Dumbass.fish prices short/medium term options by estimating the PDF (probability density function) of the underlying equity and the integrating the option payoff function over that PDF. The resulting predictions are not authoritative (predicting the future is always hairy) but represent a fair numerical model of future behavior, divorced from as many assumptions as possible.

Dumbass.fish constructs a model of the PDF of the daily log-price movements of an equity based on the recent  historical movements of the equity. This means that we're modeling variance and estimating payoff under that variance model rather than predicting whether an equity is going to go up or down.

Our variance model explicitly assumes that the discounted future expected value of an equity is equal to its current value. A closely related concept is referred to as the Martingale hypothesis and implies that the center of mass of the PDF lies at approximately the risk-free rate. This is another way of saying that the present price of an equity is a fair price and we expect purchasing an equity at the current price to be approximately as good an investment as any other.

We approximate the PDF by empirically constructing the CDF (cumulative distribution function) from recent data, passing it through a gaussian filter and then taking the derivative. Once we have computed the PDF for a given target date, we can estimate the expected value of a given call or put option by integrating the payoff function over the PDF.

From the PDF we can calculate the expected value of an option by integrating the payoff function of an option over our expectations of future prices.