Compound Option Research Articles

Capital Structure Effects on the Prices of Individual Equity Call Options

We examine whether values of equity options traded on individual firms are sensitive to the firm's capital structure. Specifically, we estimate the compound option (CO) model, which views equity as an option on the firm. Compared to the Black-Scholes (BS) model, the CO model reduces pricing errors by 20% on average, and pricing improvements monotonically increase up to 70% with both leverage and expiration. We show that the CO model implies a market value of firm leverage and allows imputation of the firm's implied volatility, both of which have potential applications in corporate finance.

The Decision-making Analysis of Multinational Enterprise' Investment under Interest Rate Uncertainty

This paper aims to explore from a dynamic perspective the best strategy for multinational enterprises to enter a market, involving the best timing and place for the expansion of international joint ventures. In most cases, the strategy for initial entry provides a platform for the company to use its advantage and ability gained as a host firm to do the later investment. We consider taking the following three steps of the expansion strategy. First of all, foreign direct investment can be interpreted as a compound option and it is found that its uncertainty, the scale of ordinary shares and the future investment / divestment opportunities play important roles. This thesis emphasizes the importance of dynamic market-entry model.

Real options analysis on strategic partnerships of biotechnological start-ups

Since there is a mismatch between long-term basic research and short-term financial markets, the dependency of biotechnology (biotech) start-ups on strategic partnerships with pharmaceutical companies is expanding more than on venture capital. The research objectives are to examine the difference between license-fee elements, try to determine the innovation valuation in strategic partnerships, and minimise the risk in partnership formation for both sides. A key concept is that a biotech start-up is defined as a portfolio of real options based on an entrepreneur's ideas about investment opportunity. Methodologies used are compound options and stochastic optimisation for innovative but risky projects. In conclusion, this paper tries to address a wider scope with a deeper theoretical grounding, by using the real options perspective for the valuation of innovation partnership, through a biotech license-fee case study for simulation. Furthermore, the real option valuation can be expected to improve open innovation from matchmaking to innovation partnership.

A comparative study on time-efficient methods to price compound options in the Heston model

The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston’s stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using Green’s function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing. The results in the numerical analysis section are important for practitioners in the financial industry to identify under which model prerequisites (for instance, Heston model where Feller condition is fulfilled or not, Heston model with piecewise time-dependent parameters or with stochastic interest rates) it is preferable to use and which of the available numerical methods.

Compound Option Pricing under Fuzzy Environment

Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For eachα, theα-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.

A Real Options Model for Generalized Meta-Staged Projects—Valuing the Migration to SOA

This paper develops an innovative real options (RO) model for valuing multistage information technology (IT) projects that can be viewed as comprising meta stages. In RO literature, multistage investment programs have been treated as either interproject or intraproject programs, with intraproject programs being evaluated using n-fold Geske compound options and interproject programs valued using the so-called “subsidy-to-exercise price” logic. Our innovative RO model integrates the Geske compound option model with the subsidy-to-exercise price approach to value sequential investment programs that are neither purely interproject nor purely intraproject in nature but are composed of meta-stages. A meta-stage as a whole can be considered an interproject stage resulting in cash flows, but internally it consists of several intraproject stages that do not result in cash flows. We show that a key problem in IT, which is migrating to a Service-Oriented Architecture (SOA) for integrating a firm's many disparate applications, systems, data, and business processes, is best viewed as an investment program comprising meta-stages. Examining SOA migration from an RO lens is particularly apt at this time not only because of the importance of SOA but also because doubts have surfaced about the value of SOA. We illustrate our RO model by applying it to the simulated case of a firm migrating to SOA. We also develop a software tool based on the MathematicaTM computational platform so that practitioners can easily apply our innovative options pricing model to determine the true value of SOA in their business contexts.

The evaluation of American compound option prices under stochastic volatility and stochastic interest rates

A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate driven by Cox–Ingersoll–Ross processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free-boundary PDE problem, which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the projected successive over-relaxation method.

