use of aleatory processes to price qablet contracts

aleatory/processes/base_eu.py

@@ -38,5 +38,22 @@ def _sample_em_process(self, n, log=False):
 
         return path
 
+    def start(self, initial):
+        """Set an initial state for all paths. initial can be a scalar or a numpy array."""
+        self.val = initial
+        self.cur_time = 0.0
+
+    def advance(self, t):
+        """Advance the process to time t, for all paths."""
+        dt = t - self.cur_time
+        if dt < 1e-10:
+            return
+        # Generate the Brownian increments, for all paths at time t
+        dws = self.rng.normal(scale=np.sqrt(dt), size=self.val.shape)
+
+        # update val for all paths
+        self.val += self.f(self.val, t) * dt + self.g(self.val, t) * dws
+        self.cur_time = t
+
     def sample(self, n):
         return self._sample_em_process(n)

requirements.txt

@@ -3,4 +3,7 @@ numpy>=1.23.5
 scipy>=1.10.0
 matplotlib>=3.6.2
 statsmodels>=0.13.5
-parameterized>=0.8.1
+parameterized>=0.8.1
+qablet_contracts>=0.2.2
+qablet-basic>=0.3.2
+pyarrow>=13.0.0

tests/test_advance.py

@@ -0,0 +1,33 @@
+from aleatory.processes import CEVProcess
+import unittest
+import numpy as np
+
+
+class TestAdvance(unittest.TestCase):
+    def test_advance_method(self):
+        cev = CEVProcess()
+
+        cev.start(np.zeros(5))
+        for t in np.arange(0.1, 1.01, 0.1):
+            cev.advance(t)
+            print(cev.val)
+
+
+if __name__ == "__main__":
+    unittest.main()
+
+"""
+Output:
+
+[0.07483507  0.06892834  0.0103775   0.08222023 -0.00520991]
+[0.1242685  0.09343143 0.0547229  0.04053699 0.07427636]
+[0.19546715 0.1776751  0.09312892 0.07602916 0.09573145]
+[0.2762749  0.25656871 0.17613864 0.12536773 0.09022976]
+[0.29868798 0.33389956 0.28908409 0.15776951 0.09993488]
+[0.40701358 0.45013018 0.30473939 0.23695351 0.16412336]
+[0.47892648 0.54385911 0.3692668  0.29175553 0.20496346]
+[0.57069992 0.66287047 0.40147713 0.33604199 0.20004954]
+[0.58912079 0.73014259 0.45835246 0.37663655 0.22481997]
+[0.63629761 0.7450066  0.50876839 0.42058831 0.32175386]
+
+"""

tests/test_qablet.py

@@ -0,0 +1,132 @@
+"""
+Create a Qablet model using the CEV Process, and use it to price vanilla options and accumulators.
+"""
+
+from aleatory.processes import CEVProcess
+import unittest
+import numpy as np
+from datetime import datetime
+import pandas as pd
+
+from qablet.base.mc import MCModel, MCStateBase
+from qablet_contracts.eq.vanilla import Option
+from qablet_contracts.eq.cliquet import Accumulator
+from qablet_contracts.timetable import py_to_ts
+from qablet.base.utils import Forwards
+
+
+class CEVModelState(MCStateBase):
+    """A Qablet Model based on alreatory.processes.CEVProcess."""
+
+    def __init__(self, timetable, dataset):
+        super().__init__(timetable, dataset)
+        # Initialize the model parameters
+        self.N = dataset["MC"]["PATHS"]
+        self.asset = dataset["CEV"]["ASSET"]
+        self.asset_fwd = Forwards(dataset["ASSETS"][self.asset])
+        self.spot = self.asset_fwd.forward(0)
+        # Create the CEV process
+        self.cev = (
+            CEVProcess()
+        )  # TODO: Set the drift and volatility based on parameters
+        self.cev.start(np.zeros(self.N))
+
+    def advance(self, new_time):
+        self.cev.advance(new_time)
+
+    def get_value(self, unit):
+        if unit == self.asset:
+            return self.spot * np.exp(self.cev.val)
+
+
+class CEVModel(MCModel):
+    def state_class(self):
+        return CEVModelState
+
+
+#
+# Use above model to test the pricing of vanilla options and accumulators
+#
+class TestContracts(unittest.TestCase):
+    def setUp(self):
+        """Setup the dataset needed for the pricing model."""
+        pricing_dt = datetime(2023, 12, 31)
+        times = np.array([0.0, 5.0])
+        rates = np.array([0.04, 0.04])
+        discount_data = ("ZERO_RATES", np.column_stack((times, rates)))
+
+        self.spot = 5000.0
+        div_rate = 0.01
+        fwds = self.spot * np.exp((rates - div_rate) * times)
+        fwd_data = ("FORWARDS", np.column_stack((times, fwds)))
+
+        self.dataset = {
+            "BASE": "USD",
+            "PRICING_TS": py_to_ts(pricing_dt).value,
+            "ASSETS": {"USD": discount_data, "SPX": fwd_data},
+            "MC": {
+                "PATHS": 10_000,
+                "TIMESTEP": 1 / 250,
+                "SEED": 1,
+            },
+            "CEV": {
+                "ASSET": "SPX",
+            },
+        }
+
+        self.model = CEVModel()
+
+    def test_option(self):
+        """Test the pricing of vanilla options."""
+
+        print("Testing vanilla options")
+        for x in [0.5, 1.0, 1.5]:
+            strike = self.spot * x
+            timetable = Option(
+                "USD",
+                "SPX",
+                strike=strike,
+                maturity=datetime(2024, 12, 31),
+                is_call=True,
+            ).timetable()
+            price, _ = self.model.price(timetable, self.dataset)
+
+            print(f"strike: {strike:6.0f} price: {price:11.6f}")
+
+    def test_accumulator(self):
+        """Test the pricing of an accumulator."""
+        print("Testing Accumulator")
+
+        for local_cap in [0.01, 0.02, 0.03]:
+            fix_dates = pd.bdate_range(
+                datetime(2023, 12, 31), datetime(2024, 12, 31), freq="1BQE"
+            )
+            timetable = Accumulator(
+                "USD",
+                "SPX",
+                fix_dates,
+                0.0,
+                local_floor=-local_cap,
+                local_cap=local_cap,
+            ).timetable()
+            price, _ = self.model.price(timetable, self.dataset)
+
+            print(f"cap/floor: {local_cap:6.3f} price: {price:11.6f}")
+
+
+if __name__ == "__main__":
+    unittest.main()
+
+"""
+Output of test_option:
+
+Testing Accumulator
+cap/floor:  0.010 price:    2.790405
+cap/floor:  0.020 price:    5.575411
+cap/floor:  0.030 price:    8.314456
+.Testing vanilla options
+strike:   2500 price: 5538.443450
+strike:   5000 price: 3138.557753
+strike:   7500 price:  802.604143
+
+"""