Pricing Geometric Asian Options under the CEV Process

Abstract

This paper discusses the pricing of geometric Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price geometric Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of geometric Asian options when the stock price follows the CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in the CEV process.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

Risk aversion,fanning preference and volatility smirk on S&P 500 index options

This article proposes a novel way of pricing S&P 500 index options in the presence of jump risk. Our analysis is built upon an equilibrium option pricing rule for a representative agent economy. In particular, we use the weighted utility’s certainty equivalent to specify agent’s risk preference, which displays a fanning-out characteristic. We find that the fanning effect captures a remarkably large portion of the total market risk premium implicit in options. As a result, the model with fanning effect generates pronounced volatility smirks.     

Aggregation under homogeneous ambiguity: a two-fund separation result

Contrary to the common prior model, the construction of a representative agent whose preferences follow the multiple-priors model (1989) requires strong restrictions on sets of priors and on an aggregate endowment process if we permit a large deviation among agents’ degrees of risk aversion. This paper shows that if agents’ felicity functions belong to a family of linear risk tolerance functions with the same marginal risk tolerance, the representative agent always exists at an interior equilibrium without such restrictions, and two-fund separation holdsI am grateful to a referee and to participants at the conference, Uncertainty in Economic Theory, held at Yale University (October 2004) for their valuable comments and suggestions     

What matters in the finance–growth nexus of advanced economies? Evidence from OECD countries

Over the last decades, a large strand of finance and growth literature has provided ample evidence on the importance of financial deepening for economic development. Yet, recently, the focus of public debate has shifted towards the role of the financial system structure, an area in which empirical research remains relatively sparse and exploratory in nature. With this article, we aim to contribute to that debate by analysing the role the financial system structure plays in economic growth and risk. Focusing on stock markets and studying OECD economies over 1994–2013, we find that, ceteris paribus, financial systems with relatively larger stock markets facilitate economic growth and dampen economic risk. Our findings remain robust under application of instrumental variable and system generalized method of moments estimators, as well as when we use an alternative definition of stock market development, estimate median regressions, examine relatively high-frequency annual data, control for systemic banking crises or apply quadratic specifications. We find no such effect for private bond markets or private credit volume. Overall, our results suggest that financial system structure matters for the economic development of advanced economies and highlight the importance of a debate about the optimal structure of an economy’s financial system.     

Export Flexibility And Currency Hedging*

This article studies the behavior of an export‐flexible firm under exchange rate uncertainty. We show that the separation theorem holds if selling exclusively in the domestic market is suboptimal even under the most unfavorable spot exchange rate. Otherwise, the firm's optimal output depends on its preferences and on the underlying uncertainty. We further show that the full‐hedging theorem holds only when the firm always finds it optimal to sell its entire output in the foreign market. Otherwise, export flexibility introduces a convexity into the firm's foreign exchange risk exposure, which calls for the use of currency options for hedging purposes.     

Option-implied preferences adjustments, density forecasts, and the equity risk premium

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and several alternative risk adjustments. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at 4- and 8-week horizons. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. We show that risk adjustments based on a power specification for the stochastic discount factor—which is the approach used so far in the literature that derives the objective density function from option prices- generates an excessive volatility of risk premia. We use alternative risk adjustments and find that the forecasting performance of the distribution improves slightly in some cases when risk aversion is allowed to be time-varying. Finally, from October 1996 to December 2004, the ex-ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18% higher than the premium required to compensate the same investors for the realised volatility in stock market returns.      

Labour market effects of public capital stock: evidence for the Spanish private sector

This paper provides a new rationale for the positive effect of public capital stock on employment and wages. We show that higher levels of public capital reduce wages along the wage equation and enhance employment due to the resulting larger elasticity of labour demand with respect to wages. The estimation of a structural model for the Spanish private sector reveals that this wage channel is empirically relevant. We use the estimated parameters to simulate the recent incidence of the ratio of public to private capital stock on the private sector economic performance. We find (i) sizeable effects on employment, capital stock and gross domestic product, and (ii) that the wage channel is particularly important for employment.     

Option implied beta and option return

We study the information content of option-implied betas for future equity option returns, using data on the S&P 500 index options and all of the component stock options. We find a significantly strong relation between option-implied betas and option returns cross-sectional. The paper presents evidence that call (put) option returns increase (decrease) with the option-implied betas of the underlying stock. A trading strategy of buying high (low) implied beta call (put) option portfolio and selling low (high) implied beta call (put) option portfolio generates a statistically and economically significant return. Our results are robustly persistent even after controlling for various cross-sectional effects and are not explained by the risk factors in asset pricing.     

FREQUENT NEWS AND PURE SIGNALS: THE CASE OF A PUBLICLY TRADED FOOTBALL CLUB

We use stock market data for Borussia Dortmund GmbH & Co. KGaA – one of the leading German football clubs – for an application of the news model. Owing to the specific characteristics of the news‐generating process, the case of a publicly traded sport club is a very appropriate candidate for testing this model. By applying a traditional as well as a reversed news model, we elaborate whether new information can explain subsequent changes in the stock price of Borussia Dortmund. We find that sport as well as corporate governance‐related variables are important drivers of the stock price.     

