'''
MIT License
Copyright (c) 2026-present eigenView Inc.
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
'''
import numpy as np
import pandas as pd
import jax
from jax import random
import jax.numpy as jnp
import time
import matplotlib.pyplot as plt
t0 = time.process_time()
#Random Number
seed=12345678
rng0 = jax.random.PRNGKey(seed)
rng0, rng1 = random.split(rng0)
rng1, rng2 = random.split(rng1)
rng2, rng3 = random.split(rng2)
rng3, rng4 = random.split(rng3)
rng4, rng5 = random.split(rng4)
#Trades
n_trades = 1000 #number of transactions
notional = jax.random.randint(rng0, shape=(n_trades,), minval = -100_000, maxval = 100_000)  # Notional
float_rate_current = jax.random.uniform(rng1, shape=(n_trades,), minval = 0.015, maxval = 0.025) #float rate at reference date
fixed_rate = jax.random.uniform(rng2, shape=(n_trades,), minval = 0.01, maxval = 0.03)       # fixed rate
max_remaining_maturity = 10
remaining_maturity = jax.random.uniform(rng3, shape=(n_trades,), minval = 0.1, maxval = max_remaining_maturity) #remaining maturity
freq_type = jnp.array([1, 2, 4]) 
freq = jax.random.choice(rng4, freq_type, shape=(n_trades,))                # Interest payment frequency
#Parameters
n_paths = 100_000        # Monte Carlo Paths
num_steps_year = 24           # observation times a year
num_steps = num_steps_year * (int(jnp.max(remaining_maturity)) + 1)
dt = (int(jnp.max(remaining_maturity)) + 1.0) / num_steps
## Hull-White
a_HW = 0.1
sigma = 0.0075
r0 = 0.015
# Temporary yield curve for testing purposes
# y(t)=sqrt(coeff_r + r0^2)
coeff_r = 0.0001 #

# Swap revaluation at each point in time
def F0(t): # instantaneous spot rate at time 0. The formula is only for this simulation.
    return jnp.sqrt(coeff_r*t + r0*r0)
def diff_F0(t): #Derivative of instantaneous spot rate curve
    return coeff_r/(2*F0(t))
def f0tT(t, T):  #The forward rate for the period between time t and T as seen at time 0.
    return 2*(F0(T)**3 - F0(t)**3)/((3*coeff_r)*(T-t))
    
def dicountFactor(t, T, r): #The discount factor for the period between time t and T as seen at time t.
    BtT = (1 - jnp.exp(-a_HW*(T-t)))/a_HW
    AtT = jnp.exp(-f0tT(t, T)*(T-t) + F0(t)*BtT - (sigma**2)/(4*(a_HW**3))*((jnp.exp(-a_HW*T) - jnp.exp(-a_HW*t))**2)*(jnp.exp(2*a_HW*t) - 1))
    BtTr = r[:, jnp.newaxis]*BtT
    df=AtT[jnp.newaxis,:]*jnp.exp(-BtTr)
    return df
def R(t,T, r): #The zero rate for the period between t and T
    return -jnp.log(dicountFactor(t, T, r))/(T-t)[jnp.newaxis, :]
def price_swap(t, r, beginning_pay_date, ):
    def batch_transactions():
        #beginning_pay_date: The first payment date as of the record date
        #first_pay_date: First payment date for each time grid
        n_payment = (jnp.ceil((remaining_maturity - t) * freq)).astype(jnp.int32)
        max_n_payment = jnp.max(n_payment)
        first_pay_date = remaining_maturity - (n_payment - 1)/freq 
        float_rate = jnp.where(t < beginning_pay_date, float_rate_current[jnp.newaxis,:], R(first_pay_date-1.0/freq, first_pay_date, r))
        df = dicountFactor(t, first_pay_date, r)
        cf = notional*(jnp.exp(float_rate/freq) - jnp.exp(fixed_rate/freq))
        cfdfsum = cf*df
        def cf_summation(j, price):
            def gen_cf():
                cf_date = first_pay_date + j/freq
                float_rate = R(cf_date - 1/freq, cf_date, r)
                df = dicountFactor(t, cf_date, r)
                cf = jnp.exp(float_rate/freq) - jnp.exp(fixed_rate/freq)
                return notional*cf * df
        
            cfdf = jnp.where(n_payment > j, gen_cf(), 0)
            price += cfdf #No compensated summation is necessary here.
            return price
            
        price = jnp.zeros([n_paths, n_trades])
        cfdfsum += jax.lax.fori_loop(1, max_n_payment, cf_summation, price)
        return cfdfsum
    exposure = jnp.where(remaining_maturity > t, batch_transactions(), 0)
    
    return jnp.sum(exposure,axis=1) #The Compensated summation is necessary here.

