Order Book

Uniswap V3 Simulation

Here we utilize UniswapPy to simulate an order book in Uniswap V3
Medium Article: How to Simulate a Uniswap V3 Order Book in Python
To download notebook to this tutorial, see here

📘 Notable Classes

Class: 📘 defipy.math.model.BrownianModel
- Purpose: Geometric Brownian process.
- Methods:
  - gen_gbms(mu: float, sigma: float, n_step: int, T: int = 1)
    - Parameters:
      - mu: asset drift (float).
      - sigma: asset volatility (int).
      - n_step: number of steps. (int).
      - T: time unit (optional) (int).
Class: 📘 defipy.math.model.TokenDeltaModel
- Purpose: Random sample of Gamma distribution representing an experimental token amount.
- Methods:
  - delta(p: int = 1)
    - Parameters:
      - p: buy/sell probability associated (buy = 1, sell = -1, optional) (int).
Class: 📘 defipy.analytics.simulate.CorrectReserves
- Purpose: Applies SolveDeltas to Correct x/y reserve amounts so that price reflects desired input price; in the marjority of cases, the input price would be the most recent outside market price .
- Methods:
  - delta(price: float, lwr_tick: int = None, upr_tick: int = None)
    - Parameters:
      - price: token price (int).
      - lwr_tick: Lower tick of the position. (optional) (int).
      - upr_tick: Upper tick of the position. (optional) (int).

from defipy import *
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

user_nm = MockAddress().apply()
eth_amount = 100
tkn_amount = 1000

fee = UniV3Utils.FeeAmount.MEDIUM
tick_spacing = UniV3Utils.TICK_SPACINGS[fee]

Simulate prices

Simulate prices using a geometric brownian motion process

n_steps = 1000
start_price = eth_amount/tkn_amount
mu = 0.1; sigma = 0.5
n_paths = 1

b = BrownianModel(start_price)
p_arr = b.gen_gbms(mu, sigma, n_steps, n_paths)
exp_p_arr = np.median(p_arr, axis = 1)

accounts = MockAddress().apply(50)

Setup pool

eth = ERC20("ETH", "0x09")
tkn = ERC20("TKN", "0x111")

exchg_data = UniswapExchangeData(tkn0 = eth, tkn1 = tkn, symbol="LP",
                                   address="0x011", version = 'V3',
                                   tick_spacing = tick_spacing,
                                   fee = fee)

factory = UniswapFactory("ETH pool factory", "0x2")
lp = factory.deploy(exchg_data)

lwr_tick = UniV3Helper().get_price_tick(lp, -1, 10, 1000)
upr_tick = UniV3Helper().get_price_tick(lp, 1, 10, 1000)

Join().apply(lp, user_nm, eth_amount, tkn_amount, lwr_tick, upr_tick)
lp.summary()

Exchange ETH-TKN (LP) Real Reserves: ETH = 96.70469739529014, TKN = 1000.0 Gross Liquidity: 6440.3320664241655

Simulate liquidity pool

arb = CorrectReserves(lp, x0 = 1/exp_p_arr[0])
p_intervals = [500, 800, 1000, 1200, 1500, 1700, 2000]
lp_prices = [lp.get_price(tkn)]
lp_liquidity = [lp.total_supply]
lp_swaps = []; lp_net_deposits = [];

for k in range(1, n_steps):
    p = 1/exp_p_arr[k]
    arb.apply(p, lwr_tick, upr_tick)

    select_tkn = EventSelectionModel().bi_select(0.5)
    rnd_add_amt = TokenDeltaModel(25).delta()
    rnd_swap_amt = TokenDeltaModel(15).delta()
    user_add = random.choice(accounts)
    user_swap = random.choice(accounts)

    p_interval = random.choice(p_intervals)
    lwr_tick = UniV3Helper().get_price_tick(lp, -1, lp.get_price(eth), p_interval)
    upr_tick = UniV3Helper().get_price_tick(lp, 1, lp.get_price(eth), p_interval)

    if(select_tkn == 0):
        AddLiquidity().apply(lp, eth, user_add, rnd_add_amt, lwr_tick, upr_tick)
        out = Swap().apply(lp, eth, user_swap, rnd_swap_amt)
    else:
        AddLiquidity().apply(lp, tkn, user_add, p*rnd_add_amt, lwr_tick, upr_tick)
        out = Swap().apply(lp, tkn, user_swap,  p*rnd_swap_amt)

    lp_prices.append(lp.get_price(tkn))
    lp_liquidity.append(lp.total_supply)
    lp_swaps.append(rnd_swap_amt)
    lp_net_deposits.append(rnd_add_amt)

lp.summary()

Exchange ETH-TKN (LP) Real Reserves: ETH = 153089.57969951717, TKN = 1063580.263806977 Gross Liquidity: 6723644.391607661

