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# 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, Sequence, Tuple
from utils.misc import Number
__all__ = ['PathGenerator']
@dataclass
class PathGenerator:
"""
Class for generating underlying prices using MC techniques.
Attributes
----------
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)
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)
PathGenerator(S=100.0, r=0.1, div=0.01, vol=0.3)
"""
S: Number
r: Number
div: Number
vol: Number
@property
def net_r(self) -> float:
"""Net risk free rate."""
return float(self.r - self.div)
def generate(self, T: Sequence[Number]) -> List[float]:
"""
Generate a random path {S_t1, S_t2, ..., S_tn}.
Parameters
----------
T : Sequence of Numbers
Set of times {t1, t2, ..., tn} in years.
Returns
-------
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: 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}
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: 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 : Sequence of Numbers
Set of times {t1, t2, ..., tn} in years.
Returns
-------
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: List[float] = [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)
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