# Interest rate simulation(Euler-Maruyama method)
# dr = (theta(t) - a*r)dt + sigma*dW
def theta(t): #HW Parameter theta
    return diff_F0(t)+a_HW*F0(t)
def find_efv_area():
    r = jnp.zeros((num_steps + 1, n_paths))
    r = r.at[0, :].set(r0)
    norm_rand = jax.random.normal(rng5, shape=(num_steps + 1, n_paths))
    def mc_path(i, ir):
        t = i * dt
        dr = (theta(t) - a_HW*ir[i, :]) * dt + sigma * jnp.sqrt(dt) * norm_rand[i, :]
        ir = ir.at[i+1, :].set(ir[i,:] + dr)
        return ir
    r = jax.lax.fori_loop(0, num_steps, mc_path, r)
    r.block_until_ready()
    n_payment = (jnp.ceil(remaining_maturity * freq)).astype(jnp.int32)
    beginning_pay_date = remaining_maturity - (n_payment - 1)/freq  # The first payment date as of the record date
    efv_epe_ene_list = jnp.zeros([4,num_steps+1])
    def ee_timestep(step, efv_epe_ene_list,):
        step_time = step * dt
        current_r = r[step, :]
        ee = price_swap(step_time, current_r, beginning_pay_date,)
        epe = jnp.maximum(ee,0)
        ene = jnp.minimum(ee,0)
        efv_epe_ene_list = efv_epe_ene_list.at[0, step].set(step_time)
        efv_epe_ene_list = efv_epe_ene_list.at[1, step].set(jnp.mean(ee))
        efv_epe_ene_list = efv_epe_ene_list.at[2, step].set(jnp.mean(epe))
        efv_epe_ene_list = efv_epe_ene_list.at[3, step].set(jnp.mean(ene))
        return efv_epe_ene_list
    
    efv_epe_ene_list = jax.lax.fori_loop(0, num_steps + 1, ee_timestep, efv_epe_ene_list).block_until_ready() 
    
    df = pd.DataFrame(efv_epe_ene_list.T)
    df.to_csv('EE_EPE_ENE.csv')
    area = jnp.zeros([2])
    def area_summation(i, ar):
        ar = ar.at[0].set(ar[0] + abs(efv_epe_ene_list[2,i] + efv_epe_ene_list[2,i+1])/2*(efv_epe_ene_list[0,i+1]-efv_epe_ene_list[0,i]))
        ar = ar.at[1].set(ar[1] + abs(efv_epe_ene_list[3,i] + efv_epe_ene_list[3,i+1])/2*(efv_epe_ene_list[0,i+1]-efv_epe_ene_list[0,i]))
        return ar
    epe_area = jax.lax.fori_loop(0, num_steps, area_summation, area).block_until_ready()  ##
    print("EPE Area ",epe_area[0])
    print("ENE Area ",epe_area[1])
    return jnp.sum(epe_area), efv_epe_ene_list

if __name__ == '__main__':
    efv_area, ee_epe_ene = find_efv_area()
    efv_area.block_until_ready() 
    fig, ax = plt.subplots()
    x = ee_epe_ene[0]
    y0 = ee_epe_ene[1]
    y1 = ee_epe_ene[2]
    y2 = ee_epe_ene[3]
    ax.grid()
    ax.set_title('EFV(t), EPE(t) and ENE(t)') 
    ax.set_xlabel('t')  
    ax.set_ylabel('Amount')
    ax.plot(x, y0, label='EFV')
    ax.plot(x, y1, label='EPE')
    ax.plot(x, y2, label='ENE')
    ax.legend(loc=4)
    fig.tight_layout() 
    
    plt.show()
    print("Elapse time ",time.process_time()-t0,"s")