From Physics to Finance

Scientific Computing in High-Frequency Trading

The transition from physics research to quantitative finance is more natural than you might think. Both fields deal with noisy data, stochastic processes, and the need for computational efficiency.

The Physics-Finance Connection

| Physics Concept | Finance Application | |----------------|---------------------| | Brownian motion | Stock price modeling | | Monte Carlo simulation | Option pricing | | Signal processing | Market microstructure | | Differential equations | Risk models | | Statistical mechanics | Portfolio theory |

Stochastic Differential Equations

The Black-Scholes equation is just a diffusion equation in disguise:

import numpy as np

def geometric_brownian_motion(S0, mu, sigma, T, dt):
    """
    Simulate stock price using GBM
    Same math as particle diffusion!
    """
    n_steps = int(T / dt)
    S = np.zeros(n_steps + 1)
    S[0] = S0
    
    for t in range(1, n_steps + 1):
        dW = np.random.normal(0, np.sqrt(dt))
        S[t] = S[t-1] * np.exp((mu - 0.5*sigma**2)*dt + sigma*dW)
    
    return S

Monte Carlo Methods

The same techniques I used to simulate particle physics work for option pricing:

def monte_carlo_option_price(S0, K, r, sigma, T, n_simulations=100000):
    """
    Price a European call option using Monte Carlo
    """
    # Simulate terminal prices
    Z = np.random.standard_normal(n_simulations)
    ST = S0 * np.exp((r - 0.5*sigma**2)*T + sigma*np.sqrt(T)*Z)
    
    # Calculate payoffs
    payoffs = np.maximum(ST - K, 0)
    
    # Discount to present value
    price = np.exp(-r*T) * np.mean(payoffs)
    
    return price

Key Takeaways

1. Physics trains you to think about uncertainty quantification
2. Scientific computing skills transfer directly
3. Both fields reward rigorous hypothesis testing

The universe is probabilistic. So are markets.