Spiros H. Martzoukos

Real (investment) options with multiple sources of rare events

Abstract We value real (investment) options when the underlying asset follows a mixed jump-diffusion process involving various types (sources) of rare events (jumps). These jumps are assumed independent of each other, with each type having a log-normally distributed jump size and a random (Poisson-distributed) arrival time. They may represent uncertainties about the arrival and impact (on the underlying investment) of new information concerning technological innovation, competition, political risk, regulatory effects and other sources. An analytic solution is presented for European claims (call or put options) with multiple sources of jumps. A discrete-time (Markov-chain) methodology (implemented within a finite-difference scheme) is proposed for the valuation of American as well as European options. The approach is also applicable to financial options with multiple types of rare events. The approach is illustrated through valuing complex real options with compound features involving interactions between optimal investment and subsequent operating decisions. Specifically, we value a growth option and an extension option.

Pricing and trading European options by combining artificial neural networks and parametric models with implied parameters

We compare the ability of the parametric Black and Scholes, Corrado and Su models, and Artificial Neural Networks to price European call options on the S&P 500 using daily data for the period January 1998 to August 2001. We use several historical and implied parameter measures. Beyond the standard neural networks, in our analysis we include hybrid networks that incorporate information from the parametric models. Our results are significant and differ from previous literature. We show that the Black and Scholes based hybrid artificial neural network models outperform the standard neural networks and the parametric ones. We also investigate the economic significance of the best models using trading strategies (extended with the Chen and Johnson modified hedging approach). We find that there exist profitable opportunities even in the presence of transaction costs.

Optimal timing of transmission line investments in the face of uncertain demand: An option valuation approach

Abstract Grid-based electrification programmes involve irreversible transmission line investments that can be delayed by temporarily resorting to decentralized powet supply technologies. In this context, decision-makers face the difficulty that the future evolution of demand and, thus, the returns from postponing the transmission line investment are uncertain. This imposes an opportunity cost resembling the value of a financial call option. Therefore, standard option valuation techniques can be applied to solve the problem of timing transmission line investments in the presence of stochastic demand. It is shown, analytically and in terms of numerical examples, that demand uncertainty may provide a strong incentive to defer the extension of the grid beyond the date that would be optimal under deterministic conditions.

Real R&D options with time-to-learn and learning-by-doing

We model R&D efforts to enhance the value of a product or technology before final development. Such efforts may be directed towards improving quality, adding new features, or adopting technological innovations. They are implemented as optional, costly and interacting control actions expected to enhance value but with uncertain outcome. We examine the interesting issues of the optimal timing of R&D, the impact of lags in the realization of the R&D outcome, and the choice between accelerated versus staged (sequential) R&D. These issues are also especially interesting since the history of decisions affects future decisions and the distributions of asset prices and induces path-dependency. We show that the existence of optional R&D efforts enhances the investment option value significantly. The impact of a dividend-like payout rate or of project volatility on optimal R&D decisions may be different with R&D timing flexibility than without. The attractiveness of sequential strategies is enhanced in the presence of learning-by-doing and decreasing marginal reversibility of capital effects.

Real Options with Random Controls and the Value of Learning

In this paper we propose a conceptual framework for continuous-time valuation of real (investment) options in the presence of costly controls with random outcomes (learning), that affect the value of the underlying asset or a relevant state-variable. These controls represent optional efforts by management to add value to the underlying real investments over which it has monopoly power, albeit with uncertain results. Special cases of such controls include pure learning (but costly) actions, as in many research and development, marketing research or natural resource exploration projects. We demonstrate a discrete-time Markov-chain solution methodology implemented in a finite-difference scheme, and we discuss numerical results. The impact of such uncertain jumps is seen to be relatively more significant in the case of non-profitable options than in the case of very profitable real (investment) options. When the potential for information revelation is significant, we are even willing to pay for an action with a negative expected outcome. With numerical simulations we capture the value of embedded exploration (pure learning) options and we demonstrate the improvement over the traditional (sequential/compound) real options approach. We show that such exploration options enhance the value of investment opportunities in the most significant manner, and justify the (mostly unexplained) observed practice of “overpaying” for the purchase of rights to natural resources extraction.

