation parameter (let's call it Hurst exponent) to 0.5 (just think about it as the 0 point).
But what if we want to play around with that and see how price behaves under serious mean-reversion or trend? no problem MC sim for the rescue...

You see, we can use it to simulate pretty much any price dynamic we want (given very few parameters...)
By now you are probably asking "So why are we still using BM and not fBm, if we can get much more flexible with fBm?"

The main problem with fBm is that it lack one very important property that our good old BM has - markovianity . Because our log-prices are autocorrelated
we cannot treat them as independent... so why am I going on and on about fBm, because great minds in quant finance have come up with markovian approximation (which means that with few tweaks we can use fBm in MC sim)

If you are interested check out:
arxiv.org/pdf/2007.02113…
I would be bold and say that the groundbreaking work in the field of rough volatility is going to change the way we model volatility (both for pricing and trading).

I think that vol traders should definitely take this research field seriously (especially with crypto modeling)

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# More from @VolQuant

1 Jun

While most option/derivatives books have already been covered by others, I thought of comprising a list of "Essential Quants" for volatility trading
Few thing before we begin:

1. the list is broken down into Quant All-Star team (equivalent of best pound-for-found in boxing), and major league quants (essential reading, but more topic specific)

2. the list is in random order. Everyone on this list influenced my work
and way of thinking about vol trading and pricing, so they are well deserved of acknowledgement

3. I left out the OGs of Quant Finance - Bachelier, Black & Scholes

4. Only a fraction of them has a Twitter account, so go and follow those who have (assuming they are active)
14 May
FX/Commodity Correlation -

One thing that I like playing in FX space is commodity beta currencies, as they tend to have various source of risks to fuel their volatility (both RV and IV)... currencies like EM commodity producing (ZAR, MXN, RUB, BRL) and DM (CAD, NOK, AUD, NZD)
are always the places where you can find both idiosyncratic monetary policy risks (see hawkish BoC/Norges Bank), and commodity driven price action...

The most noticeable currency on my vol radar right now is CAD for the two reasons mentioned above
1. BoC turned quite hawkish on its last meeting, but very likely to play down further CAD strength in its next meeting (after the next two CPI/Payroll reading prior to its July 14th meeting)

2. Some decent unwinding in commodity complex going on, which drives down oil prices
8 May
Lessons from the Boxing Gym - Never skip a "Leg Day"

One thing that you learn early on in boxing is that you should never skip a "leg workout". I'm not necessarily talking about lower body strength but rather the general concept of training the basics and fundamentals
You can see many fancy pad flows and mitt works/combos on IG/TikTok, but at the end of the day these are the fundamentals that win round and do the work of win fights. Basic head movement, footwork, jabs and consistency go a long way in putting you in a position of strength.
When I train (and work with fighters) I dedicate a significant amount of time to working the fundamentals (hell, I occasionally train for about 30min just working the jab on the heavy bag...), as sharpening the basics will make a huge difference in the ring
4 May
Risk today feels bit on the soft side, and while I have literally no clue whatsoever whether this is going to develop into a sell-off today or not there are few things that worth keeping an eye on:

1. USDJPY vol has been outperforming implieds for about a week now...
when you see this kind of dynamic it's definitely a good sign for risk. wider trading range of USDJPY = more volatile USD/ TYs

2. SGD realized x2 move compared its 1m vol. We are talking about a currency that almost never moves

3. very weak HY currencies (EM, commodity G10)
4. FX vols coming of a somewhat low base, which means that gamma is cheap to own (short gamma more painful, less buffers)

5. Inflation expectations creeping higher w/ commodities but treasury yields are somewhat low
10 Apr
While most of the people on my twitter feed are all about the next 5-10pts in ES and vanna/charm/gamma squeeze (or anything else which is the flavor of the month), very few look at a pretty big thing that can (and should) be alarming - China shadow banking
This "little" problem is something that unlike other crises, is an ongoing bubble-like train wrack that the CCP has to carefully deflate, so every few months they deleverage a bit more.

In 2015 they had to deleverage their stock market after a boom of margin retail accounts
that sent their stocks to the moon (think today's US market on steroids). After that they had to devalue their currency, which global markets really didn't like.

After that they kept on letting thousands of companies to under in a controlled way, and occasionally drained
8 Apr
One of the biggest misconception in boxing is that the southpaw stance indicates left-hand domination (@Ksidiii should know a thing or two about that...)

Ex-soviet union coaches (Cubans are actually known for the overwhelming portion of southpaw fighters) teach from young age
boxers to fight in a southpaw stance, and I can assure you that most of them are right-hand dominant.

So you are probably asking how this is all has to do with trading, right?

Very much like in boxing, experimenting different strategies/models/market helps you develop arsenal
of tools that can become handy under different market regimes...

I'm an orthodox fighter, so my default stance a leading left hand, but I do train at least twice/week in a southpaw stance to be able working both stances. This helps me become more versatile as a fighter