Optimal investment and production decisions and the value of the firm

We explore the effects of uncertainty on a firm that can respond by modifying its investment or production schedule (or both simultaneously) to variations in output price. Investment may increase capacity and/or reduce costs. We consider a firm with finite resources.Our model uses option theory instead of the more traditional net present value framework. One of the early papers using this approach is Brennan and Schwartz (1985) in which an investment project to extract a finite natural resource is valued. In that paper, the value of the firm is a function of two state variables, the finite resource to be extracted (output to be produced in the future) and the commodity spot price. In order to maximize firm value, the manager can respond by modifying one control variable, the production level. In our model we handle instead three state variables (spot price, resources, accumulated investment) and two control variables (production rate and investment rate), and solve numerically.We obtain both the value and the optimal policy of a firm that has investment projects that increase capacity and/or reduce costs and illustrate optimal policies as resources and available investments decrease over the life of the firm. Firms may start by only investing, then invest and produce, to end only producing.We thank Scott Wo, the referee and the editor for their comments and suggestions. Cortázar and Lowener acknowledge the financial support from FONDECYT and FONDER.     

Real Options: Experimental Evidence

Empirical testing of the real options theory has been very limited. This is primarily due to various inherent problems with obtaining field data for many components of real options theory. This paper utilizes experimental methodology to generate the data. The advantage of the experimental approach is that it enables the investigator to generate reliable and replicable data in a controlled environment. The results of the experiment indicate that fundamental insights of real options theory are not evident to individual investors. The majority invested too early and thus failed to recognize the benefit of the option to wait. However, when the investors had to compete with others for the right to invest, their bids generally reflected the value of the embedded option. Furthermore, as predicted by the theory, their bids increased with greater uncertainty about future cash flows from the investment.     

An option pricing approach to corporate dividends and the capital investment financing decision

In light of a growing trend toward viewing dividends as an investable asset class, this article opens up a new perspective on their valuation. We show that dividends can be viewed as options on the cash flow of the firm. That is, a firm either pays zero dividends, in which case the option expires out‐of‐the‐money, or it pays a positive dividend, the value of which corresponds to the option's moneyness. The exercise price is determined by the capital budget, the flexibility of the company to use external financing, and whether it has minimum and maximum dividends. The model is also capable of accommodating a stochastic capital budget, which allows for uncertain growth opportunities and their correlation with the firm's cash flows. We also present an application of the model using actual data for a large multinational company.     

The investment decision with technological and market uncertainties

This paper examines how technological uncertainty affects current investment; specifically, what is the impact on a firm’s investment in an existing technology when an improved technology might arrive in the future. The firm can invest in the current technology and upgrade to the new technology after its arrival (sequential investing), or it can bypass the current technology and invest directly in the new technology (leapfrogging). The main result is that, in the presence of market risk, future technological uncertainty has a non-monotonic effect on investment, with the investment trigger being a U-shaped function of the expected speed of arrival of the new technology. In this U-shaped relationship, the investment trigger starts rising later if the new technology is more attractive and also when volatility and interest rate are high and growth rate low; thus, technological uncertainty is more likely to have a positive effect on investment under these conditions. Finally, we apply the model to the sequential versus leapfrog investment decision, and find that leapfrogging becomes more attractive relative to sequential investment when interest rate and new technology earnings enhancement are higher, and when market volatility, growth rate and new technology investment cost are lower.     

Real investment and risk dynamics

We ask to what extent the negative relation between investment and average stock returns is driven by risk. We show that: (i) the average return spread between low and high asset growth and investment portfolios is largely accounted for by their spread in systematic risk, as measured by the loadings on the Chen, Roll, and Ross (1986) factors; (ii) as predicted by q-theory and real options models, systematic risk falls during large investment periods; (iii) the returns of factors formed on the investment-to-assets, asset growth, and investment growth all forecast aggregate economic activities. Our evidence suggests that risk plays an important role in explaining the investment-return relation.     

Discrete-time bond and option pricing for jump-diffusion processes

This paper provides a methodology for numerically pricing generalized interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion setting. Numerical illustrations compare jump-diffusion and pure-diffusion models.I am especially grateful to Darrell Duffie, who provided me immensely valuable input on the paper. I would also like to thank Dilip Madan and Rangarajan Sundaram for alleviating my confusion with helpful comments.     

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.     

High-speed rail transport valuation and conjecture shocks

In this paper, we derive the optimal investment policy in a high-speed rail transport (HSR) project. We assume that the source of uncertainty comes from the annual demand, and that it follows a geometric Brownian motion with jumps of random magnitude, occurring in random times, according to a Poisson process. We assess the impact of these shocks on the demand threshold, along with the investment opportunity value and option to differ. We consider several distributions for these jumps, and we compare with the no-jumps case. Numerical results are presented, showing the importance of assumptions about the underlying stochastic process.     

Real Options, (Dis)Investment Decision-Making and Accounting Measures of Performance

This paper suggests that a residual income-type measure of performance can be designed which supports optimal investment and disinvestment decision-making in a real options framework involving the options to wait before investing and to abandon. The measure has a number of advantages and disadvantages. Nonetheless, the balance of advantage versus disadvantage for the proposed measure must be set against the inadequacies of other competing measures of performance and associated organisational designs. Even if the measure of performance suggested is not regarded as practically useful, it has another general advantage – it can be used as a benchmark against which to evaluate other performance measures with regard to their support of optimal investment and disinvestment decision-making in a real options framework.     

