## Abstract

Multiple financial stocks are due to report earnings in the coming weeks. Option traders can profit from the rise in implied volatility as the earnings report approaches. The daily implied volatility for Bank of America (BAC), JP Morgan (JPM), and Wells Fargo (WFC) was calculated during the lead up to recent earnings reports. The calculated implied volatility was graphed and used to determine appropriate low and high levels of implied volatility for each stock.

## Introduction

It is well documented that implied volatility in options increases before an earnings release and Seeking Alpha contributor Kim Klaiman writes extensively on the subject. An increase in implied volatility can change the value of a stock option position. The rate of change in the value of an option position for a change in implied volatility is a calculated quantity referred to as Vega. Option positions that have the greatest increase in implied volatility are those with the nearest date of expiration. This is significant because an option position losses value at an increasing rate as the date of expiration nears. The change in value of an option position for each passing day is also a calculated quantity referred to as Theta. In order to profit from a rise in implied volatility as earnings approach the change in value of an option position attributable to the increase in implied volatility must be greater than the change in value loss to time.

An investor who is attempting to profit from a rise in implied volatility should have a realistic goal for the increase in implied volatility as the earnings report approaches. The investor can look at option prices leading up to past earning reports to predict what implied volatility may rise to.

The implied volatility of any option position can be calculated by a partial differential equation referred to as the Black-Scholes formula. The Black-Scholes formula uses variables of the underlying stock price, strike price, time until expiration, risk-free interest rate, implied volatility, and value of a call position. If five of the six variables are known the sixth can be calculated. This youtube video does a great job of explaining how anyone can use the Black-Scholes formula in excel.

## Methodology

The Black-Scholes formula was used to calculate implied volatility for a few different financial stocks that will soon release earnings. The stocks that were analyzed were BAC, JPM, and WFC.

Historical option data provided by Think or Swim was used for the calculations in this article. The historical data includes the bid and ask price for all calls and puts at each strike price and date of expiration at the closing bell for each day. The closing price of each stock is also included. The implied volatility is rarely included but everything necessary to calculate it is included in the data or readily accessible.

Because implied volatility varies according to date of expiration and strike price it is important to keep a consistent method when calculating and comparing implied volatility. The increase in implied volatility before an earnings release is greatest for options that are soon to expire, therefore the weekly option created the week before earnings release was evaluated. The strike price was always the first strike price below the closing stock price on the Thursday that the weekly option was created. This strike price was used regardless of any changes in the stock price before the option expires.

*click to enlarge*

*Figure 1: Historical Option Data for BAC on January 12, 2012. The earnings were released on January 19, 2012. Using the methodology described above the $6 call option was used to calculate implied volatility.*

The Black-Scholes formula also requires a risk-free interest rate. 2% was used for all calculations. The time remaining before expiration is expressed in years and was calculated by dividing the number of days before expiration by 365.

At this point all the information necessary to calculate the call price is readily available except the implied volatility. The implied volatility was calculated using a guess and check methodology. An initial guess of the implied volatility was used to calculate a price for the call option. This calculated price for the call option was compared to the actual bid price of the call option as reported in the data. The implied volatility was adjusted until the calculated call price equaled the bid price of the call according to the available data.

## Results and Conclusions

The results for BAC, JPM, and WFC were graphed and presented below. Citigroup (C) was also analyzed but the low stock price for most of the recent earnings reports made accurately calculating implied volatility difficult. Therefore, it was decided to not be included.

*Bank of America*

BAC reports earnings April 19. The implied volatility for weekly BAC options is presented in the chart below.

*Figure 2: The implied volatility of BAC before earnings.*

Figure 2 shows some clear trends in the implied volatility of weekly options before Bank of America's earnings. A target implied volatility of 80% appears to be a reasonable goal when trading IV before BAC earnings, likewise an implied volatility below 50% appears to be a good entry point.

*JP Morgan*

JPM reports earnings April 13. The implied volatility for weekly JPM options is presented in the chart below.

*Figure 3: The implied volatility of JPM before earnings.*

Figure 3 shows the rise in implied volatility of JP Morgan weekly options before earnings. The earnings period with a significantly greater overall implied volatility corresponds to last October when volatility was up in the entire market. The trend in the graph indicates that an implied volatility of 55% is a reasonable target with implied volatility below 35% indicating a good entry point.

*Wells Fargo Company*

WFC reports earnings April 13. The implied volatility for weekly WFC options is presented in the chart below.

*Figure 4: The implied volatility of WFC before earnings.*

Figure 4 shows the implied volatility of WFC before earnings. The day corresponding to the earnings release is yellow. JPM did not show an obvious trend in implied volatility like BAC and WFC did. However, it would be reasonable to assume a 35% implied volatility or less is a reasonable entry point and anything approaching 50% is to be considered a good point of exit.

It is certainly possible to profit from a rise in implied volatility in all three stocks as their earnings release nears, however the key is disciplined investing and well timed trades. By evaluating implied volatility before entering a trade an investor can enter at a point of low implied volatility and therefore inexpensive entry point. Likewise, an investor can evaluate implied volatility to determine a proper trade exit.

**Disclosure: **I am long BAC.

**Additional disclosure:** I may make a trade non-directional trade based on an anticipated rise in implied volatility over the next 72 hours.

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