Black–Scholes Pricing of European Calls and Puts in C++

Summary

The article explains how the analytic Black–Scholes formulas for European vanilla calls and puts can be translated into a procedural C++ implementation. It defines the underlying price, strike, interest rate, volatility, and time to maturity, then uses the standard normal distribution functions and the intermediate d-values to calculate option prices. The put formula is related to the call through put–call parity.

The example implements a standard normal density and an approximation to its cumulative distribution, followed by separate functions for the call and put prices. It presents output for one illustrative parameter set and notes that the implementation is intended to connect formulas with code rather than optimize performance. The article mentions that closed-form Greeks and other option types could be added, but does not calculate them. Its pricing setup assumes the Black–Scholes model’s inputs, including constant volatility, and the normal CDF approximation may affect numerical accuracy.

Key ideas

• The Black–Scholes analytic solution prices European vanilla calls and puts from the underlying, strike, rate, volatility, and maturity.
• The calculation uses intermediate d-values and the standard normal cumulative distribution function.
• Put pricing can be expressed using the corresponding call relationship through put–call parity.
• The example uses an approximation for the normal CDF and is presented for clarity rather than optimization.
• The article assumes the Black–Scholes framework and leaves Greeks and other option types for later work.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.