Stock Price Modeling - Learn Math Through Real Applications

Model stock prices by analyzing Tesla historical data to generate plausible future prices, rather than reusing past values, and prepare the data by downloading max history from Yahoo Finance.

Learn how to model future stock prices by analyzing day-to-day returns. Compare absolute and percentage returns in Excel, visualize with scatter plots, and prefer percentage returns to remove scale effects.

Analyze Tesla's daily percentage returns to uncover patterns through visual plotting, distinguishing deterministic trends from randomness, and framing outcomes with discrete and continuous probability distributions.

Convert frequencies to probabilities across 10, 20, and 40 bins, revealing bell-shaped distributions that shrink with finer bins, while emphasizing probability density as stable across binning for continuous distributions.

Group outcomes into density bins to reveal a pattern and seek an underlying formula, using log returns to fit bell-curve distributions like normal or Cauchy for stock returns.

Explore how logarithms transform percentage returns into log returns, enabling a natural rate of change to model continuous growth or decay in stock prices.

Break down net growth into small steps using the log operation, attributing growth to a mother unit and its offspring, and show convergence to the natural growth rate around 0.6931.

Learn how the log operation computes the natural rate of decay and natural growth, standardizes per-unit changes, and why log returns can exceed percentage returns.

Model stock price changes using log returns instead of percentage returns, and explore calculating, visualizing, and analyzing their distribution with Excel histograms and probability density.

We simulate log returns to model stock prices, using a bell-curve distribution to assign proper probabilities and translate outcomes into future prices.

Explore probability distributions from uniform to normal, using probability density functions to relate outcomes to area under the curve, with mu as center and density depending on x.

Use the probability density function to derive probabilities for continuous distributions by binning and multiplying density by bin width, with a normal density model and area under curve equals one.

Use a normal density to assign probabilities to wheel slices, convert incremental probabilities into slice sizes and locations, and model spins in Excel for a symmetric, probabilistic wheel.

Model random spinning with a pseudo-random number generator using a seed, multiplier, and divisor to produce location numbers from 0 to 1, and convert results via Excel modulo.

Learn how a linear congruential generator uses a multiplier and added constant with a time-based seed to generate varied random sequences for stock price modeling, comparing with Excel RAND.

Demonstrate simulating stock log returns with a spinning wheel in Excel, mapping random location numbers to a normal distribution and using symmetry for p<0.5 and the inverse normal formula.

Simulate thousands of Tesla-like stock prices using a normal-distribution model of daily log returns, implemented in Excel with rand and normal inverse, for option valuation.

See how e expresses continuous growth to simplify multi-day stock price simulations by aggregating iid normal daily returns into a single multi-day return.

Explore how to compute binomial coefficients by counting selections of k items from n, using factorials and the ratio of numerator and denominator, and recognize the binomial theorem.

Compute e from a binomial expansion of n period growth, using factorial series and inverse factorials to reveal the limit e, then relate continuous growth and compound interest to e.

Apply the no arbitrage principle to value futures and options, deriving fair prices from the spot price and interest, and understand how arbitrage drives equilibrium between future and spot prices.

Hedge option risk by pairing with stock, using no-arbitrage to value options. Define the hedge ratio or delta to offset changes, leading toward the Black-Scholes equation.

Use Monte Carlo simulation to value European options by simulating future stock prices under a risk-neutral measure, and compute the discounted average payoff, comparing results with the Black Scholes formula.

Learn to value European options using the Black Scholes formula, understanding d1 and d2, moneyness, and the role of volatility and standard normal probabilities, with Monte Carlo comparison.