143 research outputs found

    Valuing multifactor real options using an implied binomial tree

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    Includes bibliographical references (page 23).This paper proposes an approach for solving a multifactor real options problem by approximating the underlying stochastic process with an implied binomial tree. The implied binomial tree is constructed to be consistent with simulated market information. By simulating European option prices as artificial market information, we apply the implied binomial tree method for real options valuation when the options are contingent on the value of market uncertainties that are not traded assets. Compared to the discrete approximations suggested in the current literature, this method offers a more flexible distribution assumption for project values and therefore provides an alternative approach to estimating the value of high-dimensional real options. For risk managers, it serves as a capital budgeting method for projects with managerial flexibility

    Decision support for firm performance by real options analytics

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    This paper develops a real options decision support tool for raising the performance of the firm. It shows how entrepreneurs can use our intuitive tool quickly to assess the nature and type of action required for improved performance. This exploits our estimated econometric relationship between precipitators of entrepreneurial opportunities, time until exercise, and firm performance. Our 3D chromaticity plots show how staging investments, investment time, and firm performance support entrepreneurial decisions to embed, or to expedite, investments. Speedy entrepreneurial action is securely supported with this tool, without expertise in econometric estimation or in formulae for real options valuation

    The History of the Quantitative Methods in Finance Conference Series. 1992-2007

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    This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

    Simulation-Based Pricing of Convertible Bonds

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    We propose and empirically study a pricing model for convertible bonds based on Monte Carlo simulation. The method uses parametric representations of the early exercise decisions and consists of two stages. Pricing convertible bonds with the proposed Monte Carlo approach allows us to better capture both the dynamics of the underlying state variables and the rich set of real-world convertible bond specifications. Furthermore, using the simulation model proposed, we present an empirical pricing study of the US market, using 32 convertible bonds and 69 months of daily market prices. Our results do not confirm the evidence of previous studies that market prices of convertible bonds are on average lower than prices generated by a theoretical model. Similarly, our study is not supportive of a strong positive relationship between moneyness and mean pricing error, as argued in the literature.Convertible bonds, Pricing, American Options, Monte Carlo simulation

    Flexible Option Valuation Methods

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    This thesis is concerned with methods of option valuation that fall completely outside of the Black-Scholes-Merton (BSM) framework. Data on S&P500 Index options are used to demonstrate the proposed methods. Some of our favoured methods are based on semi-parametric regression; others on simulation. The thesis consists of a number of chapters. In Chapter 2, we outline existing option valuation methods, with particular attention paid to the binomial-tree model and the Black-Scholes formula. We demonstrate that under some circumstances these two methods are equivalent. We also demonstrate using the binomial tree method that a “TGARCH effect” (which plays an important role in later chapters) can explain the well-known “smirk” pattern that is often observed in market option price data. In Chapter 3, we use regression analysis to investigate the ways in which features of an option actually determine the market price. We start with polynomial regressions, and progress to additive models, with components obtained using the B-spline technique. The focus in these regression models is the role of volatility. Historical measures of volatility are used as explanatory variables in the regression, with one objective being to discover how far back into the past option traders are going when computing volatility. It is proposed that this approach gives rise to an alternative measure of implied volatility that is completely free of the Black-Scholes framework. We use the Practitioner Black Scholes (PBS) model as a Benchmark for comparison. The best of our regression models is found to perform better than the Black-Scholes formula in out-of-sample prediction of market prices. In Chapter 4, we focus on the underlying (S&P500) Index, and consider a number of varying volatility models (ARCH, GARCH and TGARCH) of daily returns. We found that the TGARCH model is the best model to represent the volatility process. Then we simulated data from the models considered using the coefficients from the estimated models. After that, we found that the simulated ARCH family volatility models worked correctly, since the “true” parameter values are included in the confidence intervals. Chapter 5 continues with the simulations of daily return data, in building a Monte Carlo program for the valuation of European options that allows for varying volatility. Of particular interest is whether superior models of the underlying stock price (i.e. ARCH, GARCH and TGARCH) result in option valuations that are superior to the Black-Scholes valuation. Superiority in this context is defined primarily in terms of ability to predict market prices. We find that all models perform better than the benchmark (PBS) model. Which model performs best depends on the type of market and time to expiry: ARCH is the best model for predicting the short and medium term put options for both bear and calm market and GARCH is the best one for predicting the long term put options in the bear market. In the crash market, TGARCH Monte Carlo simulation is the best model for predicting the long term European call and put options

    An empirical comparison using both the term structure of interest rates and alternative models in pricing options on 90-day BAB futures

