├── .gitignore ├── power_perp.py ├── gbm.py ├── test_gbm.py ├── black_scholes.py ├── test_pricing.py └── power_perp_prices.ipynb /.gitignore: -------------------------------------------------------------------------------- 1 | venv 2 | .idea 3 | .ipynb_checkpoints -------------------------------------------------------------------------------- /power_perp.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | 4 | def power_perp_price(spot, time, vol, drift, power): 5 | return spot ** power * np.exp( 6 | (power - 1) * (drift + power / 2 * vol ** 2) * time 7 | ) 8 | 9 | def everlasting_power_perp_price(spot, funding_period, vol, drift, power): 10 | return spot ** power * ( 11 | 1 / (2* np.exp(-funding_period/2 * (power - 1) * (2 * drift + power * vol **2)) - 1) 12 | ) 13 | -------------------------------------------------------------------------------- /gbm.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | 4 | def get_sample(spot, time, vol, drift): 5 | """Computes new price randomly based on price and volatility and updates""" 6 | rand = np.random.normal(loc=0.0, scale=1.0) 7 | 8 | return spot * np.exp( 9 | ((drift - (0.5 * (vol ** 2))) * time) + (vol * np.sqrt(time) * rand) 10 | ) 11 | 12 | 13 | def get_samples(num_samples, spot, time, vol, drift): 14 | return np.array([get_sample(spot, time, vol, drift) for _ in range(num_samples)]) -------------------------------------------------------------------------------- /test_gbm.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from gbm import * 3 | 4 | def test_gbm(): 5 | num_samples = 10000 6 | spot = 2 7 | time = 0.5 8 | vol = 0.8 9 | drift = 0.1 10 | samples = get_samples(num_samples,spot,time,vol,drift) 11 | 12 | avg = np.mean(samples) 13 | var = np.var(samples) 14 | 15 | expected_avg = spot*np.exp(drift*time) 16 | expected_var = (spot**2)*np.exp(2*drift*time)*(np.exp(vol**2*time) - 1) 17 | 18 | assert np.abs(avg - expected_avg)/expected_avg < 0.05, (avg, expected_avg) 19 | assert np.abs(var - expected_var)/expected_var < 0.05, (var, expected_var) 20 | 21 | 22 | if __name__ == "__main__": 23 | test_gbm() -------------------------------------------------------------------------------- /black_scholes.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | # from https://numba.pydata.org/numba-examples/examples/finance/blackscholes/results.html 4 | def cnd(d): 5 | A1 = 0.31938153 6 | A2 = -0.356563782 7 | A3 = 1.781477937 8 | A4 = -1.821255978 9 | A5 = 1.330274429 10 | RSQRT2PI = 0.39894228040143267793994605993438 11 | K = 1.0 / (1.0 + 0.2316419 * np.abs(d)) 12 | ret_val = (RSQRT2PI * np.exp(-0.5 * d * d) * 13 | (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))))) 14 | return np.where(d > 0, 1.0 - ret_val, ret_val) 15 | 16 | # SPEEDTIP: Despite the memory overhead and redundant computation, the above 17 | # is much faster than: 18 | # 19 | # for i in range(len(d)): 20 | # if d[i] > 0: 21 | # ret_val[i] = 1.0 - ret_val[i] 22 | # return ret_val 23 | 24 | 25 | def black_scholes(stockPrice, optionStrike, optionYears, Riskfree, Volatility): 26 | S = stockPrice 27 | X = optionStrike 28 | T = optionYears 29 | R = Riskfree 30 | V = Volatility 31 | sqrtT = np.sqrt(T) 32 | d1 = (np.log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT) 33 | d2 = d1 - V * sqrtT 34 | cndd1 = cnd(d1) 35 | cndd2 = cnd(d2) 36 | 37 | expRT = np.exp(- R * T) 38 | 39 | callResult = S * cndd1 - X * expRT * cndd2 40 | 41 | return callResult -------------------------------------------------------------------------------- /test_pricing.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from gbm import * 3 | from black_scholes import black_scholes 4 | from power_perp import power_perp_price, everlasting_power_perp_price 5 | 6 | # Demonstrate sampling gives the same result as black scholes 7 | def test_black_scholes(): 8 | num_samples = 10000 9 | spot = 2 10 | time = 0.5 11 | vol = 0.8 12 | drift = 0.2 13 | samples = get_samples(num_samples,spot,time,vol,drift) 14 | 15 | strike = spot * 1.1 16 | 17 | discounted_payoff = np.mean(np.maximum(samples-strike,0) * np.exp(time*drift*-1)) 18 | 19 | calced = black_scholes(spot, strike, time, drift, vol) 20 | 21 | assert np.abs(discounted_payoff - calced)/calced < 0.05, (discounted_payoff, calced) 22 | 23 | # Demonstrate our power perp pricing is the same as sampling 24 | def test_power_perp(): 25 | num_samples = 100000 26 | spot = 2 27 | time = 0.5 28 | vol = 1.2 29 | drift = 0.2 30 | power = 3 31 | samples = get_samples(num_samples,spot,time,vol,drift) 32 | 33 | discounted_payoff = np.mean(samples**power * np.exp(time*drift*-1)) 34 | 35 | calced = power_perp_price(spot, time, vol, drift, power) 36 | 37 | assert np.abs(discounted_payoff - calced)/calced < 0.05, (discounted_payoff, calced) 38 | 39 | def test_everlasting_power_perp(): 40 | spot = 2 41 | vol = 1.2 42 | drift = 0.2 43 | power = 3 44 | funding_period = 1/7 45 | 46 | num_iters = 1000 47 | est = 0 48 | for i in range(1,num_iters,1): 49 | est += power_perp_price(spot, i * funding_period, vol, drift, power) / 2**i 50 | 51 | calced = everlasting_power_perp_price(spot, funding_period, vol, drift, power) 52 | 53 | assert np.abs(est - calced)/est < 0.05, (est, calced) 54 | 55 | 56 | 57 | if __name__ == "__main__": 58 | test_everlasting_power_perp() 59 | 60 | for period in range(1,100): 61 | print((period,everlasting_power_perp_price(2,1/period,1.2,0,3))) -------------------------------------------------------------------------------- /power_perp_prices.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 2, 6 | "id": "35199322", 7 | "metadata": {}, 8 | "outputs": [], 9 | "source": [ 10 | "import numpy as np\n", 11 | "import matplotlib.pyplot as plt\n", 12 | "%matplotlib inline\n", 13 | "import seaborn as sbn\n", 14 | "import pandas as pd\n", 15 | "from matplotlib.pyplot import figure\n", 16 | "from itertools import cycle, islice\n", 17 | "from power_perp import everlasting_power_perp_price" 18 | ] 19 | }, 20 | { 21 | "cell_type": "code", 22 | "execution_count": 60, 23 | "id": "11e4a2a4", 24 | "metadata": {}, 25 | "outputs": [], 26 | "source": [ 27 | "vol = 1.5\n", 28 | "drift = 0\n", 29 | "funding_period = 1/365\n", 30 | "spot = np.arange(1000., 4000., 50.)" 31 | ] 32 | }, 33 | { 34 | "cell_type": "code", 35 | "execution_count": 61, 36 | "id": "89f04413", 37 | "metadata": {}, 38 | "outputs": [ 39 | { 40 | "data": { 41 | "text/plain": [ 42 | "Text(0.5, 1.0, 'Normalized ETH^2 Perpetual Price vs. Spot Price (150 vol)')" 43 | ] 44 | }, 45 | "execution_count": 61, 46 | "metadata": {}, 47 | "output_type": "execute_result" 48 | }, 49 | { 50 | "data": { 51 | "image/png": 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\n", 52 | "text/plain": [ 53 | "
" 54 | ] 55 | }, 56 | "metadata": { 57 | "needs_background": "light" 58 | }, 59 | "output_type": "display_data" 60 | } 61 | ], 62 | "source": [ 63 | "power = 2\n", 64 | "payoff = spot ** power / spot[0]**(power-1)\n", 65 | "price = everlasting_power_perp_price(spot, funding_period, vol, drift, power) / spot[0]**(power-1)\n", 66 | "\n", 67 | "data = pd.DataFrame({'spot ETH': spot, f'ETH^{power}': payoff, f'ETH^{power} perp price': price}).set_index('spot ETH')\n", 68 | "figure(figsize=(12, 9), dpi=80)\n", 69 | "ax = sbn.lineplot(data=data)\n", 70 | "ax.set_ylabel(\"value\")\n", 71 | "ax.set_title(f\"Normalized ETH^{power} Perpetual Price vs. Spot Price ({int(vol*100)} vol)\")" 72 | ] 73 | }, 74 | { 75 | "cell_type": "code", 76 | "execution_count": 63, 77 | "id": "bd5f6a2e", 78 | "metadata": {}, 79 | "outputs": [ 80 | { 81 | "data": { 82 | "text/plain": [ 83 | "Text(0.5, 1.0, 'Normalized ETH^3 Perpetual Price vs. Spot Price (150 vol)')" 84 | ] 85 | }, 86 | "execution_count": 63, 87 | "metadata": {}, 88 | "output_type": "execute_result" 89 | }, 90 | { 91 | "data": { 92 | "image/png": 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\n", 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" 95 | ] 96 | }, 97 | "metadata": { 98 | "needs_background": "light" 99 | }, 100 | "output_type": "display_data" 101 | } 102 | ], 103 | "source": [ 104 | "power = 3\n", 105 | "payoff = spot ** power / spot[0]**(power-1)\n", 106 | "price = everlasting_power_perp_price(spot, funding_period, vol, drift, power) / spot[0]**(power-1)\n", 107 | "\n", 108 | "data = pd.DataFrame({'spot ETH': spot, f'ETH^{power}': payoff, f'ETH^{power} perp price': price}).set_index('spot ETH')\n", 109 | "figure(figsize=(12, 9), dpi=80)\n", 110 | "ax = sbn.lineplot(data=data)\n", 111 | "ax.set_ylabel(\"value\")\n", 112 | "ax.set_title(f\"Normalized ETH^{power} Perpetual Price vs. Spot Price ({int(vol*100)} vol)\")" 113 | ] 114 | }, 115 | { 116 | "cell_type": "code", 117 | "execution_count": null, 118 | "id": "8b78f946", 119 | "metadata": {}, 120 | "outputs": [], 121 | "source": [] 122 | } 123 | ], 124 | "metadata": { 125 | "kernelspec": { 126 | "display_name": "Python 3", 127 | "language": "python", 128 | "name": "python3" 129 | }, 130 | "language_info": { 131 | "codemirror_mode": { 132 | "name": "ipython", 133 | "version": 3 134 | }, 135 | "file_extension": ".py", 136 | "mimetype": "text/x-python", 137 | "name": "python", 138 | "nbconvert_exporter": "python", 139 | "pygments_lexer": "ipython3", 140 | "version": "3.8.8" 141 | } 142 | }, 143 | "nbformat": 4, 144 | "nbformat_minor": 5 145 | } 146 | --------------------------------------------------------------------------------