Real R&D options with endogenous and exogenous learning

Publisher Summary This chapter focuses on the analytic solution of the continuous random controls. Much of the theory of real (investment) options captures the value of waiting to invest, and the flexibility to switch among modes of operation without explicit consideration of managerial actions to enhance value and acquire more information. Many industries with heavy research and development expenditures, exploration, experimentation, or clinical testing activities, and similar actions like marketing research and advertisement, face too many uncertainties in their capital-intensive investment process to ignore efforts for information acquisition. This chapter presents a model, which allows managers to estimate how much to spend in order to enhance the value of their investment opportunities. This value enhancement is pursued either directly through impact control-type actions or indirectly through pure learning (information acquisition) actions. Modeling managements decision process with contingent claims (real options) tools is required; neglecting such actions would provide erroneous results for both the investment value and the optimal investment timing decision.

Real R&D options and optimal activation of two-dimensional random controls

We value investments under uncertainty with embedded optional costly controls (impulse-type with uncertain outcome) that capture managerial intervention for value enhancement and/or information acquisition (exploration, R&D, advertising, marketing research, etc). Implementing real option models but neglecting such embedded managerial actions can severely underestimate investment opportunities and lead to erroneous investment decisions. Optimal decisions are solutions to a maximization problem where the trade-off between the controls cost and the value added by such actions is explicitly taken into consideration. In this paper, we generalize such a methodology from one dealing with the special case of actions affecting only one state-variable, to one with actions that affect several. Asset values follow geometric Brownian motion or jump-diffusion processes with multiple generating sources of jumps. The Markov-chain numerical methodology we provide can handle sequential controls. Although we report the results with open-loop policies, the approach can be readily extended to accommodate dependency among the controls.

The option on n assets with exchange rate and exercise price risk

Solutions to the call option on the maximum or the minimum of n assets are explicitly provided when the exercise price is stochastic, and all assets carry both asset price and exchange rate risk in a n+1 country model with 2(n+1) state variables. The model can be seen as an extension of Johnson (Johnson, H., 1987. Options on the maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis 22, 227–283), Margrabe (Margrabe, W., 1978. The value of an option to exchange one asset for another. Journal of Finance 33, 177–186), and Reiner (Reiner, E., 1992. Quanto mechanics, RISK, March, 59–63), and it is useful for valuation of both financial and real options. As an application, a contract is valued that allows a portfolio manager to participate in the out-performance of the returns of international assets, portfolios or stock indexes.

European Option Pricing by Using the Support Vector Regression Approach

We explore the pricing performance of Support Vector Regression for pricing S&P 500 index call options. Support Vector Regression is a novel nonparametric methodology that has been developed in the context of statistical learning theory, and until now it has not been widely used in financial econometric applications. This new method is compared with the Black and Scholes (1973) option pricing model, using standard implied parameters and parameters derived via the Deterministic Volatility Functions approach. The empirical analysis has shown promising results for the Support Vector Regression models.

Implied non-recombining trees and calibration for the volatility smile

In this paper we capture the implied distribution from option market data using a non-recombining (binary) tree, allowing the local volatility to be a function of the underlying asset and of time. The problem under consideration is a non-convex optimization problem with linear constraints. We elaborate on the initial guess for the volatility term structure and use nonlinear constrained optimization to minimize the least squares error function on market prices. The proposed model can accommodate European options with single maturities and, with minor modifications, options with multiple maturities. It can provide a market-consistent tree for option replication with transaction costs (often this requires a non-recombining tree) and can help pricing of exotic and Over The Counter (OTC) options. We test our model using options data for the FTSE 100 index obtained from LIFFE. The results strongly support our modelling approach.