C is ideal for this because pricing engines often need to run thousands of iterations (Monte Carlo simulations) in milliseconds. The Implementation: Black-Scholes Call Option

In a production environment, you would extend this to calculate Delta , Gamma , and Theta by taking the partial derivatives of the price function.

AI responses may include mistakes. For financial advice, consult a professional. Learn more

This code calculates the theoretical price of an option based on the underlying price, strike price, time to maturity, risk-free rate, and volatility.

We use the erfc (complementary error function) to calculate the cumulative distribution function, which is the probability that the option will end up "in the money."

#include #include // Cumulative Normal Distribution Function (approximation) double normal_cdf(double x) { return 0.5 * erfc(-x * M_SQRT1_2); } // Black-Scholes Formula for a European Call Option double calculate_call_price(double S, double K, double T, double r, double sigma) { double d1 = (log(S / K) + (r + 0.5 * sigma * sigma) * T) / (sigma * sqrt(T)); double d2 = d1 - (sigma * sqrt(T)); double price = S * normal_cdf(d1) - K * exp(-r * T) * normal_cdf(d2); return price; } int main() { // Parameters double stock_price = 100.0; // Spot price (S) double strike_price = 105.0; // Strike price (K) double time_to_expiry = 1.0; // Years (T) double risk_free_rate = 0.05; // 5% (r) double volatility = 0.20; // 20% (sigma) double price = calculate_call_price(stock_price, strike_price, time_to_expiry, risk_free_rate, volatility); printf("--- Option Pricing Engine ---\n"); printf("Underlying Price: %.2f\n", stock_price); printf("Strike Price: %.2f\n", strike_price); printf("Call Option Price: %.4f\n", price); return 0; } Use code with caution. Copied to clipboard Components of the Engine

Since this uses stack-allocated doubles, it is extremely fast and can be called inside a loop for "Greeks" sensitivity analysis or volatility surfaces.

The library provides the necessary transcendental functions ( the square root of empty end-root