Mathematical Finance with Python : Theory and Practice

Explore basic statistics by defining mean, median, standard deviation, and mode, and learn how these measures reveal central tendency in datasets.

Model bond valuation by calculating face value and coupon value with Python, using semiannual coupons and a yield to maturity to discount cash flows.

Explore probability distributions from discrete to continuous, then dive into lognormal distributions for finance, deriving and modeling their probability density and cumulative density functions, with lab coding in Python.

Demonstrate how the natural logarithm of x being normal yields a lognormal distribution, and visualize its pdf and cdf in Python for finance.

Model option payoffs by stock movements and strike price, using call payoff max(F-K,0) and put payoff max(K-S,0) to capture the extra payoff beyond the option price.

Explore Python-based options payoff modeling, deriving call and put payoffs using max(stock - strike, 0) and max(0, strike - stock), with function-based implementation.

Implement the Black Scholes Merton model in Python, coding call and put pricing formulas, and plot option values across varying stock prices.

Explore the Black-Scholes dividend model, deriving call and put prices with dividend yield Q using D1 and D2, and note dividends lower calls and raise puts.

Explore delta, the sensitivity that measures how option value changes with the underlying stock price, using e^{-q t} N(d1). Learn how leverage relates to delta for calls and puts.

Explore delta, the key option greek, and see how dividend and time to expiration shape option price and sensitivity under the BSM dividend model.

Learn how delta, the key option sensitivity, links price changes to the underlying asset, and how dividend and time to expiration affect delta in the Black-Scholes framework.

Learn put-call parity by equating call and put prices under the dividend model, applying Black-Scholes, with r, q, and sigma adjustments.

Explore put-call parity in option pricing and verify its equality with the Black-Scholes price using Python functions and a dividend model.

Explore differentiation and integration through function behavior, slope, tangent, limits, and area under the curve, highlighting antiderivatives and the link between rate of change and accumulation.

Explore probabilistic modelling in finance, showing how trials reduce uncertainty and drive convergence toward expected outcomes. Apply regress to mean and coin-flip simulations in Python to support decision making.

Explore regression to the mean through extreme events, extremes in coin flips, and observe how averages revolve around mean with Monte Carlo simulation and stochastic modeling for financial predictive analytics.

Explore histogram creation from random number generation and learn how Monte Carlo simulation uses repeated trials to reveal data distributions, bin behavior, and uncertainty.

Explore geometric Brownian processes and random walks as models of continuous-time, continuous-value randomness in finance and science. See how these tools describe stock movements and dynamics in physics and biology.

Explore random walk modeling using Python by implementing a location class, a field, and step-based movement to simulate euclidean distances from the origin and analyze mean distances over multiple trials.

Explore biased random walks with south preference and restricted east-west movement, implement multiple drunk classes, and visualize how step choices affect distance from the origin through simulations.

Convert theory into a Monte Carlo stock-price estimator using geometric Brownian motion, exploring steps, trials, and inputs while highlighting the deterministic and stochastic parts.

Price options with Monte Carlo simulation under the Black-Scholes framework, including dividend considerations. Calculate terminal payoffs, average to the expected payoff, and visualize the distribution with histograms.

Explore Monte Carlo simulation for options pricing, compare Black-Scholes results with simulated prices, and visualize outcomes using histograms of calls and puts across varying inputs like strike, volatility, and dividends.

Explore basic data visualization techniques for financial analytics with Amazon stock data from 2006 to 2018, including open, high, low, close, volume, and rolling mean plots.

Explore open-high-low-close charts and interactive OHLC visuals to analyze stock data, compare monthly and weekly windows, and identify bullish and bearish candlestick patterns.

Analyze stock data using market research techniques and candlestick pattern chart. Connect price moves to events and preview machine learning driven predictive analytics in finance.

Read and prepare a multi-stock dataset, filter Amazon 2013–2018, convert dates to datetime, and set up time-series plots to enable predictive analytics in finance.

Learn linear and nonlinear regression, including line of best fit and polynomial (quadratic, cubic) fits, to estimate and predict future values with generalized additive and moving-average time-series concepts.

Predict stock prices using the generalized additive model via the profit package, regressing only on date and close price to forecast one year ahead with confidence intervals.

Explore the moving average technique to reveal stock price direction and trends by smoothing price data with customizable windows, without predicting exact future values.

Examine stock price trends with rolling means and moving averages across 20, 50, and 150 days, visualized as blue actual data and orange mean.