Arbitrage Trading Decision Model

 

                                                   Directly taken from my Kaggle notebook

The formula can be adapted into an arbitrage-trading decision model like below, but by itself it is not an arbitrage formula.

$$R(t)=R_{\max}m(t) =\frac{R_{\max}}{7}\sum_{i=1}^{7}s_i(t)$$

where the 7 signals $s_i(t)$ are normalized signals and $R(t)$ is a dynamically calculated risk/reward/allocation value.

For arbitrage, I would use the same concept like this:

$$A(t)=\frac{1}{7}\sum_{i=1}^{7}s_i(t)$$

where the signals could be:

1. Price spread

2. Bid/ask spread

3. Trading fees

4. Slippage

5. Market liquidity

6. Transfer/settlement latency

7. Historical spread reliability

Then calculate the actual arbitrage profit:

$$P_{\text{arb}}= Q(P_{\text{sell}}-P_{\text{buy}}) -F_{\text{buy}}-F_{\text{sell}} -S_{\text{buy}}-S_{\text{sell}} -C_{\text{transfer}}$$

and the net arbitrage percentage:

$$ROI_{\text{arb}}= \frac{P_{\text{arb}}}{Q P_{\text{buy}}}\times100$$

For example:

Parameter	Exchange A	Exchange B
Buy price	$100,000	—
Sell price	—	$100,800
Quantity	0.10 BTC	0.10 BTC
Gross spread		$80

Gross profit:

$$0.10(100800-100000)=\$80$$

Suppose total fees + slippage + other costs = $35:

$$P_{\text{net}}=80-35=\boxed{\$45}$$

So:

$$ROI=\frac{45}{10000}\times100=\boxed{0.45\%}$$

Then your 7-signal formula can decide whether to execute:

$$A(t)= \frac{ s_{spread}+s_{fee}+s_{slippage}+s_{liquidity}+s_{latency}+s_{reliability}+s_{volatility} }{7}$$

For example, if the normalized signals are:

$$[0.9,0.8,0.7,0.85,0.6,0.9,0.75]$$

then:

$$A(t)=0.786$$

You could define:

$$\boxed{\text{Execute if } P_{\text{net}}>0 \text{ AND } A(t)>0.75}$$

This becomes much more interesting when you're thinking about an actual AI/ML arbitrage system: the 7-signal surface can become a dynamic execution score, while the deterministic pricing equation guarantees that you don't execute trades where fees, slippage and latency eliminate the arbitrage.

You can find the full Kaggle notebook here