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@justinhou95
Created March 28, 2023 09:25
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{
"cells": [
{
"cell_type": "code",
"execution_count": 46,
"id": "Emjzvl3dVbIv",
"metadata": {
"id": "Emjzvl3dVbIv"
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import torch"
]
},
{
"cell_type": "code",
"execution_count": 47,
"id": "9v-kbi1hVbIw",
"metadata": {
"id": "9v-kbi1hVbIw",
"outputId": "d9515c27-2976-47c7-e024-59f252de1483"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Default device: cpu\n"
]
}
],
"source": [
"torch.manual_seed(42)\n",
"DEVICE = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
"print(\"Default device:\", DEVICE)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "u_XyKvKdVbIw",
"metadata": {
"id": "u_XyKvKdVbIw"
},
"outputs": [],
"source": [
"# In each epoch, N_PATHS brownian motion time-series are generated.\n",
"N_PATHS = 50000\n",
"# How many times a model is updated in the experiment.\n",
"N_EPOCHS = 200"
]
},
{
"cell_type": "markdown",
"id": "vG-uYllrVbIx",
"metadata": {
"id": "vG-uYllrVbIx",
"tags": []
},
"source": [
"### Financial models"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "Ux6BCwEaVbIy",
"metadata": {
"id": "Ux6BCwEaVbIy",
"outputId": "8ef5fba5-3f21-4fb0-cf1f-76f937d57df0"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'_buffers': OrderedDict(), 'sigma': 0.2, 'mu': 0.0, 'cost': 0.0, 'dt': 0.004, 'dtype': None, 'device': None}\n"
]
},
{
"data": {
"text/plain": [
"torch.Size([50000, 101])"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from pfhedge.instruments import BrownianStock\n",
"stock_GBM = BrownianStock()\n",
"print(stock_GBM.__dict__)\n",
"\n",
"stock_GBM.simulate(n_paths=N_PATHS, time_horizon = 100 / 250, init_state=(1.0,))\n",
"paths_GBM = stock_GBM.spot\n",
"\n",
"plt.plot(paths_GBM[:10].T)\n",
"plt.grid()\n",
"paths_GBM.shape"
]
},
{
"cell_type": "markdown",
"id": "55b7e6c1",
"metadata": {},
"source": [
"### Financial Derivatives"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "b05586a7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'pricer': None, 'cost': 0.0, '_clauses': OrderedDict(), '_underliers': OrderedDict([('underlier', BrownianStock(sigma=0.2000, dt=0.0040))]), 'call': True, 'strike': 1.0, 'maturity': 0.08}\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from pfhedge.instruments import EuropeanOption\n",
"EuropeanCallOption = EuropeanOption(stock_GBM)\n",
"print(EuropeanCallOption.__dict__)\n",
"\n",
"\n",
"EuropeanCallOption.simulate(N_PATHS)\n",
"payoff = EuropeanCallOption.payoff_fn()\n",
"underlying = EuropeanCallOption.ul()\n",
"prices = underlying.spot[:,-1]\n",
"plt.scatter(prices,payoff)\n",
"plt.grid()\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "57RladX7VbIz",
"metadata": {
"id": "57RladX7VbIz"
},
"source": [
"### Hedgers"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "TehxEXcXVbIz",
"metadata": {
"id": "TehxEXcXVbIz"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/homebrew/Caskroom/miniforge/base/envs/env_torch/lib/python3.8/site-packages/torch/nn/modules/lazy.py:178: UserWarning: Lazy modules are a new feature under heavy development so changes to the API or functionality can happen at any moment.\n",
" warnings.warn('Lazy modules are a new feature under heavy development '\n"
]
}
],
"source": [
"from pfhedge.nn import Hedger\n",
"from pfhedge.nn import MultiLayerPerceptron\n",
"\n",
"model = MultiLayerPerceptron()\n",
