Option Pricing

Detailed analytic and numerical calculations of financial option values and their Greeks.

Analytically calculated option values/greeks:

• European call and put

Option pricing models:

• Cox, Ross, and Rubinstein (1979)

Examples
Get the code
Run the tests
Build the jar

Examples

References:

• Hull (2014): Hull, J. (2014) Options, Futures and Other Derivatives. 9th Edition, Prentice Hall, Upper Saddle River.
• Hull SSM (2014): Hull, J. (2014) Student Solutions Manual for Options, Futures, and Other Derivatives. 9th Edition, Prentice Hall, Upper Saddle River.

Analytically priced options

Hull SSM (2014), page 166, Problem 15.13: European call option

// S_0 = 52, K = 50, τ = 0.25, σ = 0.3, r = 0.12, q = 0
AnalyticOption option = AnalyticOptionFactory.createEuropeanCall(52, 50, 0.25, 0.3, 0.12, 0);
double price = option.price();
assertThat(price).isEqualTo(5.06, withPrecision(0.01));

Calling option.calculation() will return an AnalyticCalculation model with details about the pricing calculation. The getSteps() method returns a String[][] which contains the LaTeX mathematical expressions for the calculation steps. The equations are split by line and equals sign, leaving the formatting up to the user. For example, the parts can be joined and wrapped in the LaTeX align environment with:

String[][] steps = option.calculation().getSteps();
String latex = "\\begin{align*} ";
for (String[] step : steps) {
    latex += "& ";
    latex += String.join(" = ", step);
    latex += " \\\\";
}
latex += " \\end{align*}";

Which will produce the following LaTeX expression:

Similar functionality is provided for the following Greeks: delta, gamma, vega, theta, rho.

Cox, Ross, and Rubinstein

Hull SSM (2014): page 142, Problem 13.17: American put option, 2 time steps

// S_0 = 1500, K = 1480, τ = 1, σ = 0.18, r = 0.04, q = 0.025
Option option = new OptionBuilder(1500, 1480, 1, 0.18, 0.04, 0.025)
    .styleAmerican()
    .typePut()
    .build();
int timeSteps = 2;
PricingModel pricingModel = PricingModelSelector.coxRossRubinstein(timeSteps);
double price = pricingModel.price(option);
assertThat(price).isEqualTo(78.41, withPrecision(0.01));

Calling pricingModel.calculation() will return a model with details about the pricing calculation, i.e. the tree parameters along with an array of the tree nodes. The return value of the method must be typed to the appropriate calculation model (CoxRossRubinstein). e.g.

PricingModel<CoxRossRubinstein> pricingModel = PricingModelSelector.coxRossRubinstein(timeSteps);
CoxRossRubinstein result = pricingModel.calculation(option);
System.out.println(
    String.format("Δt = %f, u = %f, d = %f, p = %f",
        result.getDeltat(), result.getU(), result.getD(), result.getP())
);
for (CoxRossRubinstein.Node node : result.getNodes()) {
    System.out.println(
        String.format("i = %d, j = %d, S = %f, V = %f, exercised = %b",
            node.getI(), node.getJ(), node.getS(), node.getV(), node.getExercised())
    );
}

Will produce the following output:

Δt = 0.500000, u = 1.135734, d = 0.880488, p = 0.497717
i = 0, j = 0, S = 1500.000000, V = 78.413718, exercised = false
i = 1, j = 0, S = 1320.731682, V = 159.268318, exercised = true
i = 1, j = 1, S = 1703.601141, V = 0.000000, exercised = false
i = 2, j = 0, S = 1162.888117, V = 317.111883, exercised = true
i = 2, j = 1, S = 1500.000000, V = 0.000000, exercised = false
i = 2, j = 2, S = 1934.837898, V = 0.000000, exercised = false

Get the code

Use one of the methods given below to get the project source code on your local machine.

Clone

SSH:

git clone git@github.com:peterrhodesdev/option-pricing-java.git

HTTPS:

git clone https://github.com/peterrhodesdev/option-pricing-java.git

GitHub CLI:

gh repo clone peterrhodesdev/option-pricing-java

Fork and clone

gh repo fork peterrhodesdev/option-pricing-java --clone=true

Add a remote + pull

mkdir option-pricing-java
cd option-pricing-java
git init
git remote add option-pricing-java git@github.com:peterrhodesdev/option-pricing-java.git
git pull option-pricing-java main

Run the tests

Run the below command from the project root directory to run the test suite.

mvn verify

This will also apply the following code stylers/formatters:

• checkstyle
• spotbugs
• PMD

Build the jar

Run the below command from the project root directory to create the option-pricing-${project.version}.jar file.

mvn package