Option Pricing Calculator

On October 14, 1997, the presence and legitimacy of options dramatically grew more apparent, as the Nobel Prize for Economics was awarded to Robert Merton and Myron Scholes. Along with the deceased Fischer Black, Merton and Scholes developed a standardized formula for the valuation of options, a breakthrough that helped give rise to the $148 billion standardized options industry. The publication of the Black-Scholes formula in 1973 removed the guesswork and reliance on individual brokerage firms from options pricing and brought it under a theoretical framework that is applicable to other derivative products as well. What exactly is the Black-Scholes formula and how does it work? Basically, it values an option as a function of the following elements:

• Stock Price and Strike Price- The most important factor determining the price of an option is the underlying stock price relative to the striking price. This determines whether an option is in-the-money or out-of-the-money, and quantifies the option’s intrinsic value (the amount by which a stock price exceeds or is below the strike for calls and puts, respectively).

• Time until Expiration- The passage of time works against the options buyer, as the price of out-of-the-money options decreases at an accelerating rate as the expiration date approaches. This is called "time decay."

• Implied Volatility- Volatility reflects the propensity of the underlying stock to fluctuate either up or down. Premiums for on-the-money options are directly proportional to the expected volatility of the underlying stock.

• Dividend Status- Larger dividends reduce call prices and increase put prices, because paying out a dividend reduces the stock price by the amount of the dividend. Dividends increase the attractiveness of holding stock rather than buying calls and holding cash. Conversely, short-sellers must pay out dividends, so buying puts is more desirable than shorting stock.

• Interest Rates- Rising interest rates increase call premiums and decrease put premiums. Higher rates increase the underlying stock’s forward price, which is assumed by the model to be the stock price plus the risk-free interest rate over the life of the option.

One of the major assumptions of the Black-Scholes formula is that stock price movement is random. The model incorporates the "efficient market hypothesis," which holds that stock prices reflect the full knowledge and expectations of investors, and therefore there are no trending stocks. Many options investors, therefore, trade primarily on volatility projections (i.e., buy low volatility and sell high volatility) rather than predictions of the underlying stock price. We believe, however, that there is a trending bias in the market, whereby prices are dependent on each other over time. Using fundamental, technical, and sentiment analysis, we look for trending stocks to identify profitable option buying opportunities. In this way, we gain an edge on the options pricing model by buying trending stocks that the model prices cheaply by assuming random price movement. The result is that big price movements and low volatilities can coexist, providing the options buyer with a trading advantage.