Option pricing by large risk aversion utility¶under transaction costs

We consider a multi-asset continuous-time model of a financial market with transaction costs and prove that, for a strongly risk-averse investor, the reservation price of a contingent claim approaches the super-replication price increased by the liquidation value of the initial endowment.     

A continuous-time portfolio turnpike theorem

We prove a continuous-time portfolio turnpike theorem. The proof uses the theory of martin-gales and is more intuitively appealing than the usual discrete-time mode of proof using dynamic programming. When the interest rate is strictly positive, the present value of any contingent claim having payoffs bounded from above can be made arbitrarily small when the investment horizon increases. Thus an investor concentrates his wealth in buying contingent claims that have payoffs unbounded from above at the very beginning of his horizon. As a consequence, it is the asymptotic property of his utility function as wealth goes to infinity that determines his optimal investment strategy at the very beginning of his horizon.     

Large traders and illiquid options: Hedging vs. manipulation

In this article, we study the effects on derivative pricing arising from price impacts by large traders. When a large trader issues a derivative and (partially) hedges his risk by trading in the underlying, he influences both his hedge portfolio and the derivative's payoff. In a Black–Scholes model with a price impact on the drift, we analyze the resulting trade-off by explicitly solving the utility maximization problem of a large investor endowed with an illiquid contingent claim. We find several interesting phenomena which cannot occur in frictionless markets. First, the indifference price is a convex function of the contingent claim – and not concave as in frictionless markets – implying that for any claim the buyer's indifference price is larger than the seller's indifference price. Second, the seller's indifference prices of large positions in derivatives are smaller than the Black–Scholes replication costs. Therefore, a large trader might have an incentive to issue options if they are traded at Black–Scholes prices. Furthermore, he hedges option positions only partly if he has a negative price impact and thus exploits his ability to manipulate the option's payoff. For a positive price impact he overhedges the option position leading to an extra profit from the stock position exceeding a perfect hedge. Finally, we also study a model where the large shareholder has a price impact on both drift and volatility.     

Historical resources, uncertainty and preservation values: An application of option and optimal stopping models

State agencies and private historical organizations frequently acquire historical sites with unknown characteristics. In this paper, we provide two approaches to evaluating the preservation decision. In the first approach, we show that a historical site which is not permanently preserved provides citizens with a certain flexibility whose value can be measured as an option on the maximum between the current real estate value and the preservation value. In the second approach, we assume that the organization has an infinite planning horizon and chooses the optimal sale date. Using a contingent valuation estimate of the public's willingness to pay for preservation of a specific historical site and the real estate price, we provide simulation values of the preservation option value and the optimal stopping rule.     

Option pricing with an illiquid underlying asset market

We examine how price impact in the underlying asset market affects the replication of a European contingent claim. We obtain a generalized Black–Scholes pricing PDE and establish the existence and uniqueness of a classical solution to this PDE. Unlike the case with transaction costs, we prove that replication with price impact is always cheaper than superreplication. Compared to the Black–Scholes case, a trader generally buys more stock and borrows more (shorts and lends more) to replicate a call (put). Furthermore, price impact implies endogenous stochastic volatility and an out-of-money option has lower implied volatility than an in-the-money option. This finding has important implications for empirical analysis on volatility smile.     

存货购销中最优期权合约交易量研究

在分析利用期权合约规避价格波动风险的原理的基础上,分别给出存货购销两个环节中可以运用的期权策略,然后利用均值方差模型计算使投资组合达到效用最大化时所对应的最优期权合约交易量及其对经营利润的影响,研究发现：在存货采购环节,企业可以通过购入看涨期权、购入看涨期权同时售出看跌期权两种策略控制采购价格波动的风险,在存货销售环节,企业可以通过购入看跌期权、同时购入看跌期权并售出看涨期权两种策略来稳定销售利润;从最优期权合约交易量及其对企业经营利润的影响来看,期权工具在控制存货采购价格、稳定销售利润中可以发挥良好作用。     

