American Options Pricing

This is a repo for American Options pricing. Usually the trading apps will give a Black-Scholes model output, which is only valid for European Options.

The core module contains C++ code for calculating the options pricing.

The service is written in Express.js, websocket and dockerized for easiness of development and use.

TODO: Add CTest to test the exceptions and calculation.

Core Pricing Module

To build the core module, install CMake version >= 3.10, and run

cmake core

# Go to the build folder, then
make

The output binary is in ./core/build/out/BinomialAmericanOption

Arguments:

• -S Stock Price (underlying)
• -K Strike
• -r Risk-free rate in decimal (not percentage)
• -q Dividend yield in decimal (not percentage)
• -T Days to expiration (in days, assuming 365 days per year)
• -s Volatility of underlying/IV in decimal (not percentage)
• -n Number of steps on the binomial tree
• -c is call, otherwise put or -p

The maximum steps is set to be 1,000. This can be overriden in core/include/bopm.hpp

The calculation uses an array of array pointers. This would be faster than representing each node in a binary tree.

For fewer steps, you can perhaps allocate a contiguous 2D-array on stack.

WebSocket Server

The server is in the app directory. It takes a JWT_SECRET env variable for authentication and PORT for port.

The server is bootstraped on a express.js server, where the http will upgrade to a websocket connection upon authorization.

The authorization is pending implementation in src/utils/auth.ts

Authorization would initiate with POST /auth, and the username and password in the request body.

It will return a ephemeral token for upgrading connection with the WebSocket server. This can be enhanced by adding a counter to invalidate the token after use.

For more info on securing WebSocket Server, see this article on StackOverflow.

Currently the token is set for longer expiration time for debugging and development purposes. Check src/routes/auth.ts.

The request body format:

{
    requestTime: string,  // For logging purposes in future
    price: number,
    strike: number,
    riskFreeRate: number,
    dividendYield: number,
    daysToExpiration: number,
    volatility: number,
    stepsOfBimondalTree: number,
    isCall: boolean
}