The options market has begun to price in a sizable amount of volatility for shares of Hertz Global Holdings, Inc. (HTZ). This comes as the rental car company deals with a tumultuous time. Still reeling from a difficult quarter last time around, Hertz has wrestled with depreciation issues, an IT upgrade and a tough industry environment. All while a famously vocal investor increases his share in the company and the company enacts a major leadership change.Hertz is coming up on its next quarterly report in less than a week, the first under its new CEO. Investors have not reacted well to the company's last two earnings reports, but there is at least one analyst who says a going-private transaction may be in the offing if shares continue to fall.Implied Volatility for HTZ began drifting higher in late January. The advance has continued into the end of February, with IV reaching 69.7, its highest level since November. It ticked off that level slightly early this week.IV for Hertz spiked in November amid two pieces of news.First, the company released a disappointing third-quarter report. The company posted an adjusted quarterly profit of $1.58 per share, down from $2.00 per share a year ago. Revenues slipped 1% to $2.5 billion. The company also dramatically cut its full-year guidance, saying it now expected between $0.51 and $0.88 per share, compared to its previous forecast of $2.75 to $3.50. The reduction came on an adjustment in the depreciation rate of its fleet of vehicles.On the news, shares dropped 22.5%. Going into the report, the options market was pricing in 10.5% move on the earnings announcement.This followed a disappointing quarterly report in August, which saw the company post a quarterly loss and prompted a 5% drop in its stock price.In the second revelation that impacted HTZ in November, news came out that activist investor Carl Icahn more than doubled his stake in the company. According to a regulatory filing, Icahn bought an additional 15.1 million shares of HTZ, boosting his stake to more than 30%.With his increased stake, Icahn has already begun affecting change at the company, starting with a leadership shakeup. CEO John Tague was replaced by Kathryn Marinello earlier this year - its third chief executive since 2014. Meanwhile, CFO Jeffrey Foland is slated to end his tenure with the company at the end of this month.Last week, the stock was hit by a downgrade from Credit Suisse. Analyst Anjaneya Singh lowered the firm's rating on shares of HTZ to Underperform from Neutral, part of the aftermath of a disappointing earnings report from rival Avis Budget Group (CAR). Hertz's price target was also cut, from $27 to $15. Singh noted that Hertz is facing a weak business environment, with "flattish pricing and inflationary fleet costs." In the same note to clients, Credit Suisse downgraded Avis as well. While Avis has significantly outperformed Hertz over the past year in terms of stock price, the company's most recent quarterly report included negative volume growth. Singh downgraded Avis to Neutral from Outperform.In the report, Singh noted that Icahn could look to take Hertz private if the downward slide in its stock continued.Hertz's next quarterly report is due out on February 27. The company is projected to lose $0.49 per share on the quarter, compared to a profit of $0.05 per share in the same period last year. Revenue is projected to fall more than 15%, with analysts predicting a top-line figure just above $2 billion.The ATM Straddle premium for HTZ for the March 17 expiration is $2.95, or 14.8%. Looking further out, the January 2018 expiration has a premium of $9.10, or 45.5%. The premium for the January 2019 expiration is currently at $12.80, or 64.1%.