为 Python 中的期权定价绘制蒙特卡洛模拟

Question

I am trying to show the monte carlo barrier prices for different number of simultations in the x axis. This is what i tried so far but i'm getting the error -> ValueError: x and y must have same first dimension, but have shapes (10,) and (5,). I am new to python and as hard as i try i cannot find the error

import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt

def mc_single_barrier_do(S0, K, T, H, r, vol, N, M):

    # Constants
    dt = T / N  # change in time
    nudt = (r - 0.5 * vol ** 2) * dt  # deterministic component
    volsdt = vol * np.sqrt(dt)  # diffusion coefficient
    erdt = np.exp(r * dt)  # discount factor

     # Standard Error Placeholders
    sum_CT = 0
    sum_CT2 = 0
     # Monte Carlo Method
    for i in range(M):

        # Barrier Crossed Flag
        BARRIER = False
        St = S0

        for j in range(N):
            epsilon = np.random.normal()
            Stn = St * np.exp(nudt + volsdt * epsilon)
            St = Stn
            Ptn = np.exp(-2. * (H - St) * (H - Stn) / (St ** 2. * volsdt ** 2.))
            Pt = Ptn
            if Pt >= npr.uniform():
                BARRIER = True
        if np.amin(St) > H and BARRIER == False:
            CT = np.maximum(St - K, 0)

        else:
            CT = 0.

        sum_CT = sum_CT + CT
        sum_CT2 = sum_CT2 + CT * CT

    C0_MC = np.exp(-r * T) * sum_CT / M
    return C0_MC


def sim_iterator(max_sample, N, S0, T, r, vol, K, H, method):

    assert (method in ['MC', 'AV', 'CV'])
    
    mean_payoffs = np.zeros(int(np.ceil(max_sample / 10)))
    
    if method == 'MC':
        for n_sample in range(10, max_sample + 1, 10):
            payoffs = mc_single_barrier_do(n_sample, S0, K, T, H, r, vol, N)
            mean_payoffs[int(n_sample / 10 - 1)] = np.mean(payoffs)
        
    return mean_payoffs

r = 0.1
vol = 0.2
T = 2
N = 20
dt = T / N
S0 = 50
K = 50
H = 45
max_sample = 100

MC_price_estimates = sim_iterator(S0, T, r, vol, K, H, max_sample, N, method='MC')
x_axis1 = range(10, max_sample + 1, 10)
plt.plot(x_axis1, MC_price_estimates)
plt.xlabel("No. of Simulations")
plt.ylabel("Estimated option price")
plt.title("Ordinary Monte Carlo Method")
plt.legend()
plt.show()

Answer 1

in your function definition you used:

def sim_iterator(max_sample, N, S0, T, r, vol, K, H, method):

while when using the function you used:

MC_price_estimates = sim_iterator(S0, T, r, vol, K, H, max_sample, N, method='MC')

python has positional arguments, which means the arguments are mapped according to their position, not their name, so in the first position is mapped to the first argument, which means S0 in the second line was mapped to max_sample in the first line, just fix the arguments arrangement, or use keyword arguments S0=S0 .

MC_price_estimates = sim_iterator(S0=S0, T=T, r=r, vol=vol, K=K, H=H, max_sample=max_sample, N=N, method='MC')

this is what your code will look like when you fix all arguments to be keyword arguments.

def mc_single_barrier_do(S0, K, T, H, r, vol, N, M):
    # Constants
    dt = T / N  # change in time
    nudt = (r - 0.5 * vol ** 2) * dt  # deterministic component
    volsdt = vol * np.sqrt(dt)  # diffusion coefficient
    erdt = np.exp(r * dt)  # discount factor

    # Standard Error Placeholders
    sum_CT = 0
    sum_CT2 = 0
    # Monte Carlo Method
    for i in range(M):

        # Barrier Crossed Flag
        BARRIER = False
        St = S0

        for j in range(N):
            epsilon = np.random.normal()
            Stn = St * np.exp(nudt + volsdt * epsilon)
            St = Stn
            Ptn = np.exp(-2. * (H - St) * (H - Stn) / (St ** 2. * volsdt ** 2.))
            Pt = Ptn
            if Pt >= npr.uniform():
                BARRIER = True
        if np.amin(St) > H and BARRIER == False:
            CT = np.maximum(St - K, 0)

        else:
            CT = 0.

        sum_CT = sum_CT + CT
        sum_CT2 = sum_CT2 + CT * CT

    C0_MC = np.exp(-r * T) * sum_CT / M
    return C0_MC

def sim_iterator(max_sample, N, S0, T, r, vol, K, H, method):
    assert (method in ['MC', 'AV', 'CV'])

    mean_payoffs = np.zeros(int(np.ceil(max_sample / 10)))

    if method == 'MC':
        for n_sample in range(10, max_sample + 1, 10):
            payoffs = mc_single_barrier_do(M=n_sample,S0= S0, K=K, T=T, H=H, r=r, vol=vol, N=N)
            mean_payoffs[int(n_sample / 10 - 1)] = np.mean(payoffs)

    return mean_payoffs


r = 0.1
vol = 0.2
T = 2
N = 20
dt = T / N
S0 = 50
K = 50
H = 45
max_sample = 100

MC_price_estimates = sim_iterator(S0=S0, T=T, r=r, vol=vol, K=K, H=H, max_sample=max_sample, N=N, method='MC')
x_axis1 = range(10, max_sample + 1, 10)
plt.plot(x_axis1, MC_price_estimates)
plt.xlabel("No. of Simulations")
plt.ylabel("Estimated option price")
plt.title("Ordinary Monte Carlo Method")
plt.legend()
plt.show()