The analysis and valuation of interest rate options

This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.     

To Invest or not to Invest: A real options approach to FDIs and tax competition

Foreign investment decisions of firms are often characterized by investment irreversibility, uncertainty, and the ability to choose the optimal timing of foreign investments. We embed these characteristics into a real option theory framework to analyze international competition among countries to attract mobile investments when firms, after the investment is sunk, can shift profit to low tax countries by transfer pricing. We find that an increase in the uncertainty of profit income reduces the equilibrium tax rates, whilst lower investment costs or larger profits, counteracts the negative fiscal externality of tax competition leading to higher equilibrium tax rates. JEL Code H25     

Binomial basis for linear information dynamics: real options, dividends and the valuation of equity

Analytical research has confirmed that real options give rise to the kind of nonlinearities observed in practice between equity prices and the figures appearing on corporate financial statements. We develop these real option values in terms of a quasi 'supply-side' model of linear information dynamics based on simple discrete time binomial filtration processes. Our analysis shows that the linear models that pervade the empirical (and analytical) work of the area, will almost certainly suffer from an omitted variables problem. Parameter estimation will then be inconsistent and inefficient.     

A real options approach for evaluating the implementation of a risk-sensitive capital rule in banks

I evaluate a bank's incentives to implement a risk-sensitive regulatory capital rule. The decision making is analyzed within a real options framework where optimal policies are derived in terms of threshold levels of credit risk. I provide a numerical example for the implementation of internal ratings based models for credit risk (the IRB approach) under the new Basel Accord (Basel II).     

Making sense of future uncertainties using real options and scenario planning

Healthcare across the world is facing many uncertainties. In Dutch healthcare, a recent policy change is forcing health organizations to deal more efficiently with their real estate, and this increases the need for real estate strategies that are more flexible. In order to support managers in incorporating flexibility in their decision-making over the design of new healthcare facilities, we have developed a method that combines scenario planning and real options. Scenario planning enhances sensemaking over the consequences of future uncertainties, and real options should help in addressing flexibility in decision-making through weighing the pros and cons of flexibility measures. We illustrate the sensemaking process by applying the method to a hospital, to a forensic clinic and to a care organization for vulnerable citizens. Data collection took place through interviews and workshops. We found that the identity and characteristics of the workshop participants influenced the sensemaking process. The method proved a useful means of making sense of abstract uncertainties that influence an organization, aspects that are normally outside the scope of real estate managers. The real options approach offered a more structured way of balancing the costs and benefits of strategies in dealing with future uncertainties.     

Real (adaptation) options and the valuation of equity: some empirical evidence

Data from 1,374 firms across four broad industrial groupings are used to assess the contribution that real (adaptation) options make to overall equity values. The analysis indicates that real (adaptation) options make a significant contribution to the equity value of firms with a market to book ratio (of equity) of around unity or less. As the market to book ratio grows beyond this level, however, the contribution made by real (adaptation) options decays quickly away and equity values are mainly comprised of the present value of the dividends that firms are expected to pay. This means that for around one in every five of the firms in our sample real (adaptation) options make a significant contribution to overall equity value. Thus, while linear equity valuation models would seem to be appropriate for the substantial majority of firms on which our sample is based, there is a sizeable minority of firms where real (adaptation) options have a significant impact on equity values. For this latter group of firms there will be a non-linear relationship between equity value and its determining variables. This has important implications for the regression procedures that are applied in this area of accounting research.     

Analyzing firms' strategic investment decisions in a real options' framework

Within the context of investment under uncertainty, the real options literature has led to models that capture primarily the time to wait flexibility of monopolistic corporations' investment decision. In this paper, we propose an approach which relies on barrier options to model production and/or sales delocalization flexibility for multinational enterprises making decisions under exchange rate uncertainty. We then extend the model by introducing game theoretic considerations to show how the information set and the competitive structure of the market may lead firms to act strategically and exercise their delocalization options preemptively at an endogenously fixed exchange rate barrier.     

The market premium for the option to close: evidence from Australian gold mining firms

This study shows the market value of gold mining firms contains a premium for the option to close. The sample uses 41 gold mining producers listed on the Australian Stock Exchange from 1987 to 2013. The premium of the market price over the present value of cash flows is isolated and a pooled cross‐sectional regression tests the degree of association between that premium and theoretical option premiums. The results show market prices incorporate a premium reflecting the option to temporarily close operations. The magnitude of the option premium to close depends on whether firms are out or in the money options.     

Organisational change and performance in long-lived small firms: a real options approach

This paper supports two key principles of real options reasoning: (a) the value of waiting and (b) the value of staging. It tests whether real options logic applies to small firms implementing significant changes (e.g. in technology) in a model of small firm performance, estimated on data collected by interviews with entrepreneurs. We found that to achieve a higher value by waiting, a delicate balance of precipitators of change against time until exercise is necessary (e.g. if there were just one or two precipitators, then waiting would certainly raise the value). Similarly, to achieve a higher value by staging, the entrepreneur needs to balance embedding against investment time. Thus, provided that investment time is less than 1¼ years, we found that embedding will raise the value. Overall, this implies that strategic flexibility in investment decisions is necessary for good long-run performance of small firms.     

The commodity super price cycle and real options: Implications for the Greeks of mining firms

The Real Options Approach (ROA) to the management and valuation of mining firms should impart a distinctive pattern to the time path of the Greeks displayed by such firms during the recent price super cycle. This paper simulates the delta, gamma, vega and rho of a gold mining firm holding a portfolio of heterogeneous mines over the recent gold price cycle, to find out the telltale signs that the ROA should leave on the trajectories exhibited by such variables during that period. We show that the ROA and the standard NPV approach to mine management and valuation predict markedly different trajectories for the Greeks.     

