VaR Backtesting

Thu, 28 May 2026 17:25:00 +0800

Task 3. VaR Backtesting

VaR Backtesting

most of the time, we assume daily return follow normal distribution and as the question say, Var is caculated at 99% confidence.

Import Libraries

`1`	`await __import__("piplite").install('numpy', 'scipy', 'matplotlib', 'pandas', 'tabulate')`

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# hyy:fix the import failed issue
await __import__("piplite").install('tabulate')

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# hyy:fix excel issue, miss the excel read library, install here.
await __import__("piplite").install('openpyxl')

import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt
from tabulate import tabulate

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# set precision
pd.set_option('display.precision', 4)

Load Data

Pricing Options using Monte Carlo Simulation

Thu, 28 May 2026 16:01:00 +0800

Pricing European and Binary Options using Monte Carlo Simulation

1. Introduction

This report investigates the pricing of European and Binary call options using Monte Carlo simulation under the risk-neutral framework. According to the Fundamental Theorem of Asset Pricing, the value of an option $V(S,t)$ is the expected value of its discounted payoff under the risk-neutral measure $\mathbb{Q}$:

$$V(S, t) = e^{-r(T-t)} \mathbb{E}^\mathbb{Q} [\text{Payoff}(S_T)]$$

We assume the underlying asset follows Geometric Brownian Motion (GBM) governed by the Stochastic Differential Equation (SDE): $$dS_t = r S_t dt + \sigma S_t dW_t$$ where $r$ is the risk-free rate, $\sigma$ is the volatility, and $dW_t$ is a Wiener process.

Quant on H&W

VaR Backtesting

Task 3. VaR Backtesting

VaR Backtesting

Pricing Options using Monte Carlo Simulation

Pricing European and Binary Options using Monte Carlo Simulation

1. Introduction