Optimal multiple stopping models of reload options and shout options

The reload provision in an employee stock option entitles its holder to receive one new (reload) option from the employer for each share tendered as the payment of strike upon the exercise of the stock option. The number of reloads allowed can be finite or infinite. The shout feature in a call option allows its holder to reset the option's strike price to the prevailing stock price upon shouting. We explore a symmetry relationship between the price functions of the employee reload options and shout call options. When the dividend yield of the underlying stock is zero, the value of the employee reload option can be expressed in terms of the price functions of a shout call option and a forward contract. For an employee reload option with an infinite number of allowable reloads, the payoff of the employee reload option can be related to the lookback feature of the stock price process. We also examine the optimal exercise policies of the multi-reload employee stock options. The behavior of the critical stock price at which the holder should exercise optimally is shown to depend on the relative magnitude of the dividend yield, interest rate and volatility. Our analysis of the multi-reload and multi-shout options contributes to the literature on optimal stopping policies of contingent claims with multiple stopping rights.     

Chicago board call options as predictors of common stock price changes

The intent in this study is to determine, using response surface methodology, whether call option prices can be relied upon to predict future rises in common stock prices. If call option prices are bid up by insiders prior to the time that new information becomes available to stock traders, recognition of this price action could form the basis of a stock trading strategy yielding returns superior to buy and hold. Evidence of such an advantage would be inconsistent with the efficient market hypothesis.     

Dichotomous‐choice contingent valuation with ‘dont know’ responses and misreporting

A new approach is presented that simultaneously deals with Misreporting and Don't Know (DK) responses within a dichotomous‐choice contingent valuation framework. Utilising a modification of the standard Bayesian Probit framework, a Gibbs with Metropolis–Hastings algorithm is used to estimate the posterior densities for the parameters of interest. Several model specifications are applied to two contingent valuation datasets: one on wolf management plans, and one on the US Fee Demonstration Program. We find that DKs are more likely to be from people who would be predicted to have positive utility for the bid. Therefore, a DK is more likely to be a YES than a NO. We also find evidence of misreporting, primarily in favour of the NO option. The inclusion of DK responses has an unpredictable impact on willingness‐to‐pay estimates, since it impacts differently on the results for the two datasets we examine. Copyright © 2009 John Wiley & Sons, Ltd.     

VALUING NON-MARKET GOODS USING CONTINGENT VALUATION

Abstract. Contingent valuation is a technique being developed by economists for the valuation of environmental commodities not traded in markets. This paper discusses the major problem areas associated with this method of value estimation. These comprise bias (strategic, hypothetical and design biases); the discrepancy between willingness-to-pay and compensation demanded; the aggregation procedure; the choice of question format; and non-use values. Some evidence from comparative studies is reported, and comments made on the accuracy of contingent valuation answers, Finally, the conditions under which contingent valuation seems to operate best are set out.     

Market undervaluation of risky convertible offerings: Evidence from the airline industry

We assess market valuation of airline convertible preferred stocks using a contingent claims valuation model that was extensively tested by Ramanlal et al. (Rev Quant Financ Account 10:303–319, 1998). Our sample consists of 4,096 daily price observations of 11 convertible preferred stocks issued by the U.S. airlines in 1980–1991. For each convertible we estimate daily model prices for 2 years after issuance and compare them with market prices by calculating pricing errors. While the entire sample’s mean pricing error is found to be negative 3.8%, the panel data analysis and the mean pricing errors of the sub-samples indicate that the undervaluation is much more severe in the first 6 months of trading. The results suggest that airlines leave about 10% on the table when they raise capital by issuing convertible securities.     

The impact of option listing on the price volatility and trading volume of underlying OTC stocks

This paper examines the impact of an initial option listing on the price volatility and trading volume of underlying OTC stocks. The sample is divided by market value to determine whether larger firms are impacted differently by option listing than smaller firms. We find relative trading volume increases significantly, with the small and medium market value firms showing the largest gain. However, the tests show no evidence of changes in price volatility following option listing. No significant changes were found in either the firms' betas or variance following option initiation. The results provide further evidence that option listing does not destabilize the market for the underlying stock.     

Choice Modelling Approaches: A Superior Alternative for Environmental Valuatioin?

In this paper, we examine some popular 'choice modelling' approaches to environmental valuation, which can be considered as alternatives to more familiar valuation techniques based on stated preferences such as the contingent valuation method. A number of choice modelling methods are consistent with consumer theory, and its focus on an attribute‐based theory of value permits a superior representation of many environmental management contexts. However, choice modelling surveys can place a severe cognitive burden upon respondents and induce satisficing rather than maximising behavioural patterns. In this framework, we seek to identify the best available choice modelling alternative and investigate its potential to 'solve' some of the major biases associated with standard contingent valuation. We then discuss its use in the light of policy appraisal needs within the EU. An application to the demand for rock climbing in Scotland is provided as an illustration.     

