September 16, 2025

September 16, 2025

BSM Option Pricing Model

BSM Option Pricing Model

BSM Option Pricing Model

A web-based interactive tool for pricing European call and put options using the Black-Scholes-Merton (BSM) model. This project allows users to input option parameters, visualize results, and analyze sensitivities through heatmaps and charts. It is built for finance professionals, students, and anyone interested in quantitative finance.

A web-based interactive tool for pricing European call and put options using the Black-Scholes-Merton (BSM) model. This project allows users to input option parameters, visualize results, and analyze sensitivities through heatmaps and charts. It is built for finance professionals, students, and anyone interested in quantitative finance.

A web-based interactive tool for pricing European call and put options using the Black-Scholes-Merton (BSM) model. This project allows users to input option parameters, visualize results, and analyze sensitivities through heatmaps and charts. It is built for finance professionals, students, and anyone interested in quantitative finance.

model
model
model

Year

2025

Client

Me, i still need projects.

Category

Finance \\ Python

Product Duration

1 Week
What is the Black-Scholes-Merton (BSM) model?
What is the Black-Scholes-Merton (BSM) model?
What is the Black-Scholes-Merton (BSM) model?

The Black-Scholes-Merton (BSM) model is a mathematical model used to calculate the theoretical price of European-style options. Developed by Fischer Black, Myron Scholes, and Robert Merton, it revolutionized financial markets by providing a closed-form solution for option pricing.


Core Concepts: 

Purpose: Computes fair prices for European call and put options, helping traders and investors make informed decisions.

Inputs: 

  • Current price of the underlying asset

  • Strike price of the option

  • Time to maturity (in years)

  • Volatility of the underlying asset (annualized standard deviation)

  • Risk-free interest rate (annualized, continuous compounding)

Outputs: The model provides the theoretical price for both call and put options, as well as sensitivities like delta and gamma.

Assumptions
Assumptions
Assumptions

Assumptions: 

  • The underlying asset follows a geometric Brownian motion with constant volatility and drift.

  • No dividends are paid during the life of the option.

  • Markets are frictionless (no transaction costs or taxes).

  • The risk-free rate and volatility are constant.

  • The option can only be exercised at expiration (European style).

Practical Use: 

  • The BSM model is widely used in financial markets for pricing, risk management, and strategy development.

  • It also provides "Greeks" (sensitivities) like delta and gamma, which are crucial for hedging and risk assessment

Example
Example
Example
from scipy.stats import norm
from numpy import log, sqrt, exp

class BlackScholes:
    def __init__(self, time_to_maturity, strike, current_price, volatility, interest_rate):
        self.time_to_maturity = time_to_maturity
        self.strike = strike
        self.current_price = current_price
        self.volatility = volatility
        self.interest_rate = interest_rate
    def calculate_prices(self):
        d1 = (log(self.current_price / self.strike) + (self.interest_rate + 0.5 * self.volatility ** 2) * self.time_to_maturity) / (self.volatility * sqrt(self.time_to_maturity))
        d2 = d1 - self.volatility * sqrt(self.time_to_maturity)
        call_price = self.current_price * norm.cdf(d1) - (self.strike * exp(-(self.interest_rate * self.time_to_maturity)) * norm.cdf(d2))
        put_price = (self.strike * exp(-(self.interest_rate * self.time_to_maturity)) * norm.cdf(-d2)) - self.current_price * norm.cdf(-d1)
        return call_price, put_price
Technologies
Technologies
Technologies

Technologies

  • Streamlit : (web application framework)

  • NumPy: (numerical computations)

  • Pandas: (data manipulation)

  • SciPy: (statistical functions, e.g., normal CDF)

  • Matplotlib: (data visualization)

  • Seaborn: (statistical data visualization)

  • Plotly: (interactive plots)

  • More Works More Works

03

//FAQ

Concerns

Frequently

Asked Questions

01

Who Am I?

Hi! Myself Aryan-currently a CSE Undergrad Student specialising in Machine Learning and Artificial Intelligence.

02

What am I doing right now?

03

What do I do?

04

Do I do freelance projects?

03

//FAQ

Concerns

Frequently

Asked Questions

01

Who Am I?

Hi! Myself Aryan-currently a CSE Undergrad Student specialising in Machine Learning and Artificial Intelligence.

02

What am I doing right now?

03

What do I do?

04

Do I do freelance projects?

//FAQ

Concerns

Frequently

Asked Question

Who Am I?
What am I doing right now?
What do I do?
Do I do freelance projects?

03

//FAQ

Concerns

Frequently

Asked Questions

01

Who Am I?

Hi! Myself Aryan-currently a CSE Undergrad Student specialising in Machine Learning and Artificial Intelligence.

02

What am I doing right now?

03

What do I do?

04

Do I do freelance projects?

Let'S WORK

TOGETHER

BASED IN New Delhi,

INDIA

Data Science & Analysis + UI/UX

Outcome-focused Computer Science undergrad student specializing in Artificial Intelligence and Machine Learning with a strong foundation in data engineering, data analysis, and scalable pipeline development. Proficient in Python, SQL, Pandas, and data visualization, with hands-on experience in building end-to-end data workflows, cleaning large datasets, and deploying models into real-time environments.

Let'S WORK

TOGETHER

BASED IN New Delhi,

INDIA

Data Science & Analysis + UI/UX

Outcome-focused Computer Science undergrad student specializing in Artificial Intelligence and Machine Learning with a strong foundation in data engineering, data analysis, and scalable pipeline development. Proficient in Python, SQL, Pandas, and data visualization, with hands-on experience in building end-to-end data workflows, cleaning large datasets, and deploying models into real-time environments.

Let'S WORK

TOGETHER

Outcome-focused Computer Science undergrad student specializing in Artificial Intelligence and Machine Learning with a strong foundation in data engineering & Data analysis.

Let'S WORK

TOGETHER

BASED IN New Delhi,

INDIA

Data Science & Analysis + UI/UX

Outcome-focused Computer Science undergrad student specializing in Artificial Intelligence and Machine Learning with a strong foundation in data engineering, & data analysis.

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