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blackModel76.py
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blackModel76.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 18 12:19:03 2019
@author: paragonhao
"""
import math
from scipy.stats import norm
class BlackModel76:
tenor = None #tenor of swap in years
fRate = None #forward rate of underlying swap
xRate = None #strike rate of swaption
rfRate = None #risk-free interest rate
T = None #time to expiration in years
sigma = None #volatility of the forward-starting swap rate
m = None #compoundings per year in swap rate
d1 = None
d2 = None
df = None
def __init__(self, tenor, fRate, xRate, rfRate, T, sigma, m):
self.tenor = tenor
self.fRate = fRate
self.xRate = xRate
self.rfRate = rfRate
self.T = T
self.sigma = sigma
self.m = m
self.d1 = (math.log(fRate/xRate) + 0.5 * (sigma ** 2) * T)/(sigma * math.sqrt(T))
self.d2 = self.d1 - sigma * math.sqrt(T)
self.df = math.exp(-1 * self.rfRate * self.T)
def getPayerSwaptionPrice(self):
temp = 1/ (1 + (self.fRate/self.m)) ** (self.tenor * self.m)
nd1 = norm.cdf(self.d1)
nd2 = norm.cdf(self.d2)
return ((1 - temp)/self.fRate) * self.df * (self.fRate * norm.cdf(self.d1) - self.xRate * norm.cdf(self.d2))
def getReceiverSwaptionPrice(self):
temp = (1 + (self.fRate/self.m)) ** (self.tenor * self.m)
nd1_neg = norm.cdf(-1 * self.d1)
nd2_neg = norm.cdf(-1 * self.d2)
return ((1 - temp)/self.fRate) * self.df * (self.xRate * nd2_neg - self.fRate * nd1_neg)