A methodology for the choice of the best fitting continuous-time stochastic models of crude oil price

The crude oil price is generally considered as the fundamental factor in the valuation of undeveloped reserves but it is not the unique one. Undeveloped field value also depends on the uncertainty relating to the convenience yield and the risk-free interest rate. The purpose of this paper is to decide on the best continuous-time stochastic models for these risk factors. The Generalized Method of Moments and the Maximum Likelihood Estimation are implemented to fit the parameters of continuous-time stochastic processes. The results of unit root tests without breaks reveal a mean reversion in convenience yield series. Multiple structural change tests show that the risk-free interest rate can be considered constant. The simulation of continuous-time stochastic processes and the mean error between the simulated prices and the market ones show that the Geometric Brownian Motion with jumps is the best model for the oil price compared to the other commonly used processes.     

基于实物期权法的风险投资项目估价方法——一个文献综述

本文理清了实物期权及其在风险投资项目估价中应用的发展脉络,并提出了实物期权在风险投资项目估价应用中需要发展的地方。     

Shadow costs of incomplete information and short sales in the valuation of the firm and its assets

This paper presents a simple framework for the valuation of compound options within shadow costs of incomplete information and short sales. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton's (1987. Journal of Finance 42, 510) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (1996. Review of Quantitative Finance and Accounting, 7, 136) who propose an incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales.When deriving the compound call option formula, we consider a call option on a stock, which is itself an option on the assets of the firm. Our methodology incorporates shadow costs of incomplete information and short sales on the firm's assets as well as the effects of leverage in the capital structure. The formula can be useful in the valuation of several corporate liabilities in the presence of information uncertainty and short sales constraints about the firm and its cash flows. Our analysis can be used for the valuation of several real options.     

Optimal prepayment of Dutch mortgages*

Valuation of the prepayment option in Dutch mortgages is complicated. In the Netherlands, mortgagors are not allowed to prepay the full mortgage loan without a compensating penalty. Only a limited amount of the initial mortgage loan can be prepaid penalty‐free. We introduce a general model formulation for the valuation of limited callable mortgages, based on binomial trees. This model can be used for determining both the optimal prepayment strategy and the value of embedded prepayment options. For some mortgage types the prepayment option can be valued exactly, whereas other types require approximative methods for efficient valuation. The heuristic we propose here determines the prepayment option value efficiently and accurately for general mortgage types.     

A closer look at Black–Scholes option thetas

This paper investigates Black–Scholes call and put option thetas, and derives upper and lower bounds for thetas as a function of underlying asset value. It is well known that the maximum time premium of an option occurs when the underlying asset value equals the exercise price. However, we show that the maximum option theta does not occur at that point, but instead occurs when the asset value is somewhat above the exercise price. We also show that option theta is not monotonic in any of the parameters in the Black–Scholes option-pricing model, including time to maturity. We further explain why the implications of these findings are important for trading and hedging strategies that are affected by the decay in an option’s time premium.

基于增长期权的并购目标企业价值评估

实物期权评价方法的引入弥补了传统现金流量法在并购目标企业价值评估中的不足,并充分考虑了管理灵活性所具有的价值。首先,回顾了国内运用实物期权评价法对并购目标企业价值评估的研究;然后,建立包含增长期权的并购目标企业价值评估模型,在对其中增长期权的定价中加入市场竞争及企业竞争力的影响;最后,运用案例演示具体计算过程。     

A female ghetto? Women's careers in call centres

Although several studies have shown that women make up the majority of the call centre workforce, their role and position in this new and expanding industry has not yet been examined. This article makes a contribution to the research gap by exploring the extent and nature of the career opportunities open to women within call centres. Current portrayals of call centre work appear to indicate that these new workplaces offer very little in the way of either job satisfaction or potential for career progression. Indeed, on the basis of existing research evidence it could be concluded that call centres represent little more than female job ‘ghettos’. The article assesses this claim by drawing on women's own accounts of their work experiences and their perceptions of their prospects.