"hedger = Hedger(model, inputs=[\"log_moneyness\", \"expiry_time\", \"volatility\"])\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "4cdb42d6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"MultiLayerPerceptron(\n",
" (0): LazyLinear(in_features=0, out_features=32, bias=True)\n",
" (1): ReLU()\n",
" (2): Linear(in_features=32, out_features=32, bias=True)\n",
" (3): ReLU()\n",
" (4): Linear(in_features=32, out_features=32, bias=True)\n",
" (5): ReLU()\n",
" (6): Linear(in_features=32, out_features=32, bias=True)\n",
" (7): ReLU()\n",
" (8): Linear(in_features=32, out_features=1, bias=True)\n",
" (9): Identity()\n",
")"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "9201cc49",
"metadata": {},
"outputs": [],
"source": [
"# compute hedge\n",
"hedges = []\n",
"for t in range(10):\n",
" inputs = hedger.inputs.of(EuropeanCallOption, hedger).get(t)\n",
" hedge = hedger.model(inputs)\n",
" hedges.append(hedge)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "6087801b",
"metadata": {},
"outputs": [],
"source": [
"# compute terminal wealth\n",
"wealth = 0\n",
"for t in range(10):\n",
" wealth += hedges[t][:,0,0]*(paths_GBM[:,t+1] - paths_GBM[:,t])\n",
"terminal_wealth = wealth - EuropeanCallOption.payoff_fn()"
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "07c49878",
"metadata": {},
"outputs": [],
"source": [
"# compute loss \n",
"from pfhedge.nn.functional import entropic_risk_measure\n",
"loss = entropic_risk_measure(terminal_wealth)"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "ohwFU1YtVbIz",
"metadata": {
"id": "ohwFU1YtVbIz",
"outputId": "2f5826cd-088d-4a6e-a041-8871268cfe69"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loss=0.0227: 100%|██████████| 200/200 [12:30<00:00, 3.75s/it]\n"
]
}
],
"source": [
"history = hedger.fit(EuropeanCallOption, n_epochs=N_EPOCHS, n_paths=N_PATHS, n_times=20)"
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "3Vl3wXCoVbI0",
"metadata": {
"id": "3Vl3wXCoVbI0",
"outputId": "3935e914-cfda-4a15-85d3-10b50e2feb42"
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(history)\n",
"plt.xlabel(\"Number of epochs\")\n",
"plt.ylabel(\"Loss (entropic risk measure)\")\n",
"plt.title(\"Loss histories for a European option\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "9wgWwZ4gVbI0",
"metadata": {
"id": "9wgWwZ4gVbI0",
"outputId": "c8924550-f35e-488a-e96b-7e30131676da"
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def to_numpy(tensor: torch.Tensor) -> np.array:\n",
" return tensor.detach().numpy()\n",
"\n",
"derivative = EuropeanCallOption\n",
"pnl = hedger.compute_pnl(derivative, n_paths=50000)\n",
"\n",
"plt.figure()\n",
"plt.hist(to_numpy(pnl), bins=100)\n",
"plt.title(\"Profit-loss histograms of 50000 price paths for a European option\")\n",
"plt.xlabel(\"Profit-loss\")\n",
"plt.ylabel(\"Number of events\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 59,
"id": "p4b-g77pVbI0",
"metadata": {
"id": "p4b-g77pVbI0",
"outputId": "19483d22-fa1f-44b6-fd6e-d30e18506cf1"
},
"outputs": [
{
"data": {
"text/plain": [
"tensor(0.0220)"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"price = hedger.price(derivative)\n",
"price"
]
},
{
"cell_type": "markdown",
"id": "9zan7H7HVbI0",
"metadata": {
"id": "9zan7H7HVbI0"
},
"source": [
"### Black-Scholes' Delta-Hedging Strategy"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "J7HLpbJ0VbI0",
"metadata": {
"id": "J7HLpbJ0VbI0"
},
"outputs": [],
"source": [
"from pfhedge.nn import Hedger\n",
"from pfhedge.nn import BlackScholes\n",
"\n",
"model = BlackScholes(derivative)\n",
