Emission Allowance as a Derivative on Commodity-Spread

We provide a valuation formula for emission allowance. Assuming that the value of emission allowance on the last day of a trading phase is equal to a spread of commodity prices (e.g. electricity and natural gas) when the spread is positive and less than the penalty, we show that the emission allowance price is equal to the value of a portfolio of European call options on the spread of the commodities. Using the formula, we obtain a hedging strategy for emission allowance trading. We also empirically analyze option value embedded in emission allowance, and find by numerical analysis that the option value is relatively large.     

Analytical Approach to Value Options with State Variables of a Levy System

In this paper we present an analytical method in pricing Europeancontingent assets, whose state variables follow a multi-dimensionalLévy process. We give an explicit formula for the hypotheticalEuropean "two-price" call option price by means of the conditionacharacteristic transform. The work not only unifies and extendsthe option pricing literature, which focuses on the use of thecharacteristic function, but also provides the way to formalizeandunify the valuation of the option price, the valuation of thediscount bond price, the valuation of the scaled-forward price,and the valuation of the pricing measure in incomplete markets.JEL Classification codes: G13     

CEO compensation, option incentives, and information disclosure

This paper examines the impact of information disclosure on the valuation of CEO options and the incentives created by those options. Prior executive compensation research in the US has made assumptions about key input variables that can affect the calculation of option values and financial incentives. Accordingly, biases may have ensued due to incomplete information disclosure about noncurrent option grants. Using new data on a sample of UK CEOs, we value executive option holdings and incentives for the first time and estimate the levels of distortion created by the less than complete US-style disclosure requirements. We also investigate the levels of distortion in the UK for the minority of companies that choose to reveal only partial information. Our results suggest that there have to date been few economic biases arising from less than complete information disclosure. Furthermore, we demonstrate that researchers using US data, who made reasonable assumptions about the inputs of noncurrent option grants, are unlikely to have made significant errors when calculating CEO financial incentives or option wealth. However, the recent downturn in the US stock market could result in the same assumptions, producing exaggerated incentive estimates in the future.     

Valuing Assets Using Real Options: An Application to Deregulated Electricity Markets

This paper provides a detailed case of the application of real options valuation techniques to value a contract for the use of a power generation facility. The authors' aim is not primarily to offer a valuation "recipe" for a specific type of asset, but to show how the real options framework can be actually made to work in a variety of situations.
The case illustrates how minor adaptations that take into account the ways in which actual settings differ from the assumptions of standard formulas like Black-Scholes can be used to increase the precision and realism of results. By introducing relatively simple changes to a standard options valuation model, the authors obtain results that are reasonably close to those reported for actual transactions involving similar types of assets. Despite the industry-specific context of the analysis, the applicability of the techniques discussed in the paper should extend beyond the energy industry to other contexts characterized by similar types of uncertainty and production process, particularly those associated with minerals and other commodities.     

Determinants of discretionary fair value measurements: the case of Level 3 assets in the banking sector

The objective of our research was to respond to the call of Barth and Taylor ( 2010 ) for more research to examine the role of discretion in fair value estimates. Specifically, we investigate factors that explain banks’ accounting choices to use Level 3 valuation inputs from the fair value measurement hierarchy. Using hand‐collected data from a sample of international banks during 2009–2013, we find that incentives to use discretionary Level 3 valuation inputs, which can provide an opportunity to manage earnings, are associated with both firm‐level and country‐level determinants. Additional tests provide evidence that Level 3 ‘transfer‐in’ behaviour is related to changes in bank characteristics.     

Saddlepoint approximations to option price in a regime-switching model

In this paper we consider the saddlepoint approximation for the valuation of a European-style call option in a Markovian, regime-switching, Black–Scholes–Merton economy, where the price process of an underlying risky asset is assumed to follow a Markov-modulated geometric Brownian motion. The standard option pricing procedure under this model becomes problematic as the occupation time of chains for a given state cannot be evaluated easily. In the case of two-state Markov chains, we present an explicit analytic formula of the cumulant generating function (CGF). When the process has more than two states, an approximate formula of the CGF is provided. We adopt a splitting method to reduce the complexity of computing the matrix exponential function. Then we use these CGFs to develop the use of the saddlepoint approximations. The numerical results show that the saddlepoint approximation is an efficient and reliable approach for option pricing under a multi-state regime-switching model.     

