Deriving Options

What do olive presses, Las Vegas, and random walks have in common? The Black-Scholes Option Pricing model! A really interesting Veritasium video walks through a brief history of options and the mathematics behind the Black-Scholes model. And while the video does a good job of explaining option basics, it also discusses some of the beauty behind the math.

Retirement Options

When dealing with option valuation, you should always remember is that an option always has value until it is exercised or expires. And, more importantly, an option can never have a negative value. COVID-19 lockdowns and the resulting economic uncertainty have affected many colleges and universities. In August, a top private university offered its faculty members over 70 a chance to accept a buyout if they retire by June 2021. In response, the faculty responded negatively to the buyout plan, essentially arguing against being offered something of value, the option to retire with a buyout, for nothing.

VIX Volatility

The VIX, which measures the volatility of the S&P 500, has recently had an increased volatility, reaching levels not seen since the financial crisis of 2008. The level of the VIX is still in the area that generally occurs when the economy is in a recession. A JPMorgan analyst argued that the increased volatility was the result of price-insensitive traders who had "trend following strategies (CTAs), risk parity portfolios, and volatility managed strategies", all of which served to increase market volatility.

Option Straddles

So now that you have learned about options, maybe you think you are ready to buy and sell options. A popular option trading strategy is a straddle. With a straddle, you buy a call and a put with the same exercise price and expiration date. You are betting on the volatility of the underlying stock. That is, you make money with a big price movement either up or down. However, as with any investing strategy there are risks. With a straddle, you will lose if the stock price doesn't move enough to offset the price of both options. For more on straddles, check out this article.

Option Volatility

In the Black-Scholes option pricing model, the only variable that is not directly observable is the volatility of the stock. In practice, an implied volatility is often calculated. To do this, we take all of the observable variables including the option price, plug them into Black-Scholes, and solve for the standard deviation that gives us the current option price. Doing this calculation directly is not possible. You must use trial and error, or a computer program.

As you can imagine, when company specific news is expected in the future, the implied volatility rises. One announcement that can cause a large swing in the stock price is earnings. It is fairly common for the implied volatility to rise when a company's earnings announcement draws near. In this video, Dan Passarelli discusses the implied volatility of HP's options near the company's earnings announcement, as well as option trading strategies for HP stock. Note, the option trading strategies he discusses are fairly advanced.