The edge in details

Behind the code

At the core of our innovative approach, a key focal point is the development of a volatility model tailored for each asset pair. This foundational work sets the stage for more advanced tactics, especially when we incorporate Monte Carlo simulations to anticipate potential price trajectories. Our volatility model unlocks a wealth of insights, ranging from option pricing, profit forecasts, to visual depictions of liquidity pool boundaries and associated probabilities.

Volatility model with GBM

One widespread assumption in forecasting asset prices is their propensity to align with a log-normal distribution through the lens of Geometric Brownian Motion (GBM).

The conventional formula is:

$$X_t = \exp\left[\left(\mu - \frac{\sigma^2}{2}\right) t + \sigma Z_t\right], \quad t \in [0, \infty)$$

where: 𝜇 = drift 𝜎 = variance 𝑍 = standard Brownian Motion

While this GBM-centric view is often accurate for numerous scenarios, it's essential to note its limitations. Real-world asset price fluctuations sometimes stray from this model, especially during events caused by leverage-effects, unexpected market anomalies, other forms of liquidity shortages, and intentional market manipulations. These deviations challenge the GBM's assumption of a log-normal distribution in asset price movements, especially in smaller timeframes.

Beyond the Bounds of GBM

Why the persistent reliance on GBM, despite its limitations? At its heart, GBM often hits the mark—its utility lies in its general accuracy. The succinct reason? Sheer convenience. Other factors playing into GBM's continued use encompass computational efficiency, its integration into derivative pricing dynamics, and its established historical standing. Take, for instance, the use of Black-Scholes with GBM in Bitcoin options pricing. The appeal here is that integrating GBM often results in lower option prices for buyers compared to other distributions. Market makers (mostly there are options sellers), ever savvy, frequently hedge these risks. Offering a marginally reduced option price might seem counterintuitive, but with the right hedging, it remains a sound strategy—particularly when the profit model revolves around offering liquidity rather than direct trading.

It's pivotal to highlight that seasoned financial experts recognize GBM's constraints. Many craft bespoke volatility models tailored to distinct scenarios—much like our approach. We're building on this foundation, optimizing for our specific needs.

Introducing GARCH and its variations

While GBM has its merits, it isn't without flaws. The financial world has responded with a slew of other volatility models better attuned to the nuances of asset price behaviors. Enter GARCH and its offshoots. Each GARCH variation tailors to specific assets and market climates.

It's crucial to delineate GBM from GARCH: the former is a distribution, the latter a volatility model. This distinction permits GBM's pairing with GARCH, should one desire.

Our task? Selecting a volatility model and its distribution. This selection evolves through empirical testing, market insight, and robust viewpoints, ensuring our model stays updated with market nuances. Our current selection? The GARCH(1,1) variant combined with the skewed student-t distribution.

In brief, GARCH(1,1) is defined as:

$$\sigma_{t}^{2}=\omega+\alpha_{1}\varepsilon_{t-1}^{2}+\beta_{1}\sigma_{t-1}^{2}$$

and Skewed Student-t Distribution is express in terms of density function as:

$$\begin{split}f\left(x|\eta,\lambda\right)=\begin{cases} bc\left(1+\frac{1}{\eta-2}\left(\frac{a+bx}{1-\lambda}\right)^{2}\right) ^{-\left(\eta+1\right)/2}, & x<-a/b,\\ bc\left(1+\frac{1}{\eta-2}\left(\frac{a+bx}{1+\lambda}\right)^{2}\right) ^{-\left(\eta+1\right)/2}, & x\geq-a/b, \end{cases}\end{split}$$

Diving into derivations isn't our focus now, given these formulas' ubiquity. Instead, let's unpack the virtues of GARCH(1,1) and the Skewed student-t distribution.

The GARCH(1,1) model sheds light on the phenomenon of volatility clustering, which is commonly observed in financial assets. In essence, when a significant price shift occurs, it is likely to be followed by another similarly large shift. The notation (1,1) signifies that this model relies on a single time step for predicting volatility at the next time step.

The Skewed Student-t distribution indicates that substantial price shifts tend to favor negative (or positive, depending on the skew) price changes. Additionally, this distribution typically exhibits 'fat tails' signifying that major price shifts (greater than 3 standard deviations from the mean) occur more frequently than what the Geometric Brownian Motion (GBM) model might suggest.

By using historical data to estimate model parameters, we derive the constants necessary for generating price path patterns. When combined with Monte Carlo methods and continuous monitoring of changing market conditions, this approach allows us to aim for optimal forecasts of price path probabilities. We will continually update our analysis, adjusting our volatility model and distribution selections to adapt to evolving market dynamics.

Unpacking Our Competitive Edge

What we term as our "edge" stands out predominantly against the backdrop of retail traders less versed in financial mathematics. However, the sheer power of quantitative methods is realized only when wielded correctly, and that's our forte.

By harnessing our collective insights, borrowing wisdom from the traditional finance sector, and crafting user-friendly tools, we simplify the complex. While the math acts as the backbone, our nuanced perspective of the market and perpetual hunt for inefficiencies truly craft the edge. It's this synergy that elevates our community's prowess in crypto trading.