1. Introduction

Private equity (PE) has been a catalyst providing an important and needed boost to promising enterprises that are relevant players across diverse sectors of the economy. According to data from the Eikon Refinitiv platform (^{LSEG Data & Analytics, 2024}), a total of $402.09 billion was raised in the US in 2024. Forecasts indicate there will be $7.7 billion in assets under management by fund strategy in 2029 (^{PitchBook, 2024}).

The growing appetite for private equity raises the question of whether there is a standardized valuation method among investors to make informed, rational decisions. However, in practice, methodologies vary depending on the valuation firm’s approach and the company being evaluated. Most commonly used methodologies include discounted cash flow (DCF) and comparable companies’ analysis (^{Hooke, 2024}). Others use performance metrics, such as internal rate of return (IRR), total value paid-in capital (TVPI), or public market equivalent (PME) measures (^{Kaplan & Schoar, 2005}). Private equity has proven challenging for traditional methods, as cash flows can be volatile (^{Robinson & Sensoy, 2016}). Also, there is strong recognition that private equity involves significant exposure to multiple sources of aggregate risk (^{Gupta & Van Nieuwerburgh, 2021}), that valuation of illiquid assets tends to be difficult, and that some fund managers report inflated valuations to raise more capital (^{Cumming & Walz, 2010}). Valuations can also yield different results across companies, depending on their sector, corporate governance, and country of origin (^{Smolarski et al., 2011}).

In PE, investors allocate their resources to a PE firm that invests in companies with strong growth potential, not only pouring capital but also providing managerial expertise. This unique market provides a higher level of complexity and challenge to traditional valuation methods. By using real options, valuations are more realistic and efficient, as they include the volatility PE carries in its process.

In real option valuation, the discount rate significantly affects the outcome, as the valuation is highly sensitive to interest rates: not only can the result change, but the timing of expiration and the valuation of the investment project can be affected as well (^{Ballestra et al., 2017}).

In the last five years, some papers have examined how venture capital (VC) can be analyzed through real option models. ^{Shuwaikh et al. (2024)} argue that real options are an input to the behavioral and strategic investment framework. ^{Deng et al. (2025)} developed a model to optimize investment and exit strategies in VC portfolios, focusing on the optimal period for maximizing returns. ^{Gupta and Van Nieuwerburgh (2021)} examine PE investment strategies, with an emphasis on value creation across investment stages and on strategic timing in response to economic changes.

This paper explores the use of real options as an alternative valuation method for private equity investments. It highlights the industry’s inherent volatility and examines how interest rates affect private equity valuation using the Black-Scholes model. The model quantifies the impact of interest rate changes on the option value of PE deals, illustrating how variations in the risk-free rate influence the values of call and put options. Thus, reflecting the potential for upside gain (as represented by call options) and downside risk (as represented by put options) that are characteristic of PE transactions.

2. Literature Review

3. Methodology

The methodology is based in part on the valuation model of ^{Schwartz and Moon (2000)}, as their proposal articulates that companies (their approach is for internet companies) should reflect growth as a key driver in their valuation (^{Schosser & Ströbele, 2019}).

This situation can be studied by analyzing data from recent PE deals involving companies that were delisted. The sample is based on data availability, deal size, and completion between 2019 and 2024, as such transactions provided sufficient public information for the valuation modeling. A significant part of the firms examined are from the technology sector, reflecting the strong presence of this sector in private equity deals. This industry’s high volatility is well-suited for analyzing the sensitivity of interest rates to PE valuations, as shown in Table 1 (Table 1).

The ^{Black-Scholes option pricing model (1973)} is introduced as a benchmark for valuing European style options. For this study, this model is proposed as it was developed for financial options, providing a useful framework for valuing investment opportunities under uncertainty. The formula for a European call option is:

Where:

To make this estimation, the input parameters are:

1. (K) Strike or Price. Deal size.

2. (S) Current value of investment: Value of target firm in discounted cash flow method before the change in interest rates, as in 2019.

Legend:

DCF= discounted cash flow

CF_i= cash flow period i

r = interest rate

n = time

3. (T) Time of expiration. Average time holding period of the PE firm. According to a S&P Global study, the average holding period in 2023 was 7.1 years (^{FRED, 2024}).

4. (r) Risk-free rate. Proxy for this study. Valuation is made for the interest rates presented in January from 2019 to 2023, as shown in Figure 1 and Table 2 (see Figure 1 and Table 2).

Source: Prepared by the authors.

Figure 1 FED Interest Rates 2019-2023 

5. (sigma) Volatility = standard deviation for the price of the stock of daily returns over the last two years prior to the private equity deal, as shown in Table 3 (see Table 3):

4. Results

Compared with traditional valuation models such as DCF, real option valuations obtained in this study tend to produce lower present values at high interest rates but higher relative values when volatility is high. The difference is due to DCF methodology, which discounts expected cash flow at a fixed rate, while real option valuation models incorporate uncertainty and the option to defer or abandon the investment. This can be appreciated in Table 4 (see Table 4).

