Options pricing and the underlying asset

Options are essentially bets on the future evolution of the underlying asset's price.

For example, a put option is valuable when the spot (market) price falls below the option's strike price. The option holder may exercise the option to sell the underlying at the strike \(X\), and buy it back at the spot \(S < X\), yielding profit \(X - S\).

In this exercise you'll value and visualize a European put option on IBM stock, again applying the Black-Scholes pricing formula, as the spot \(S\) changes.

The strike X = 140, the time to maturity T is 1/2 a year, and the risk-free interest rate is 2%.

The annualized volatility of IBM is available as sigma, and the plotting axis option_axis is available to add your plot.

You can find the source code of the black_scholes() function here.

Set IBM_spot to be the first 100 observations from the IBM spot price time series data.
Compute the Numpy array option_values, by iterating through an enumeration of IBM_spot and by using the black_scholes() pricing formula.
Plot option_values to see the relationship between spot price changes (in blue) and changes in the option value (in red).

Exercise

Options pricing and the underlying asset

Instructions