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Diffstat (limited to 'utils/path.py')
| -rw-r--r-- | utils/path.py | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/utils/path.py b/utils/path.py new file mode 100644 index 0000000..6855b7f --- /dev/null +++ b/utils/path.py @@ -0,0 +1,135 @@ +# author : S. Mandalia +# shivesh.mandalia@outlook.com +# +# date : March 19, 2020 + +""" +Path generator for underlying. +""" + +import math +import random +from copy import deepcopy +from dataclasses import dataclass +from typing import List, Tuple + + +__all__ = ['PathGenerator'] + + +@dataclass +class PathGenerator: + """ + Class for generating underlying prices using MC techniques. + + Attributes + ---------- + S : Spot price. + r : Risk-free interest rate. + div : Dividend yield. + vol : Volatility. + net_r : Net risk free rate. + + Methods + ---------- + generate(T) + Generate a random path {S_t1, S_t2, ..., S_tn}. + generate_antithetic(T) + Generate a random plus antithetic path + [{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, 91.11981160354563, 94.87596210593794, 117.44132223235353] + >>> print(path.generate(T=range(4))) + [100.0, 68.73668230722738, 71.43490333826567, 70.70833180133955] + + """ + S: float + r: float + div: float + vol: float + + @property + def net_r(self) -> float: + """Net risk free rate.""" + return self.r - self.div + + def generate(self, T: List[float]) -> List[float]: + """ + Generate a random path {S_t1, S_t2, ..., S_tn}. + + Parameters + ---------- + T : Set of times {t1, t2, ..., tn} in years. + + Returns + ---------- + spot_prices : Set of prices for the underlying {S_t1, S_t2, ..., S_tn}. + + """ + # Calculate dt time differences + dts = [T[idx + 1] - T[idx] for idx in range(len(T) - 1)] + + spot_prices = [0] * len(T) + spot_prices[0] = self.S + for idx, dt in enumerate(dts): + # Calculate the drift e^{(r - (1/2) σ²) Δt} + drift = math.exp((self.net_r - (1/2) * self.vol**2) * dt) + + # Calculate the volatility term e^{σ √{Δt} N(0, 1)} + rdm_gauss = random.gauss(0, 1) + vol_term = math.exp(self.vol * math.sqrt(dt) * rdm_gauss) + + # Calculate next spot price + S_t = spot_prices[idx] * drift * vol_term + spot_prices[idx + 1] = S_t + return spot_prices + + def generate_antithetic(self, T: List[float]) -> 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. + + Returns + ---------- + prices_tuple : Set of prices for the underlying + [{S_t1, S_t2, ..., S_tn}, {S'_t1, S'_t2, ..., S'_tn}]. + + """ + # 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[0] = self.S + + a_spot_prices = deepcopy(spot_prices) + + for idx, dt in enumerate(dts): + # Calculate the drift e^{(r - (1/2) σ²) Δt} + drift = math.exp((self.net_r - (1/2) * self.vol**2) * dt) + + # Calculate the volatility term e^{σ √{Δt} N(0, 1)} + rdm_gauss = random.gauss(0, 1) + a_gauss = -rdm_gauss + vol_term = math.exp(self.vol * math.sqrt(dt) * rdm_gauss) + a_vol_term = math.exp(self.vol * math.sqrt(dt) * a_gauss) + + # Calculate next spot price + S_t = spot_prices[idx] * drift * vol_term + a_S_t = a_spot_prices[idx] * drift * a_vol_term + + # Add to data structure + spot_prices[idx + 1] = S_t + a_spot_prices[idx + 1] = a_S_t + + return (spot_prices, a_spot_prices) |
