With WTI oil remaining below $50 and the continuing uncertainty about the outcome of the tug-of-war between domestic shale producers and OPEC, there is a nontrivial probability of oil prices dipping to $40 and below. This article will present a forecast for the share price of Whiting Petroleum (NYSE:WLL) in such a scenario.

**Valuing equity as a call on assets, with strike equal to the outstanding debt**

In an earlier analysis of Whiting's assets and capital structure, I constructed a time series of estimated asset values by summing the traded values of the company's common stock, its outstanding notes and an estimate of the bank debt obligation. On the liability side, I proposed that the firm's debt structure be simplified by replacing it with a zero-coupon note with time to maturity equal to principal-weighted average maturity of Whiting's notes.

In credit analysis, *"structural credit models"* first proposed by Robert Merton *"derive the probability of default from the random variation in the unobservable value of the firm's assets."* The same thinking can be used to value common stock. Whiting's equity can then be viewed as the value of a call option on the firm's assets, with the strike equal to the face value of the equivalent zero-coupon note, or the combined amount of the principal value and the interest payments, computed to the term of the note, approximately 3.5 years from now. The ability to forecast where shares might trade at different (particularly, lower) oil prices is perhaps even more useful. This is made possible by the link between oil prices and the value of assets, established in the previous article.

To motivate the use of the Black-Scholes formula to estimate the fair value of the common stock, let's examine the series of returns on the underlying, here the estimated series of daily asset values and the frequency histogram of returns.

Chart 1: daily returns of the estimated asset value series since the beginning of 2016.

*Source: author's analysis*

The following exhibit presents the frequency distribution of the daily returns on asset value. The takeaway is that it looks rather like that of a normal distribution.

Chart 2: a frequency histogram of daily returns of the estimated asset value series since the start of 2016

*Source: author's analysis. Note that extreme value returns, those falling outside of the +/-5% band, are not shown.*

**How to use the Black-Scholes formula**

The inputs to the Black-Scholes formula are going to be as follows:

- The value of the underlying is the estimated value of Whiting's assets
- The time to maturity, currently 3.5 years, is the principal value-weighted average time to maturity of outstanding notes, issued by the company
- The strike of $3,835 million is the combined face value and interest payments, computed as if they were all made to the 3.5-year mark in September 2020
- The volatility, for the first attempt at equity valuation, is taken to be the 49% annualized value of 3.10% standard deviation of returns, computed using the daily series of estimated asset values. I will, however, delve deeper into this particular input, as we consider the potential impact of lower oil prices later in the article.
- The risk-free interest rate for 3.5-year term is taken to be 2% based on the examination of 3- and 5-year constant maturity Treasury rates

Chart 3: The resulting estimates of Whiting's share prices, compared to actual closing prices

Qualitatively, the model tracks the observed values rather well. The signs of deviations, observed early in 2016 and in the second half of the year, can be understood by looking at volatility patterns. The orange line in Chart 3 was computed using the constant volatility of 49% per annum, reflecting the average variability in Whiting's assets since the beginning of 2016. In fact, the value of assets was significantly more volatile early in 2016, exceeding 70% per annum. It then sustained a steady fall through most of 2016 to about 30%, only jumping late in the year as shares experienced a one-time appreciation on November 30, the day the OPEC deal was announced.

Chart 4: Realized volatility of estimated asset values of Whiting Petroleum, computed using a trailing 3-month window

Using a higher volatility early in 2016 would have pushed the orange curve in Chart 3 higher, in the direction of reducing the disagreement with the blue curve of actually observed prices. On the other hand, using a lower volatility later in 2016 and so far this year will pull the orange curve down, again having the effect of drawing it closer to how the market valued shares.

**What might happen to the common stock at lower oil prices?**

In an earlier analysis, I derived the relationship between medium-term oil prices and the forecast of the value of Whiting's assets. At any given oil price, for instance, at $40 per barrel, there is an estimate of the asset value. It can then be used as a variable input to the Black-Scholes formula, giving insight into the fair value of Whiting's shares at lower oil prices. I will attempt this exercise in two different volatility scenarios:

- Constant 49% annual volatility as used above, and
- A more realistic scenario, using a higher volatility when oil prices (and the value of Whiting's assets and the common stock) are lower and a lower volatility when oil is higher. Specifically, with the 6-month NYMEX WTI futures contract trading near $50 recently, the recently seen 30% volatility is appropriate. On the other hand, in view of sharply elevated volatility early in 2016, I assume a 70% volatility in Whiting's assets if oil were to drop to $30. Linearly interpolated volatility values will be used at intermediate oil prices.

Chart 5: Estimated share prices of Whiting Petroleum with oil in $30-50 range. The blue curve, representing a forecast for the scenario of volatility rising from 30% at $50 oil to 70% at $30 oil is believed to be more accurate than the flat 49% volatility case represented by the orange curve.

*Source: author's analysis*

The blue curve in the chart above, believed to be the best forecast, indicates that the fair value of shares is likely to remain above $5 as long as oil stays above $31. In comparison, shares dipped below $4 in February 2016, even as the 6-month WTI future had barely breached $33. The deleveraging undertaken in 2016 was the likely fundamental factor causing this difference.

**Conclusion**

Shares of Whiting Petroleum experience a rising volatility every time the oil prices drop. Such volatility in a declining market is an undeniable source of pain for most participants. Having a handle on the fair value is one possible approach to diverting attention away from day-to-day price noise. Today's Whiting might not be anti-fragile, yet is nonetheless much better protected from a possible downturn in oil prices than it was one year ago. I see its fair value at $9 per share or above as long as medium-term oil prices (represented by the 6th-month future) remain above $47 per barrel. The fair value is $7.07 per share with oil at $39 and $4.93 per share at $30 oil.

*Note from the author: Thank you for reading. If you like this article, please follow me by clicking the "Follow" link at the top of this page and choosing "Real-time alerts on this author" to be informed of my latest ideas.*

**Disclaimer:** Opinions expressed herein by the author are not an investment recommendation and are not meant to be relied upon in investment decisions. The author is not acting in an investment, tax, legal or any other advisory capacity. This is not an investment research report. The author's opinions expressed herein address only select aspects of potential investment in securities of the companies mentioned and cannot be a substitute for comprehensive investment analysis. Any analysis presented herein is illustrative in nature, limited in scope, based on an incomplete set of information, and has limitations to its accuracy. The author recommends that potential and existing investors conduct thorough investment research of their own, including detailed review of the companies' SEC filings and consult a qualified investment advisor. The information upon which this material is based was obtained from sources believed to be reliable, but has not been independently verified. Therefore, the author cannot guarantee its accuracy. Any opinions or estimates constitute the author's best judgment as of the date of publication and are subject to change without notice. The author explicitly disclaims any liability that may arise from the use of this material.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.