"hedger = Hedger(model, inputs=model.inputs()).to(DEVICE)"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "u6aFbxKVVbI1",
"metadata": {
"id": "u6aFbxKVVbI1",
"outputId": "95ab4532-10ec-4c68-f496-44c3a7fa3db6"
},
"outputs": [
{
"data": {
"text/plain": [
"Hedger(\n",
" inputs=['log_moneyness', 'time_to_maturity', 'volatility']\n",
" (model): BSEuropeanOption(strike=1.)\n",
" (criterion): EntropicRiskMeasure()\n",
")"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hedger"
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "NHUiF-e9VbI1",
"metadata": {
"id": "NHUiF-e9VbI1",
"outputId": "ad72e423-3ff7-4745-c3ae-e21744186411"
},
"outputs": [
{
"data": {
"text/plain": [
"tensor(0.0225)"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"price = hedger.price(derivative)\n",
"price"
]
},
{
"cell_type": "markdown",
"id": "PuqzFXxLVbI1",
"metadata": {
"id": "PuqzFXxLVbI1"
},
"source": [
"### Whalley-Wilmott's Asymptotically Optimal Strategy for Small Costs"
]
},
{
"cell_type": "code",
"execution_count": 63,
"id": "UrGQCSFvVbI1",
"metadata": {
"id": "UrGQCSFvVbI1"
},
"outputs": [],
"source": [
"from pfhedge.nn import Hedger\n",
"from pfhedge.nn import WhalleyWilmott\n",
"\n",
"model = WhalleyWilmott(derivative)\n",
"hedger = Hedger(model, inputs=model.inputs()).to(DEVICE)"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "3SivUT4CVbI1",
"metadata": {
"id": "3SivUT4CVbI1",
"outputId": "5910d635-c60c-4801-86d9-40d39e1e5e96"
},
"outputs": [
{
"data": {
"text/plain": [
"tensor(0.0225)"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"price = hedger.price(derivative)\n",
"price"
]
},
{
"cell_type": "markdown",
"id": "nXMboQaTVbI1",
"metadata": {
"id": "nXMboQaTVbI1"
},
"source": [
"### Your Own Module"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "3g24O-XwVbI1",
"metadata": {
"id": "3g24O-XwVbI1"
},
"outputs": [],
"source": [
"import torch.nn.functional as fn\n",
"from torch import Tensor\n",
"from torch.nn import Module\n",
"\n",
"from pfhedge.nn import BlackScholes, Clamp, MultiLayerPerceptron\n",
"\n",
"\n",
"class NoTransactionBandNet(Module):\n",
" def __init__(self, derivative):\n",
" super().__init__()\n",
" self.delta = BlackScholes(derivative)\n",
" self.mlp = MultiLayerPerceptron(out_features=2)\n",
" self.clamp = Clamp()\n",
"\n",
" def inputs(self):\n",
" return self.delta.inputs() + [\"prev_hedge\"]\n",
"\n",
" def forward(self, input: Tensor) -> Tensor:\n",
" prev_hedge = input[..., [-1]]\n",
" delta = self.delta(input[..., :-1])\n",
" width = self.mlp(input[..., :-1])\n",
"\n",
" min = delta - fn.leaky_relu(width[..., [0]])\n",
" max = delta + fn.leaky_relu(width[..., [1]])\n",
" return self.clamp(prev_hedge, min=min, max=max)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "NJs7gsZpVbI1",
"metadata": {
"id": "NJs7gsZpVbI1"
},
"outputs": [],
"source": [
"model = NoTransactionBandNet(derivative)\n",
"hedger = Hedger(model, inputs=model.inputs())"
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "feitwJgrVbI1",
"metadata": {
"id": "feitwJgrVbI1",
"outputId": "7d1f0f81-605a-4cb8-e5fb-8ffecaf5a406"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loss=0.0226: 100%|██████████| 200/200 [16:55<00:00, 5.08s/it]\n"
]
}
],
"source": [
"history = hedger.fit(derivative, n_epochs=N_EPOCHS, n_paths=N_PATHS, n_times=20)"
]
},
{
"cell_type": "code",
"execution_count": 68,
"id": "EVxGawUZVbI2",
"metadata": {
"id": "EVxGawUZVbI2",
"outputId": "0e173cb6-ccf7-40d0-9902-a31a09f486e7"
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(history)\n",
"plt.xlabel(\"Number of epochs\")\n",