Among the eight private equity transactions across different sections using the Black-Scholes model, as interest rates rise from 0.0216 to 0.0502, put option values decline across all firms (for example, Qualtrics from 9.17 to 8.18, Dell from 22.37 to 19.95), confirming that higher discount rates reduce the present values of expected profits. In contrast, call values remain stable and low, with almost no change, suggesting that the upside potential in PE is not as sensitive to rate increases. Software firms, such as Qualtrics, Coupa, and Squarespace, show slightly more variation in call options between low and high interest rates and between industrial and financial companies, suggesting that software company valuations are more sensitive to changes in interest rates. Overall, these results confirm that interest rate dynamics alter valuation outcomes in PE, validating the hypothesis that real option valuation models can capture the monetary policy impact that is often overlooked in traditional valuation models, which can be observed in Figure 2 and Table 4 (see Figure 2, below, and Table 4, above).

Source: Prepared by the authors based on data from ^{LSEG Data & Analytics (2024)}, modeled using R.

Figure 2 Plotted Results of Black-Scholes Valuation as Applied to Private Equity 

Figure 2 illustrates how, as interest rates increase, the put value slope moves downward, proving the inverse relationship between rates and valuation. Call values have a flat behavior, demonstrating stability on the upside. There is wider dispersion among software firms, reinforcing the role of volatility in valuation. This graph confirms the negative relationship between interest rates and put options across sectors. As interest rates increase, put option values decrease across all sectors. The decline is steeper for technology firms, showing their valuations are more sensitive to changes in interest rates. Industrial and financial companies, on the other hand, show smaller changes, which suggest their valuations are more stable. In contrast, call option values remain almost unchanged, showing little reaction to changes in interest rates.

5. Discussion

Call prices are nearly or exactly zero as the private equity funds are paying an elevated premium because the DCF value (S) is significantly lower than the acquisition price (K). Put options’ value decreases as interest rates rise, and they reflect the protection PE funds have if the deal is not profitable from a financial perspective, as a put gives the right to sell the asset at the acquisition price (strike price). Volatility in the software industry is reflected in higher option prices, as companies with low cash flows before deals were made, indicating that the industry is usually unpredictable due to rapid technological change.

Private equity interventions in the electrical equipment, financial services, and computers sectors do not offer a clear path for the industry, as companies in the same categories show mixed results. What is consistent is that larger valuations, such as Refinitiv or Dell, result in more stable cash flows and relatively balanced risk measurement, as volatility. Deals with higher acquisition prices tend to have higher option prices and greater exposure to interest rate volatility, as capital is at risk and valuation errors can be quite expensive.

Call option values are generally low, as most DCF calculations are below the strike price and prices are low, reflecting expectations of growth-the central assumption in PE. Also, higher interest rates increase the value of the call option. Put option prices in McAfee, Dell, and Refinitiv are high, which implies an elevated risk of loss. These results confirm that interest rates affect the variation in call and put prices across sectors, showing that higher discount rates increase the feasibility of holding options.

These eight deals illustrate the importance of considering risk in PE and the value of strategic insights for the buyer, showing how PE interventions in large companies are exposed to rate discounting and how much downside risk these deals embody.

6. Conclusion

Real options present the value of a company as a dynamic set of alternatives, reflecting a flexibility value that is highly common in private equity, including the impact of changing interest rates. Volatility, as an important element in real options and PE, is consistent with higher option prices in the software industry. Also, companies that reported negative cash flows before PE intervention reflected higher put option prices as a signal of risk. In almost all deals, the DCF valuation was below the price paid, showing that PE deals are not based on current values but on potential values driven by the opportunity for PE firms to intervene. The deals presented show low call option values, suggesting PE funds pay more based on the firm’s long-term possible value, and this approach does not align with the commonly used DCF valuation. High put option values reflect the high risk of these investments, such as, for example, software companies in this study.

Call options are more valuable as interest rates rise, suggesting a potential incentive to keep the option open, while put options lose value. Changes in interest rates affect valuations, as monetary policy can change the cost of capital and reduce DCF valuations. Real option valuation can adjust to such changes, as the timing of acquisitions can align with monetary policy conditions.

These eight deals illustrate the relevance of considering risk in PE and the importance of getting strategic insights for the buyer, showing that the intervention of PE in large companies is exposed to rate discounting, as changes in monetary policy are a given in the current economic environment, providing parameters of certainty where decision-making must be strategic. This study goes beyond measuring how interest rates affect PE valuation; it shows that real options offer a broader view of how uncertainty and macroeconomic fluctuations affect investors’ decisions. These findings suggest that changes in monetary policy affect how PE firms invest. Sectors such as technology, which are more volatile, are especially sensitive to interest rate changes and provide evidence that adopting option-based models is a suitable alternative when evaluating PE investments.

As discussed, real option valuation is a reliable alternative for providing accurate PE valuations. A future research opportunity that arises from this study is to explore a similar approach using the ^{Cox et al. (1979)} binomial lattice model, where their simple discrete-time model, assuming price evolves step by step, provides a more flexible valuation that may be suitable for an illiquid, high-risk market.