Transparency in the Foreign Exchange Market and the Volume of International Trade

In this paper we study the impact of more transparency in the foreign exchange market on the ex ante expected volume of international trade. Transparency is measured by the informational content of publicly observable signals. These signals convey information about the use of policy instruments which affect the future exchange rate. We find that a higher level of transparency may increase or decrease the volume of international trade. In particular, the impact of greater transparency depends on the curvature of the firms’ marginal cost function. Furthermore, the firms’ex ante expected profits are higher when the foreign exchange market is more transparent.     

Corporate social irresponsibility,CEO overconfidence,and stock price crash risk

This study examines whether and how corporate social irresponsibility (CSI) influences stock price crash risk for firms with overconfident CEOs. We find that the positive association between CEO overconfidence and stock price crash risk as shown in prior studies is significantly weakened when firms have higher CSI concerns. As a result, our intriguing findings demonstrate that investors are less surprised at the negative news hoarded by overconfident CEOs of CSI firms, possibly because they are already aware of and have previously reacted to the socially irresponsible behavior in their daily operations.     

The effects of abandonment options on operating leverage and forward hedging

This paper examines the behavior of the competitive firm under output price uncertainty when the firm is endowed with an abandonment option and has access to a forward market for its output. When the realized output price is less than its marginal cost, the firm optimally exercises its abandonment option and ceases production. The firm lets its abandonment option extinguish, thereby producing up to its capacity, only when the realized output price exceeds its marginal cost. The ex post exercising of the abandonment option as such convexifies the firm's ex ante profit with respect to the random output price. We show that neither the separation theorem nor the full-hedging theorem holds in the presence of the abandonment option. The firm under-hedges its output price risk exposure in the forward market wherein the forward price contains a nonpositive risk premium. When the set of hedging instruments is expanded to include options, we show that both the separation and full-hedging theorems are restored. We further show that the firm prefers options to forwards for hedging purposes when both types of contracts are fairly priced.     

Inventories,inflation dynamics and the New Keynesian Phillips curve

We introduce inventories into an otherwise standard New Keynesian model and study the implications for inflation dynamics. Inventory holdings are motivated as a means to generate sales for demand-constrained firms. We derive various representations of the New Keynesian Phillips curve with inventories and show that one of these specifications is observationally equivalent to the standard model with respect to the behavior of inflation when the model's cross-equation restrictions are imposed. However, the driving variable in the New Keynesian Phillips curve – real marginal cost – is unobservable and has to be proxied by, for instance, real unit labor cost. An alternative approach is to impute marginal cost by using the model's optimality conditions. We show that the stock–sales ratio is linked to marginal cost. We also estimate these various specifications of the New Keynesian Phillips curve using GMM. We find that the predictive power of the inventory-specification at best approaches that of the standard model, but does not improve upon it.     

Do lucky CEOs avoid innovation?

Stock options are one of the most widely used equity-based compensation mechanisms to mitigate misalignment between managers’ and shareholders’ interests. And yet, it is sometimes suspiciously used as a method of extracting shareholders’ wealth to managers (Bebchuk et al., 2009). The typical ways to do so is using opportunistic timing such as backdating, spring-loading, etc. As shown in Bebchuk et al. (2010), opportunistic timing of option grants increases the incidence of lucky grants, or stock option grants that CEOs receive when the price is abnormally low. We investigate whether lucky grants to CEOs impact firm innovations and, by extension, long-term growth. Using patent citations as a proxy variable for innovation (Kogan et al., 2017), we find that innovation decreases if CEOs received lucky grant in the previous year. The results imply that lucky grants may reduce the incentive for CEOs to invest in risky, long-term projects and negatively affect fir innovation.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

A discrete choice contingent valuation estimate of the value of Kenai King salmon

A new method for estimating the demand curve for publicly supplied goods when quantities are restricted to a few discrete levels is introduced. The method involves fitting a conditional logit model to choices from a set of survey options in which price and quantity are both varied and consumer attitudes are explicitly controlled. The estimated parameters of the valuation function serve to trace the marginal value of the good at each level of hypothetical consumption in survey data. We apply the method to the valuation of salmon on Alaska's Kenai River. We find that there is a distinct kink in the marginal valuation function and that sport fishermen may place a negative marginal value on fish permits exceeding their desired catch levels.     

Is it the wage premium that targets worker turnovers?

The literature on FDI shows that there exists a wage premium that multinational enterprises (MNEs) pay to local workers and link this to a technology spillover argument. The MNEs pay higher wages to prevent worker turnovers and technology leakages. Literature relates the wage premium aspect of FDI using worker mobility data and uses worker turnovers and the technology spillover argument. We relate stock options in the FDI context of worker mobility and find in a simplified framework that the turnover of workers would depend on the relative payments of stock options.     

Plastic Money Diffusion and Usage: An Empirical Analysis on Italian Households

This paper tries to contribute to the empirical literature on the European consumers’ plastic money payment habits, using the Bank of Italy data over the 1993–2008 period. In line with other evidence on this topic, mainly focused on the US economy, we find that age, education, non‐durable consumptions, regional variation and income are strong predictors of plastic money possession and use in Italy. We also find that households with a higher indebtedness level have a higher propensity to hold credit cards. Furthermore, we find that technological improvements, observed in the last 15 years, do not significantly affect the marginal probabilities to hold and use plastic money conditioned to the main socio‐demographic factors.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.