📈 Dividend-Adjusted Black-Scholes Pricing Engine

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📌 Overview

Equity derivatives frequently involve discrete dividend payments. This engine properly adjusts pricing to handle both continuous dividend yield and discrete cash dividends — essential for accurate valuations in real trading desks.

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✨ Features

• ✅ European Call pricing with continuous dividend yield (Merton 1973)
• ✅ European Call pricing with discrete cash dividends (Forward Adjustment)
• ✅ Full Greeks: Delta, Gamma, Vega, Theta, Rho
• ✅ American option early exercise detection
• ✅ Binomial Tree validation (accuracy < 0.1%)
• ✅ European vs American price comparison
• ✅ 17 unit tests — all passing

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📐 Mathematical Model

Continuous Dividend Yield (Merton 1973):

d1  = [ ln(S/K) + (r - q + σ²/2) * T ] / (σ * √T)
d2  = d1 - σ * √T
Call = S * e^(-qT) * N(d1) - K * e^(-rT) * N(d2)

Discrete Dividend (Forward Adjustment):

S_adj = S0 - sum of PV(Dividends)
PV    = Dividend * e^(-r * exDate)
Call  = BlackScholes(S_adj, K, T, r, σ)

Early Exercise Condition (American Calls):

Exercise early if: Dividend > r * K * (T - exDate)

Binomial Tree (Validation):

u = e^(σ * √dt)        up factor
d = 1/u                down factor
p = (e^(r*dt) - d) / (u - d)   risk neutral probability

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🗂️ Project Structure

equity_dividend_bs_java/
├── pom.xml
├── README.md
├── data/
│   └── dividend_schedules.csv
└── src/
    ├── main/java/com/quant/equitybs/
    │   ├── Main.java
    │   ├── core/
    │   │   ├── BlackScholesEngine.java
    │   │   ├── BinomialTree.java
    │   │   ├── DiscountCurve.java
    │   │   └── DividendSchedule.java
    │   ├── model/
    │   │   └── Greeks.java
    │   └── pricer/
    │       └── AmericanPricer.java
    └── test/java/com/quant/equitybs/
        ├── BlackScholesTest.java
        └── GreeksTest.java

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🚀 How to Run

1. Clone the repository

git clone https://github.com/rupeshgoswami/equity_dividend_bs_java.git
cd equity_dividend_bs_java

2. Compile the project

mvn compile

3. Run the pricing engine

mvn exec:java

4. Run all tests

mvn test

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📊 Sample Output

===========================================
  Dividend-Adjusted Black-Scholes Engine
===========================================

SCENARIO 1: Continuous Dividend Yield (3%)
  Stock Price  : $100.00
  Strike Price : $105.00
  Expiry       : 1.0 year
  Rate         : 5%
  Volatility   : 20%
  Div Yield    : 3%
  Call Price   = $7.2345

SCENARIO 2: Discrete Cash Dividend ($2 at 6 months)
  Dividend      : $2.00 at 6 months
  PV of Dividend: $1.9506
  Adjusted Spot : $98.0494
  Call Price    = $6.8901

SCENARIO 3: Option Greeks (q = 3%)
  Delta :  0.4682
  Gamma :  0.0193
  Vega  : 38.6778
  Theta : -4.4789
  Rho   : 40.3146

SCENARIO 4: American vs European Call
  Early exercise optimal at t=0.50
  Dividend $3.00 > Interest cost $2.63
  European Call Price   : 6.5209
  American Call Price   : 6.5509
  Early Exercise Premium: 0.0300

SCENARIO 5: Binomial Tree Validation
  +--------------------------------------+
  |   Binomial Tree Validation           |
  +--------------------------------------+
  |  Black-Scholes Price :     8.0214   |
  |  Binomial Tree Price :     8.0211   |
  |  Difference          :     0.0003   |
  |  Percentage Diff     :     0.0036%  |
  |  Validation          :  PASSED      |
  +--------------------------------------+

===========================================
        All Scenarios Complete!
===========================================

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🧪 Test Results

-----------------------------------------------
 T E S T S
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BlackScholesTest  → Tests run: 8,  Failures: 0
GreeksTest        → Tests run: 9,  Failures: 0
-----------------------------------------------
Total Tests: 17 | Failures: 0 | Errors: 0
BUILD SUCCESS
-----------------------------------------------

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🐳 Docker

Pull and Run instantly (No setup required!)

docker pull rkgoswami/equity-pricing-model:v1
docker run rkgoswami/equity-pricing-model:v1

Build Docker image locally

docker build -t equity-pricing-model .
docker run equity-pricing-model

DockerHub Image

👉 https://hub.docker.com/r/rkgoswami/equity-pricing-model

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☁️ AWS EC2 Deployment

This model is containerized with Docker and deployed on AWS EC2.

Steps to deploy on AWS EC2:

# 1. Launch EC2 instance (Amazon Linux 2023, t2.micro free tier)
# 2. SSH into instance
ssh -i your-key.pem ec2-user@your-ec2-ip

# 3. Install and start Docker
sudo yum install docker -y
sudo service docker start
sudo usermod -a -G docker ec2-user

# 4. Pull and run
docker pull rkgoswami/equity-pricing-model:v1
docker run rkgoswami/equity-pricing-model:v1

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🛠️ Tech Stack

Tool	Version	Purpose
Java	17	Core language
Apache Commons Math	3.6.1	Normal distribution CDF/PDF
Maven	3.x	Build & dependency management
JUnit 5	5.10.0	Unit testing framework
Docker	latest	Containerization
AWS EC2	t2.micro	Cloud deployment

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📚 Key Concepts

Concept	Description
Forward Adjustment	Subtract PV of dividends from spot price
Continuous Yield	Modify BS drift by dividend yield q
Early Exercise	Optimal when Dividend > r × K × (T - t)
Greeks	Risk sensitivities used for hedging
Binomial Tree	Discrete time model for validation

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👤 Author

Rupesh Goswami

• GitHub: @rupeshgoswami

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📄 License

This project is licensed under the MIT License.

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