Construct order book

liquidity = {}
df_liq = pd.DataFrame(columns=['tick', 'price', 'liquidity'])
for k, pos in enumerate(lp.ticks):
    price = UniV3Helper().tick_to_price(pos)
    liq = lp.ticks[pos].liquidityGross/10**18
    df_liq.loc[k] = [pos,price,liq]

center_pos = UniV3Helper().price_to_tick(lp.get_price(eth))
price = lp.get_price(tkn)
df_liq.loc[k+1] = [center_pos,price,0]

df_liq.sort_values(by=['price'], inplace=True)
df_liq.reset_index(drop=True, inplace=True)

side_arr = []
for tick in df_liq['tick'].values:
    if (tick > center_pos):
        side_arr.append('asks')
    elif (tick < center_pos):
        side_arr.append('bids')
    else:
        side_arr.append('center')
df_liq['side'] = side_arr
idx = df_liq.index[df_liq['side'] == 'center']
df_liq.drop(idx[0], inplace=True)

df_liq

tick price liquidity side 1 15000.0 4.481353 21.875455 bids 2 15180.0 4.562744 2302.827924 bids 3 15300.0 4.617824 3.923965 bids 4 15360.0 4.645612 272.986987 bids 5 15540.0 4.729986 4858.284512 bids .. ... ... ... ... 166 25200.0 12.427031 742.064919 asks 167 25260.0 12.501813 474.771564 asks 168 25440.0 12.728872 447.693367 asks 169 25500.0 12.805471 457.990880 asks 170 25620.0 12.960055 366.017072 asks [170 rows x 4 columns]

Review simulation output

fig = plt.figure(figsize = (10, 5))

current_price = lp.get_price(tkn)
prices = 1/df_liq['price'].values
liquidity = df_liq['liquidity'].values

fig, (book_ax, price_ax, liq_ax) = plt.subplots(nrows=3, sharex=False, sharey=False, figsize=(12, 8))

book_ax.bar(prices, liquidity, color ='steelblue', width = 0.0005, label = 'liquidity', alpha=0.7)
book_ax.axvline(x=current_price, color = 'mediumvioletred', linewidth = 1, linestyle = 'dashdot', label = 'current price')
book_ax.set_xlabel("Price (USD)", size=10)
book_ax.set_ylabel("Liquidity", size=14)
book_ax.set_title("Uniswap V3: Liquidity distribution")
book_ax.legend()

x_val = np.arange(0,len(p_arr))
price_ax.plot(x_val[1:-1], p_arr[1:-1], color = 'r',linestyle = 'dashdot', label='market price')
price_ax.plot(x_val[1:-1], lp_prices[1:], color = 'b',linestyle = 'dashed', label='lp price')
price_ax.set_ylabel('Price (ETH/TKN)', size=14)
price_ax.set_xlabel('Time sample', size=10)
price_ax.legend()

liq_ax.plot(x_val[1:-1], lp_liquidity[1:], color = 'b',linestyle = 'dashed', label='lp liquidity')
liq_ax.set_ylabel('Liquidity', size=14)
liq_ax.set_xlabel('Time sample', size=10)
liq_ax.legend()
plt.tight_layout()

fig, ax = plt.subplots(1, 2, figsize=(12,5))

sns.distplot(lp_net_deposits, hist=True, kde=False, bins=int(30), color = 'darkblue',
             hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2}, ax=ax[0])

ax[0].set_title('Histogram: Net Deposit Volume')
ax[0].set_xlabel('Volume ETH')
ax[0].set_ylabel('Frequency')

sns.distplot(lp_swaps, hist=True, kde=False, bins=int(30), color = 'darkblue',
             hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2}, ax=ax[1])

ax[1].set_title('Histogram: Net Swap Volume')
ax[1].set_xlabel('Volume ETH')
ax[1].set_ylabel('Frequency')

Text(0, 0.5, 'Frequency')

Plot order book

fig, ax = plt.subplots(figsize = (10, 5))
ax.set_title(f"ETH/TKN Order Book - Scatterplot")
sns.scatterplot(x="price", y="liquidity", hue="side",
                data=df_liq, ax=ax, palette=["green", "red"])
ax.set_xlabel("Price (TKN/ETH)", fontsize = 14)
ax.set_ylabel("Liquidity", fontsize = 14)

Text(0, 0.5, 'Liquidity')

fig, ax = plt.subplots(figsize = (10, 5))
ax.set_title(f"ETH/TKN Order Book - Depth Chart")
sns.ecdfplot(x="price", weights="liquidity", stat="count",
             complementary=True, data=df_liq.query("side == 'bids'"),
             color="green", ax=ax)
sns.ecdfplot(x="price", weights="liquidity", stat="count",
             data=df_liq.query("side == 'asks'"), color="red",
             ax=ax)
ax.set_xlabel("Price (TKN/ETH)", fontsize = 14)
ax.set_ylabel("Liquidity", fontsize = 14)

Text(0, 0.5, 'Liquidity')