Real Options, (Dis)Investment Decision-Making and Accounting Measures of Performance

This paper suggests that a residual income-type measure of performance can be designed which supports optimal investment and disinvestment decision-making in a real options framework involving the options to wait before investing and to abandon. The measure has a number of advantages and disadvantages. Nonetheless, the balance of advantage versus disadvantage for the proposed measure must be set against the inadequacies of other competing measures of performance and associated organisational designs. Even if the measure of performance suggested is not regarded as practically useful, it has another general advantage – it can be used as a benchmark against which to evaluate other performance measures with regard to their support of optimal investment and disinvestment decision-making in a real options framework.     

Z-Transform and preconditioning techniques for option pricing

In the present paper, we convert the usual n-step backward recursion that arises in option pricing into a set of independent integral equations by using a z-transform approach. In order to solve these equations, we consider different quadrature procedures that transform the integral equation into a linear system that we solve by iterative algorithms and we study the benefits of suitable preconditioning techniques. We show the relevance of our procedure in pricing options (such as plain vanilla, lookback, single and double barrier options) when the underlying evolves according to an exponential Lévy process.     

On accurate and provably efficient GARCH option pricing algorithms

The GARCH model has been very successful in capturing the serial correlation of asset return volatilities. As a result, applying the model to options pricing attracts a lot of attention. However, previous tree-based GARCH option pricing algorithms suffer from exponential running time, a cut-off maturity, inaccuracy, or some combination thereof. Specifically, this paper proves that the popular trinomial-tree option pricing algorithms of Ritchken and Trevor (Ritchken, P. and Trevor, R., Pricing options under generalized GARCH and stochastic volatility processes. J. Finance, , 54(1), 377–402.) and Cakici and Topyan (Cakici, N. and Topyan, K., The GARCH option pricing model: a lattice approach. J. Comput. Finance, , 3(4), 71–85.) explode exponentially when the number of partitions per day, n, exceeds a threshold determined by the GARCH parameters. Furthermore, when explosion happens, the tree cannot grow beyond a certain maturity date, making it unable to price derivatives with a longer maturity. As a result, the algorithms must be limited to using small n, which may have accuracy problems. The paper presents an alternative trinomial-tree GARCH option pricing algorithm. This algorithm provably does not have the short-maturity problem. Furthermore, the tree-size growth is guaranteed to be quadratic if n is less than a threshold easily determined by the model parameters. This level of efficiency makes the proposed algorithm practical. The surprising finding for the first time places a tree-based GARCH option pricing algorithm in the same complexity class as binomial trees under the Black–Scholes model. Extensive numerical evaluation is conducted to confirm the analytical results and the numerical accuracy of the proposed algorithm. Of independent interest is a simple and efficient technique to calculate the transition probabilities of a multinomial tree using generating functions.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

American option pricing with discrete and continuous time models: An empirical comparison

This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.     

High-speed rail transport valuation

In this paper, the optimal timing for investing in high-speed rail projects under uncertainty in relation to the utility provided to railway users was investigated. To accomplish this, a continuous time real options analysis framework using a stochastic demand model was developed to determine the optimal time to invest. Uncertainty upon investment expenditures was also added in an extended framework. The value of the option to defer and the investment opportunity value were also assessed.     

Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

Fast and realistic European ARCH option pricing and hedging

The behavior of the implied volatility surface for European options was analysed in detail by Zumbach and Fernandez for prices computed with a new option pricing scheme based on the construction of the risk-neutral measure for realistic processes with a finite time increment. The resulting dynamics of the surface is static in the moneyness direction, and given by a volatility forecast in the time-to-maturity direction. This difference is the basis of a cross-product approximation of the surface. The subsequent speed-up for option pricing is large, allowing the computation of Greeks and the delta replication strategy in simulations with the cost of replication and the replication risk. The corresponding premia are added to the option arbitrage price in order to compute realistic implied volatility surfaces. Finally, the cross-product approximation for realistic prices can be used to analyse European options on the SP500 in depth. The cross-product approximation is used to compute a mean quotient implied volatility, which can be compared with the full theoretical computation. The comparison shows that the cost of hedging and the replication risk premium have contributions to the implied volatility smile that are of similar magnitude to the contribution from the process for the underlying asset.     

Index-option pricing with stochastic volatility and the value of accurate variance forecasts

In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, pricing of options provides the appropriate test of forecasts of asset volatility. NYSE index returns over the period of 1968–1991 suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in the Black and Scholes formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed. (JEL C22, C53, C10, G11, G12)     

房地产市场运行及未来趋势展望

2011年在以限购为主的房地产调控政策作用下,市场需求受到抑制,商品房销售增速明显低于历史同期平均水平。保障性住房全年开工建设任务已经提前完成,受其拉动,房地产开发投资保持高位。当前,保障性住房建设全面展开,以限购为主的调控政策短期不会退出,并呈现向二三线城市扩大的趋势,一些前期房价上涨过快的城市降价促销愈演愈烈,商品房价格回调趋势明显。