Market switching in shipping — A real option model applied to the valuation of combination carriers

This paper derives a real options model of flexibility and applies it to shipping, valuing the option to switch between the dry bulk market and wet bulk market for a combination carrier, a ship type that is capable of operating in both markets but that has fallen out of favor due to high price tags. The model is a mean-reverting (Ornstein–Uhlenbeck) version of a standard entry–exit model with stochastic prices. A closed form solution for the value of flexibility is derived, expressed in terms of Kummer functions. The estimated value of flexibility is related to historical price differentials between combination carriers and oil tankers of comparable size. Based on numerical experiments it is concluded that new combination carriers may enter the market in the near future.     

Equity value,implied cost of equity and shareholders’ real options

This study investigates the effects of shareholders’ real options on (i) firm financial performance and (ii) estimations of the implied cost of equity. After measuring the equity value of steady‐state operations using the residual income model, and the abandonment and expansion options using the Black‐Scholes option pricing model, I find that firms with a large expansion (abandonment) option value experience better (worse) financial performance than those with a small such value. I also find that ignoring these options results in a downward bias in implied cost of equity estimates by an average of 1.23 percentage points.     

Real options at the interface of finance and operations: exploiting embedded supply-chain real options to gain competitiveness

Exploiting embedded supply-chain real options creates powerful opportunities for competitive manufacturing in high-cost environments. Rather than seeking competitiveness through standardization as is common to lean production, real-options reasoning explores opportunities to use supply-chain variability as a strategic weapon. We present an illustrative case study of a Swiss manufacturer of cable extrusion equipment supported by a formal real-options model that aids in valuing the embedded options that make up supply-chain flexibility: postponement, contraction, expansion, switching, and abandonment. Real-options reasoning provides a plausible retrospective rationale for the case firm's use of supply-chain flexibility that provided protection against competition from low cost, but less responsive competitors. Their intuitive real-options reasoning facilitated incorporating fuller information concerning volatility, flexibility, and control into choosing what products to make, in what quantity, and with work allocated to which supplier. The case study also highlights how competing through exploiting embedded real options requires a different managerial skill set than does competing through cost reduction. Skills such as customer communication, supplier management, and ability to ensure a smooth flow of production join the ability to reduce and control lead times as key sources of competitive advantage.     

Revisiting the Tourinho real options model: outstanding issues 30 years later

This article presents and extends the first known model in real options, proposed in Tourinho (1979), and provides thoughts on addressing issues that are still outstanding 30 years later. It discusses the need to ensure the existence of market equilibrium when applying real options valuation to price assets, once all agents behave as suggested by the solution to the pricing equation. It argues that this can be achieved by using a stochastic process for the price that is sufficiently general to respond to supply and demand imbalances in the market for the resource. Once the individual decision rules are derived, the parameters of the process must be determined to ensure market equilibrium exists. For reserves of natural resources, this can be done by using a mean-reverting process for the price of the commodity and ensuring that the long-term price to which it reverts equals the trigger price for development of the marginal reserve.     

A Bayesian framework for combining valuation estimates

Discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estimates. Moreover, the valuation estimates typically disagree with market price. Can one form a superior valuation estimate by averaging over the individual estimates, including market price? This article suggests a Bayesian framework for combining two or more estimates into a superior valuation estimate. The framework justifies the common practice of averaging over several estimates to arrive at a final point estimate.     

Lookback options and diffusion hitting times: A spectral expansion approach

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the options lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.Received: 1 October 2003, Mathematics Subject Classification: 60J35, 60J60, 60G70JEL Classification: G13The author thanks Phelim Boyle for bringing the problem of pricing lookback options under the CEV process to his attention and for useful discussions and Viatcheslav Gorovoi for computational assistance. This research was supported by the U.S. National Science Foundation under grants DMI-0200429 and DMS-0223354.     

Unlocking value: Equity carve outs as strategic real options

Equity carve outs, the partial listing of a corporate subsidiary, appear to be transitory arrangements, usually dissolved within a few years by either a complete sale or a buy back. Why do firms perform expensive listings just to reverse them thereafter? We interpret carve outs of a production unit as strategic options to attract information from the market over its value as an independent entity. This improves the decision to exercise the option to sell out or to regain control. A listing is costly, as it reduces coordination of production, but generates valuable information from the market over the optimal allocation of ownership. We compute the optimal timing for the final sale or buy back decisions, the value of the strategic options embedded in the carve out and the optimal shares retained. The model explains the temporary nature of carve outs, and suggests an explanation for many empirical findings. In particular, it explains why carve outs are more common in highly uncertain sectors and in more informative markets.     

Nonlinear trends in real exchange rates: A panel unit root test approach

We analyze the possibility of nonlinear trend stationarity as the alternative to unit roots in 23 OECD real exchange rates, 1974–1998, by adding nonlinear time terms to the CIPS panel unit root test of Pesaran (2007). We follow a thorough bootstrapping approach and propose a technique to adjust statistical significance for the use of multiple tests over several time trend orders. The unit root null that all real exchange rates have unit roots is rejected at better than the 0.05 level. Bootstrapped results from a procedure of Chortareas and Kapetanios (2009) suggest that the hypothesis that all are stationary is reasonable. We argue that nonlinear trend stationarity is the most likely alternative hypothesis for at least some of the real exchange rates because: (1) the strongest CIPS rejection occurs when quadratic trends are specified; (2) nonlinear time terms are statistically significant at the 0.10 level; (3) the actual CIPS statistics are more consistent with CIPS sampling distributions from bootstrapped nonlinear trend stationary processes than from linear trend or mean stationary processes.     

A dynamic programming approach for pricing CDS and CDS options

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.