"plt.ylabel(\"Loss (entropic risk measure)\")\n",
"plt.title(\"Loss histories for a European option\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "p6Gz7zlGVbI2",
"metadata": {
"id": "p6Gz7zlGVbI2",
"outputId": "71acf86a-20cb-4d9f-a0de-44829f077a31"
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pnl = hedger.compute_pnl(derivative, n_paths=50000)\n",
"\n",
"plt.figure()\n",
"plt.hist(to_numpy(pnl), bins=100)\n",
"plt.title(\"Profit-loss histograms of 50000 price paths for a European option\")\n",
"plt.xlabel(\"Profit-loss\")\n",
"plt.ylabel(\"Number of events\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "OEvjCsiqVbI2",
"metadata": {
"id": "OEvjCsiqVbI2",
"outputId": "d0f8e772-4421-4625-9744-e032c2dbf0ef"
},
"outputs": [
{
"data": {
"text/plain": [
"tensor(0.0225)"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"price = hedger.price(derivative)\n",
"price"
]
},
{
"cell_type": "markdown",
"id": "Z9tyImh7VbI2",
"metadata": {
"id": "Z9tyImh7VbI2"
},
"source": [
"### Use Expected Shortfall as a Loss function"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "i_OYydw4VbI2",
"metadata": {
"id": "i_OYydw4VbI2"
},
"outputs": [],
"source": [
"from pfhedge.nn import ExpectedShortfall"
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "mTrsZ4XdVbI2",
"metadata": {
"id": "mTrsZ4XdVbI2"
},
"outputs": [],
"source": [
"# Expected shortfall with the quantile level of 10%\n",
"expected_shortfall = ExpectedShortfall(0.1)\n",
"\n",
"model = NoTransactionBandNet(derivative)\n",
"hedger = Hedger(model, inputs=model.inputs(), criterion=expected_shortfall).to(DEVICE)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "HZWV0zItVbI2",
"metadata": {
"id": "HZWV0zItVbI2",
"outputId": "04c351f8-07e1-4bca-fa22-738654b48ff2"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loss=0.0305: 100%|██████████| 200/200 [10:04<00:00, 3.02s/it]\n"
]
}
],
"source": [
"history = hedger.fit(derivative, n_epochs=N_EPOCHS, n_paths=N_PATHS, n_times=20)"
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "SYVLG6AdVbI2",
"metadata": {
"id": "SYVLG6AdVbI2",
"outputId": "0e9165b1-6e05-41bf-9299-78b9dde67b06"
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(history)\n",
"plt.xlabel(\"Number of epochs\")\n",
"plt.ylabel(\"Loss (entropic risk measure)\")\n",
"plt.title(\"Loss histories for a European option\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 75,
"id": "KhDkx8TEVbI2",
"metadata": {
"id": "KhDkx8TEVbI2",
"outputId": "06e5a954-de6e-4387-fa19-46c6f98ea27a"
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pnl = hedger.compute_pnl(derivative, n_paths=50000)\n",
"\n",
"plt.figure()\n",
"plt.hist(to_numpy(pnl), bins=100)\n",
"plt.title(\"Profit-loss histograms of 50000 price paths for a European option\")\n",
"plt.xlabel(\"Profit-loss\")\n",
"plt.ylabel(\"Number of events\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 76,
"id": "DTOsHByWVbI2",
"metadata": {
"id": "DTOsHByWVbI2",
"outputId": "b9e459e3-7e1d-4006-b234-c68f1f2771d4"
},
"outputs": [
{
"data": {
"text/plain": [
"tensor(0.0299)"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"price = hedger.price(derivative)\n",
"price"
]
}
],
"metadata": {
"colab": {
"name": "example_readme.ipynb",
"provenance": []
},
"interpreter": {
"hash": "c186b54c8cf1ccf367fb8bdf3e071efe85839a5daed090332edb040d14e1fa50"
},
"kernelspec": {
"display_name": "Python [conda env:env_torch] *",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.16"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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