diff options
Diffstat (limited to 'utils/path.py')
| -rw-r--r-- | utils/path.py | 87 |
1 files changed, 58 insertions, 29 deletions
diff --git a/utils/path.py b/utils/path.py index 2fbb48f..41474ef 100644 --- a/utils/path.py +++ b/utils/path.py @@ -11,7 +11,9 @@ import math import random from copy import deepcopy from dataclasses import dataclass -from typing import List, Tuple +from typing import List, Sequence, Tuple + +from utils.misc import Number __all__ = ['PathGenerator'] @@ -24,14 +26,18 @@ class PathGenerator: Attributes ---------- - S : Spot price. - r : Risk-free interest rate. - div : Dividend yield. - vol : Volatility. - net_r : Net risk free rate. + S : Number + Spot price. + r : Number + Risk-free interest rate. + div : Number + Dividend yield. + vol : Number + Volatility. + net_r Methods - ---------- + ------- generate(T) Generate a random path {S_t1, S_t2, ..., S_tn}. generate_antithetic(T) @@ -39,42 +45,51 @@ class PathGenerator: [{S_t1, S_t2, ..., S_tn}, {S'_t1, S'_t2, ..., S'_tn}]. Examples - ---------- + -------- >>> from utils.path import PathGenerator >>> path = PathGenerator(S=100., r=0.1, div=0.01, vol=0.3) - >>> print(path.generate(T=range(4))) - [100.0, 100.33539853588853, 122.76017088387074, 142.29540684005462] - >>> print(path.generate(T=range(4))) - [100.0, 73.03094019139712, 77.37310245438943, 66.54240939439934] + >>> print(path) + PathGenerator(S=100.0, r=0.1, div=0.01, vol=0.3) """ - S: float - r: float - div: float - vol: float + S: Number + r: Number + div: Number + vol: Number @property def net_r(self) -> float: """Net risk free rate.""" - return self.r - self.div + return float(self.r - self.div) - def generate(self, T: List[float]) -> List[float]: + def generate(self, T: Sequence[Number]) -> List[float]: """ Generate a random path {S_t1, S_t2, ..., S_tn}. Parameters ---------- - T : Set of times {t1, t2, ..., tn} in years. + T : Sequence of Numbers + Set of times {t1, t2, ..., tn} in years. Returns - ---------- - spot_prices : Set of prices for the underlying {S_t1, S_t2, ..., S_tn}. + ------- + spot_prices : List of floats + Set of prices for the underlying {S_t1, S_t2, ..., S_tn}. + + Examples + -------- + >>> from utils.path import PathGenerator + >>> path = PathGenerator(S=100., r=0.1, div=0.01, vol=0.3) + >>> print(path.generate(T=range(4))) + [100.0, 100.33539853588853, 122.76017088387074, 142.29540684005462] + >>> print(path.generate(T=range(4))) + [100.0, 73.03094019139712, 77.37310245438943, 66.54240939439934] """ # Calculate dt time differences dts = [T[idx + 1] - T[idx] for idx in range(len(T) - 1)] - spot_prices = [0] * len(T) + spot_prices: List[float] = [0] * len(T) spot_prices[0] = self.S for idx, dt in enumerate(dts): # Calculate the drift e^{(r - (1/2) σ²) Δt} @@ -89,27 +104,41 @@ class PathGenerator: spot_prices[idx + 1] = S_t return spot_prices - def generate_antithetic(self, T: List[float]) -> Tuple[List[float], - List[float]]: + def generate_antithetic( + self, T: Sequence[Number] + ) -> Tuple[List[float], List[float]]: """ Generate a random plus antithetic path [{S_t1, S_t2, ..., S_tn}, {S'_t1, S'_t2, ..., S'_tn}]. Parameters ---------- - T : Set of times {t1, t2, ..., tn} in years. + T : Sequence of Numbers + Set of times {t1, t2, ..., tn} in years. Returns - ---------- - prices_tuple : Set of prices for the underlying - [{S_t1, S_t2, ..., S_tn}, {S'_t1, S'_t2, ..., S'_tn}]. + ------- + prices_tuple : Tuple of two Lists of floats + Set of prices for the underlying + [{S_t1, S_t2, ..., S_tn}, {S'_t1, S'_t2, ..., S'_tn}]. + + Examples + -------- + >>> from utils.path import PathGenerator + >>> path = PathGenerator(S=100., r=0.1, div=0.01, vol=0.3) + >>> print(path.generate_antithetic(T=range(4))) + ([100.0, 106.30304144532359, 122.02501765852367, 108.71120035365013], + [100.0, 102.92972513566257, 98.11245153613649, 120.49949282794978]) + >>> print(path.generate_antithetic(T=range(4))) + ([100.0, 130.1595970941697, 103.35241529329348, 93.58800177914543], + [100.0, 84.06404968460234, 115.83835362960282, 139.97140935058962]) """ # Calculate dt time differences dts = [T[idx + 1] - T[idx] for idx in range(len(T) - 1)] # Create data structures - spot_prices = [0] * len(T) + spot_prices: List[float] = [0] * len(T) spot_prices[0] = self.S a_spot_prices = deepcopy(spot_prices) |