Volatility transmission between energy-related asset classes

Energy companies, alternative or traditional, have been in the center of both financial and political debates during the last few years all around the world. Extensive crises related to fossil fuel resources have triggered the creation of brand new sources while the further development of already-in-use alternative sources is highly encouraged. Energy portfolios are important tools in most investor strategies and the way to incorporate new alternative energy companies in those portfolios has been a large part of the debate. Regardless of the strategy, be it in derivatives or traditional stock portfolios, risk anticipation and management are keys to a successful implementation. The purpose of this study, aside from filling a gap in literature, is to aid investors in risk anticipation and asset allocation through shedding some light on risk transmission effects between energy sub-sector company portfolios and energy commodities. Sub-sectors tested in this study include petroleum, coal, natural gas, solar, nuclear, wind, and biofuel companies. We find that risk spills over from energy companies to some commodities, and not vice versa. The most influential sub-sector is found to be petroleum companies.     

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.     

The Gap between the Theory and Practice of Corporate Valuation: Survey of European Experts

The valuation of companies or their assets is at the heart of most financing and investment decisions. Over the last five decades, academics have developed several simple and sophisticated models for corporate valuation. Yet valuation estimates of a firm or its assets appear to vary widely among practitioners. It is unclear whether these differences arise from practitioners' use of different valuation models or from differences in their assumptions about the inputs used in those models. To provide some insights into this issue, the authors recently surveyed 365 European finance practitioners with CFAs or equivalent professional degrees. They find that almost all survey respondents use the Discounted Cash Flow (DCF) model (along with some version of Relative Valuation that relies on the use of “comparables”). But the estimation methods of such practitioners for almost all inputs in the DCF model, including beta, the equity market risk premium, leverage, cost of debt, and terminal value, vary widely. This can be a serious problem because even small differences in inputs can cause huge variations in valuations. Such differences arise primarily because theory provides little guidance on how to estimate parameters, leaving practitioners to make their own assumptions and judgments. In sum, the authors' findings suggest that the process of estimating valuation parameters can be as important as the choice of the valuation model itself, and requires the serious attention of academics and practitioners. The authors recommend that key valuation parameter estimates be disclosed in financial and valuation reports. Their findings are also relevant to policy makers because the concept of “fair value” plays such a central role in post‐crisis regulation.     

Highly Valued Equity and Discretionary Accruals

Abstract:  Overvalued equity provides a strong incentive for managers to report earnings that do not disappoint the market (  Jensen, 2005 ). We find that this can be extended to highly valued equity more generally. In the year following the classification as highly valued and compared to firms with less extreme valuations, highly valued firms have significantly higher discretionary accruals and exhibit a more pronounced positive association between discretionary accruals and proxies for the likelihood of failing to meet earnings targets. These findings are consistent with the use of discretionary accruals to manage earnings in support of extreme valuation. Because highly valued equity will likely result in CEOs with valuable stock and stock option portfolios, we test whether and show that the overvalued equity incentive is incremental to a CEO's equity portfolio incentive. One implication is that directors and audit committees should be especially on guard for possible earnings management when a firm has extremely high valuation multiples and when the CEO has a lot of equity at risk.     

Arbitrage bounds in markets with noisy prices and the puzzle of negative option prices implicit in bonds

The term structure of interest rates has occupied economists for many years. This is testimony to the importance of the term structure (or, equivalently, valuation operator) and to the difficulty of obtaining reliable estimates of it. Until recently, it was not possible to reconcile the theoretical existence of a multiplicity of valuation operators in an incomplete bond market and the empirical nonexistence of even a single one. MacKay and Prisman [Estimating valuation operators in incomplete market with noises: Can noise complete the market. Working paper, 1996] tackle this problem. In this paper, an amendment to and a generalization of their methodology is presented. The amendment preserves the linearity of valuation operators and allows use of efficient linear programming techniques. Further, it facilitates an admissible consideration of the puzzle of negative option prices embedded in bonds. The empirical results presented in this paper were obtained using data on extendable Government of Canada bonds. The results indicate that although the gap between the lowest and the highest prices assigned to a cash flow by different valuation operators is significant, it is not sufficient to resolve the above-mentioned puzzle.     

On the range of options prices

In this paper we consider the valuation of an option with time to expiration and pay-off function which is a convex function (as is a European call option), and constant interest rate , in the case where the underlying model for stock prices is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for “most” such models, the range of the values of the option, using all possible equivalent martingale measures for the valuation, is the interval , this interval being the biggest interval in which the values must lie, whatever model is used.     

Employee Stock Options, Equity Valuation, and the Valuation of Option Grants Using a Warrant-Pricing Model

We investigate the use of a warrant‐pricing approach to incorporate employee stock options (ESOs) into equity valuation and to account for the dilutive effect of ESOs in the valuation of option grants for financial reporting purposes. Our valuation approach accounts for the jointly determined nature of ESO and shareholder values. The empirical results show that our stock price estimate exhibits lower prediction errors and higher explanatory powers for actual share price than does the traditional stock price estimate. We use our valuation approach to assess the implications of dilution on the fair‐value estimates of ESO grants. We find that the fair value is overstated by 6% if we ignore the dilutive feature of ESOs. Furthermore, this bias is larger for firms that are heavy users of ESOs, small, and R&D intensive, and for firms that have a broad‐based ESO compensation plan.     