Evaluation of conducting capital structure arbitrage using the multi-period extended Geske–Johnson model

This study utilizes a multi-period structural model developed by Chen and Yeh (Pricing credit default swaps with the extended Geske–Johnson Model. Working paper, 2006), which extends the Geske and Johnson (J Financ Quant Anal 19:231–232, 1984) compound option model to evaluate the performance of capital structure arbitrage. In the paper, first of all, we predict the default probability for each firm using the multi-period Geske–Johnson model that assumes endogenous default barriers. Second, based on the arbitrage performance of 369 North American obligators from 2004 to 2008, we find that the extended Geske–Johnson model is more suitable than the CreditGrades model for exploiting the mispricing between equity prices and credit default swap spreads. Finally, the Geske–Johnson model also performs well in extreme market condition, such as the financial crisis around 2008.

Compound Option Pricing Model Applied in Overseas Mineral Investment

According to characteristics of selecting an overseas mineral project，such as a long period, high-risk and investment decisions in different phased, several stages is divided in the process of entire mineral investment decision-making. Using the method of the multi-stage real option pricing method, the compound option pricing model is to construct the investment in mineral based on the compound call option pricing formula of Geske model. Taking a company for example, we introduce the probability of success in different stages for sensitivity analysis. Selecting the lower successful probability at the exploration stage and higher at the mining stage to illustrate the availability and stability of the model, helping investors to make the right choice.

A Structural Approach to Estimate Short-Term and Long-Term Country Default Risk from Market Data: The Case of Argentina 2000/2001

Abstract We apply a structural pricing model to bond market data in order to estimate the default risk for Argentina in 2000/2001. The model explicitly considers short-term and long-term debt service payments and their dependencies by employing compound option theory. In this way, it is possible to take into account both the empirically observed dependency between the term structure of bond spreads and the default risk as well as the finding that the ratio of short-term to long-term debt is of special importance for default risk. The model parameters are estimated using Duan’s (1994) time series-based maximum likelihood approach.

Real Options Analysis on Strategic Partnership Dealing of Biotech Start-ups

Biotech start-ups have the competitive advantages of quicker and lower-cost at combing the innovative technologies and the niche markets, in comparing with big pharmaceutical companies. However they are facing with the short-term financing fluctuations from venture capital and initial public offering markets since this time’s financial crisis, while universities’ long-term basic research activities are continually producing life-science findings as their innovative resources. Then strategic partnerships with big pharmaceutical companies are becoming more important fundraising sources for biotech start-ups. Thus, how can such innovative but small start-ups equally negotiate their deal-structures with the resource-rich but innovation starving big pharmaceutical companies? For the research question above, a promising methodology seems the more objective metrics or analytics on the value of decision-making rather than traditional means like the comparison with similar cases or the subjective judgment based on past experience suitable for incremental improvement. Therefore this paper discusses on the opportunities and challenges of each application of the Monte Carlo simulation to cash flow forecasting of research and development investment, the rainbow sequential compound option to risk-hedge, and the stochastic optimization to negotiating the portfolio of license-fee elements.

European Compound Options Writtenon Perpetual American Options

It may seem counterintuitive, but valuing “perpetual” options, with infinite maturity, can be easier than pricing those that expire at a fixed date. At least Samuelson found it so in 1965. In this article, Barone extends the valuation models for perpetual options to cover American calls and puts on dividend-paying stocks, and European options written on these infinite maturity contracts. Formulas for the Greek letter risks are presented, as well as an analysis of how put-call parity works for them. Along the way, additional results are developed for first-touch digital options, both perpetual and finite maturity.

Investigating Time-Efficient Methods to Price Compound Options in the Heston Model

The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston’s stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using the Green’s function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing.

Real Options in Acquisitions: Effects of Option Type and Competition on Premiums

This paper considers the differences in premiums paid between different types of real options that exist in acquisitions. We compare single and compound options by considering single acquirers versus serial acquirers and find that the first group pays lower premiums for their acquisitions. This finding is in line with real option theory stating compound options are more valuable than single options as they incorporate the value of future growth options. Next, we focus on the difference between shared and proprietary nature of options in both single and compound options. In line with real option theory predictions, we find that shared options (measured by the number of bidders) require higher premiums, while proprietary options (measured by the presence of a minority stake) result in lower premiums paid for both single and compound acquisition options. The results are robust when considering serial acquirers who focus on related targets, an acquisition strategy called “buy-and-build”. We further find that acquirer market share increases the proprietary nature of acquisition options and leads to lower premiums paid.