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    The use of the term structure of interest rates to price options is relatively new in the literature. It describes the relationship between interest rates and the maturities of bonds. The first model that described the interest rate process was the Vasicek (1977) model. There have been many studies on the formulation of theoretical pricing models. Yet limited empirical research has been done in the area of actually testing the models. In this thesis we report the results of a set of tests of the models indicated below. This paper involves analysis of the pricing errors of the Black model ( 1976), Asay model (1982), Extended-Vasicek model (1990) and Heath-Jarrow-Morton model (HJM) ( 1992) as applied to call options on 90-day Bank Accepted Bill (BAB) futures. Monthly yield curves are generated from cash, futures, swap and interest rate cap data. A number of different methods of analysis are used. These include the use of inferential statistics, non-parametric sign tests and Ordinary Least Square Regressions. The Wilcoxon non-parametric sign test assists the interpretation of whether the pricing errors are from the same distribution. Ordinary Least Square Regressions are used to assess the significance of factors affecting pricing errors. In addition, data are plotted against different variables in order to show any systematic patterns in how pricing errors are affected by the changes in the chosen variables. Monthly options data on BAB futures in the year 1996 suggest that the term structure models have significantly lower pricing errors than the Black and the Asay model. The Heath-Jarrow-Morton model (1992) is overall the better model to use. For the term structure models, pricing errors show a decreasing trend as moneyness increases. The Extended-Vasicek model and the HJM model have significantly lower errors for deep-in the-money and out-of-the-money options. Higher mean absolute errors are observed for at-the-money options for both term structure models. The HJM model overprices at-the money options but underprices in and out-of-the-money options while the Extended Vasicek model underprices deep-in-the-money options but overprices options of other categories. The mean and absolute errors for both the Black model and the Asay model rise as time to maturity and volatility increases. The two models overprice in, at and out-of-the money options and the mean pricing error is lowest for in-the-money options. The results suggest that the factor time to maturity is significant at the 0.05 level to the -mean pricing error for all four models. Moneyness is the only insignificant factor when the Asay model is used. It is also negatively correlated to mean pricing error for the Black model, the Asay model, the Extended-Vasicek model and the HJM model. The R-square for the Extended-Vasicek model was found to be the lowest. Overall, the HJM model gives the lowest pricing error when pricing options on 90-Day Bank Accepted Bill Futures

    Three One-Factor Processes for Option Pricing with a Mean-Reverting Underlying: The Case of VIX

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    We challenge the two most prominent one‐factor mean‐reverting models for variance/volatility indices and propose the inhomogeneous geometric Brownian motion process to price volatility index (VIX) options. We study the roles of the equilibrium level, speed of reversion, volatility and expiry date in the pricing of VIX options and obtain analytic solutions for perpetual American options as well as some Greeks. We price the finite‐lived American options using their transformed process to build a binomial tree. We also derive the closed‐form mean first‐passage time for perpetual American options and find a long optimal exercising time. Other things being equal, the European ones are cheaper than their American counterparts, which reflect an early exercise premium

    Valuing infrastructure investments as portfolios of interdependent real options

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    The value of infrastructure investments is frequently influenced by enormous uncertainty surrounding both exogenous and endogenous factors. At the same time, however, their value is generally driven by much flexibility - i.e. options - with respect to design, financing, construction and operation. Real options analysis aims to pro-actively manage risks by valuing the flexibilities inherent in uncertain investments. Although real options generally occur within portfolios whose value is affected by both exogenous and endogenous uncertainty, most existing valuation approaches focus on single (i.e. individual) options and consider only exogenous uncertainty. In this thesis, we introduce an approach for modelling and approximating the value of portfolios of interdependent real options under exogenous uncertainty, using both influence diagrams and simulation-and-regression. The key features of this approach are that it translates the interdependencies between real options into linear constraints and then integrates these in a portfolio optimisation problem, formulated as a multi-stage stochastic integer programme. To approximate the value of this optimisation problem we present a transparent valuation algorithm based on simulation and parametric regression that explicitly takes into account the state variable's multidimensional resource component. We operationalise this approach using three numerical examples of increasing complexity: an American put option in a simple single-factor setting; a natural resource investment with a switching option in a one-factor setting; and the same investment in a three-factor setting. Subsequently, we demonstrate the ability of the proposed approach to evaluate a complex natural resource investment that features both a large portfolio of interdependent real options and four underlying uncertainties. We show how our approach can be used to investigate the way in which the value of that portfolio and its individual real options are affected by the underlying operating margin and the degrees of different uncertainties. Lastly, we extend this approach to include endogenous, decision- and state-dependent uncertainties. We present an efficient valuation algorithm that is more transparent than those used in existing approaches; by exploiting the problem structure it explicitly accounts for the path dependencies of the state variables. The applicability of the extended approach to complex investment projects is illustrated by valuing an urban infrastructure investment. We show the way in which the optimal value of the portfolio and its single, well-defined options are affected by the initial operating revenues, and by the degrees of exogenous and endogenous uncertainty.Open Acces
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