Option Valuation with Systematic Stochastic Volatility

We use an extension of the equilibrium framework of Rubinstein ( 1976 ) and Brennan ( 1979 ) to derive an option valuation formula when the stock return volatility is both stochastic and systematic. Our formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options. If the “mean,” volatility, and “covariance” processes for the stock return and the consumption growth are predictable, our option valuation formula can be written in “preference-free” form. Further, many popular option valuation formulae in the literature can be written as special cases of our general formula.     

Deferring real options with solar renewable energy certificates

This study evaluates investment in a utility-scale solar power plant using a real-options approach (ROA). Although ROAs have been widely applied in the literature, the deferring option for a utility-scale power plant has not been fully examined, especially within the context of the unique subsidy program of solar renewable energy certificates (SRECs) in the USA. Using data from one of the most developed solar electricity markets in New Jersey, we incorporate the time-varying volatility of electricity prices and bounded SREC prices in real-options valuation. Our results show that deferring real options generates significant value for the project that the traditional discount cash flow approach ignores. It is thus optimal to postpone the investment in more than 70% of cases. In addition, we demonstrate that debt financing is crucial for renewable energy investments.     

Robust stock option plans

The main purpose of this paper is to address the issue of robustness of stock option plans, which is essential for reliable accounting valuations. The introduction of the accounting standards SFAS 123R and IFRS 2 for executive stock options has led to an important change. As companies are now forced to value their stock options at grant date for accounting purposes, the robustness of prices against the choice of certain valuation models and input parameters has become a very important issue. We address this issue by first analyzing certain building blocks of existing stock option plans with regard to their robustness properties. Based on our analysis, we then show how robustness of stock option plans can be achieved. The resulting stock option plans are both transparent in structure and reasonable in respect to the incentives they provide in order to increase shareholder value. We therefore conclude that stock options can be reliably expensed, if the corresponding plans are properly designed.     

DIVIDENDS, DIVIDEND POLICY AND OPTION VALUATION: A NEW PERSPECTIVE

This paper develops a model which explicitly incorporates the impact of the payment of dividends on the underlying stock into the valuation of both American and European calls and puts. Unlike earlier models, what we call the Dividend Adjustment Merton (DAM) model neither assumes arbitrary continuous dividends nor uses ad hoc methods to adjust for discrete dividend payments. Instead, it assumes the existence of a Miller and Modigliani (1961) valuation neutral dividend policy and adjusts Merton's constant proportional dividend model to incorporate any known schedule of discrete cash dividends of this type. The DAM model produces results which are equal to or superior to those of the separate models now used to value American calls (the Roll-Geske-Whaley model) and American puts (the Geske-Johnson model) on dividend paying stocks. It has the virtue of being internally consistent in that the same model can be used to value both calls and puts. In developing the DAM model, the paper clarifies the role of dividends and dividend policy in determining option values. It also produces significantly tightened boundary conditions for option values.     

Business cycle,storage, and energy prices

This study examines the effect of the state of the economy and inventory on interest-adjusted bases and expected returns for five energy commodities. We find that interest-adjusted bases and returns have a business cycle pattern. Consistent with the theory of storage, demand shocks near business cycle peaks generate negative interest-adjusted bases and positive returns. In recessions, the bases become positive, and the average returns are negative. Our regression results also show that the interest-adjusted bases of energy commodities are counter-cyclical and the expected returns are pro-cyclical. For petroleum commodities, inventory has a significant effect on interest-adjusted bases at low levels of inventory, whereas at high inventory levels the effect of inventory on the bases is weak. Finally, we find that the bases and economic conditions predict spot returns in energy commodity markets.     

Continuous rainbow options on commodity outputs: what is the real value of switching facilities?

We develop real rainbow option models to value an operating asset with the flexibility to choose between two commodity outputs. We provide a quasi-analytical solution and a numerical lattice solution to a model with continuous switching opportunities between two commodity outputs, taking into account operating and switching costs. The models are applied to an illustrative case, demonstrating that the quasi-analytical solution and the lattice approach provide near identical results for the asset valuation and optimal switching boundaries. We find that the switching boundaries generally narrow as prices decline. In the presence of operating costs and temporary suspension, however, the thresholds diverge for low enough prices. A fertilizer plant with flexibility between selling ammonia and urea is valued in an empirical section using our real option models. Despite the high correlation between the two alternative commodities, ammonia and urea, there is significant value in the flexibility to choose between the two. Both strategic and policy implications for stakeholders in flexible assets are discussed, with some generalisations outside the fertilizer industry.