SOA investment decision-making using real options analysis

Service-oriented architecture (SOA) is still among the top priorities in IT investment planning. However, selecting proper evaluation methods to capture for flexibility and uncertainty associated with SOA implementations remains a major issue. This paper investigates investment methods and analyses the application of real options models in a particular SOA context. We explore and classify key criteria and embedded options for evaluating multi-stage SOA investments as sequential compound options. The determinants and value drivers for SOA platform acquisition and SOA application development projects are examined and general conclusions with regard to SOA investment decision-making are drawn. In this paper, we identify both the limitations of commonly used techniques as well as the concept’s importance. A visualisation of the analysis is presented through a SOA management decision-framework explaining the relations between the steps of this framework and serving as guidance for SOA investment decision-makers.

Research on European Option and Compound Option Pricing

Research on European Option and Compound Option Pricing

Irreversibility, mean reversion, and investment timing

This paper examines the effect of irreversibility on investment under mean reversion. We develop a continuous-time model wherein a risk-neutral firm is endowed with a perpetual option to invest in a project at any time by incurring a fixed investment cost at that instant. The project, once undertaken, generates a stream of cash flows that are governed by a mean-reverting stochastic process. The firm is then allowed to liquidate its project at any time to partially recover the fixed investment cost. The recovery rate of the fixed investment cost inversely gauges the degree of irreversibility of investment. Using a real options approach, we derive an analytical solution to the value of the firm that is analogous with an American compound option. We show that greater irreversibility of investment induces the firm to raise its investment trigger, thereby deferring the undertaking of the project. We further show that greater irreversibility of investment has a detrimental effect that makes the firm less valuable.

The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques

Compound options are not only sensitive to future movements of the underlying asset price, but also to future changes in volatility levels. Because the Black–Scholes analytical valuation formula for compound options is not able to incorporate the sensitivity to volatility, the aim of this paper is to develop a numerical pricing procedure for this type of option in stochastic volatility models, specifically focusing on the model of Heston. For this, the compound option value is represented as the difference of its exercise probabilities, which depend on three random variables through a complex functional form. Then the joint distribution of these random variables is uniquely determined by their characteristic function and therefore the probabilities can each be expressed as a multiple inverse Fourier transform. Solving the inverse Fourier transform with respect to volatility, we can reduce the pricing problem from three to two dimensions. This reduced dimensionality simplifies the application of the fast Fourier transform (FFT) method developed by Dempster and Hong when transferred to our stochastic volatility framework. After combining their approach with a new extension of the fractional FFT technique for option pricing to the two-dimensional case, it is possible to obtain good approximations to the exercise probabilities. The resulting upper and lower bounds are then compared with other numerical methods such as Monte Carlo simulations and show promising results.

Modeling the transitional dynamics of international joint venture policies: An option pricing approach

Real option analysis has been applied to strategies of market entry and global expansion, predominantly in combination with the formation of alliances and joint ventures. Albeit joint venturing based on option pricing theory is studied in both disciplines, financial economics and international business, the link between these strains of literature is not well developed. We use a compound option framework to analyze the impact of decision contingency and learning on formation and duration of joint ventures. Critical thresholds are presented which allow to characterize the conditions under which termination takes place and to estimate the duration of international joint ventures revealing a novel perspective on existing empirical findings. In particular, we find that exchange rate uncertainty and learning have ambiguous effects on investment. While the model also provides a number of new testable predictions the presented closed-form solution can help managers to structure explicit option clauses in JV contracts more efficiently.

Sovereign Default Risk and Recovery Rates: What Government Bond Markets Expect for Greece

AbstractBond market data on sovereign bond yields is used to estimate sovereign default risk and the amount of the expected “hair‐cut” for Greece between 2008 and 2011. Using a structural pricing model that relies on compound option theory short‐term and long‐term default probabilities and their dependencies can be inferred. Thereby bond yield spreads for different maturities are integrated. In addition, a reduced form model is applied to infer the recovery rate expected by bond market participants. The paper shows that sovereign default risk and recovery rate dynamics reflect events that are important for Greece's repayment capacity.