On pricing lookback options under the CEV process

Abstract We consider the problem of pricing European lookback options when the underlying asset price is driven by a constant elasticity of variance (CEV) process. The evaluation model is based on the binomial approximation developed by Nelson and Ramaswamy (1990) and we show how to apply it in the case of such options. We develop simple pricing algorithms that compute accurate estimates of the option prices.     

Valuing lookback options with barrier

In this paper, we introduce a new class of exotic options, termed lookback-barrier options, which literally combine lookback and barrier options by incorporating an activating barrier condition into the European lookback payoff. A prototype of lookback-barrier option was first proposed by Bermin (1998), where he intended to reduce the expensive cost of lookback option by considering lookback options with barrier. However, despite his novel trial, it has not attracted much attention yet. Thus, in this paper, we revisit the idea and extend the horizon of lookback-barrier option in order to enhance the marketability and applicability to equity-linked investments. Devising a variety of payoffs, this paper develops a complete valuation framework which allows for closed-form pricing formulas under the Black–Scholes model. Our closed-form pricing formulas provide a substantial advantage over the method of Monte Carlo simulation, because the extrema appearing in both of the lookback payoff and barrier condition would require a large number of simulations for exact calculation. Complexities involved in the derivation process would be resolved by the Esscher transform and the reflection principle of the Brownian motion. We illustrate our results with numerical examples.     

The pricing of lookback options and binomial approximation

Refining a discrete model of Cheuk and Vorst, we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in particular, that the price in the discrete model tends to the price in the continuous Black–Scholes model. Our results are based on an asymptotic expansion of the binomial cumulative distribution function that improves several recent results in the literature.     

资本预算中管理期权理念及其定价分析

传统的资本预算方法认为投资机会一旦出现,就应该立即进行投资,事实上企业不仅可以决定是否投资于某项目,而且可以决定何时从事该项目的投资,我们称之为管理期权。本文利用二叉树和复制技术对隐含在投资项目中的管理期权进行了定价,并指出"二叉树法"低估了管理期权的价值。     

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.     

Pricing American barrier options with discrete dividends by binomial trees

We are concerned with the problem of pricing plain-vanilla and barrier options with cash dividends in a piecewise lognormal model. In the plain-vanilla case, we offer a method with provides thin upper and lower bounds of the exact binomial price. In the barrier case, we provide an efficient algorithm based on suitable interpolation techniques. As by-product, we provide a new method for pricing American barrier options with continuous dividends.     

Optimal stopping made easy

This paper presents a simple discrete time model for valuing real options. A short and simple proof of optimal exercise rules for the standard problems in the real options theory is given in the binomial and trinomial models, and, more generally, when the underlying uncertainty is modelled as a random walk on a lattice. The method of the paper is based on the use of the expected present value operators. With straightforward modifications, the method works in discrete time-continuous space, continuous time-continuous space and continuous time-discrete space models.     

基于风险中性路径概率的三叉树期权定价模型

树方法是给经典期权进行定价的非常实用的数值方法,目前最流行的是二叉树模型。三叉树定价模型作为二叉树的一个扩展,其同样是在风险中性概率的基础上给经典期权进行定价,并且可以通过MATLAB实现。相比于二叉树而言,三叉树模型的定价结果具有更好的收敛性。除此之外,用三叉树模型对影响期权价格的一些因素进行敏感性分析,可以验证该模型的合理性。     

A stochastic cash model with deterministic elements

In this paper we present a simple model which gives a solution to a (one period) stochastic cash problem with a fixed cash outlay at the end of the period. We focus on the role of options as insurance contracts, as to value a constraint on the minimum cash level. It is argued that a cash level adjustment is optimal where the sum of the marginal cost of liquidity and the marginal insurance premium (options value) is zero.We like to thank Edwin O. Fischer, Jaap Spronk and three anonymous referees for helpfull comments. Excellent computational assistance by Henk Hofmans is hereby acknowledged. Of course, the usual disclaimers apply.     

Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends

In the literature there appear various kinds of binomial trees for pricing options on stocks under geometric Brownian motions (GBMs) with known cash dividends. The aim of this paper is to compare the performance of the existing binomial trees in aspect of the convergence rates, which are usually used to measure precisely how fast the approximate values converge to the exact one, and to give a theoretical proof of the convergence rates for the interpolation binomial trees which are based on a model that excludes the arbitrage possibilities. Also the paper extends the studies to the regime-switching models with known cash dividend payment.     

Smart logistics transformation collaboration between manufacturers and logistics service providers: A supply chain contracting perspective

Intelligent transformation of manufacturers requires smart logistics transformation collaboration, which improves competitiveness. In this study, we construct a Stackelberg game model based on the mutual influence and restriction in the relationship between a manufacturer and a logistics service provider (LSP) undergoing smart logistics transformation. We investigate whether cost-sharing (CS) or revenue-sharing (RS) contracts can coordinate the supply chain and suggest a hybrid CS–RS contract to improve performance. We find that, compared with decentralized options, CS and RS contracts achieve a higher level of smart logistics transformation. While the coordination and effectiveness of CS contracts are superior to those of RS contracts, neither can fully coordinate the supply chain. The proposed hybrid CS–RS contract allows the manufacturer to share the LSP’s costs before the transformation and its partial revenue after transformation, so that the LSP can reduce its service charge, thereby achieving full supply chain coordination.     

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.     

Managerial Incentives Based on Acquisition of Information

In a moral hazard setting, we model the fact that the agent may get private signals about the final outcome of his effort before the public realization of this outcome. Actions affect both the distribution of the outcome and the quality of the agent's private information. We compare simple contracts, based on output only, with revelation contracts, based on output and messages about signals. Revelation contracts give the agent some discretionary power during the course of the relationship; they are optimal if and only if lowering effort does not increase the quality of private information in the sense of Blackwell (1953). In the context of managerial compensation schemes, the revelation contracts we analyze can be viewed as allowing the agent to exercise an option on the final profits before the realization of these profits. The theory thus provides an alternative justification of the widespread use of stock options in managerial compensation schemes, as opposed to compensation schemes that rely only on salary, bonus, and (restricted) stock plans.     

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。     

An improved combinatorial approach for pricing Parisian options

Parisian options are path-dependent options whose payoff depends on whether the underlying asset’s price remains continuously at or above a given barrier over a given time interval. Costabile’s (Decis Econ Finance 25(2):111–125, 2002b) algorithm for pricing Parisian options based on a combinatorial approach in binomial tree has a time complexity of O( n³){O\left( {n^{3}}\right)}. We improve that algorithm to yield one with a time complexity of only O(n²){O\left({n^{2}}\right)}.     

Payer Competition and Cost Shifting in Health Care

This paper studies a model in which two payers contract with one hospital. True costs per patient are not a possible basis for payment, and contracts can only be written on the basis of allocated cost. Payers choose a contract that is fully prospective or fully based on cost allocation, or a payment scheme that would give some weight to each of these two. We characterize the payers'equilibrium contracts arid show how in equilibrium hospital input decisions are distorted by the payers' incentives to engage in cost shifting. Two cost-shifting incentives work in opposite directions, and equilibrium can be characterized by too little or too much care relative to the socially efficient level.     

Relational retention

This paper uses a repeated-game model to study the retention of talented workers in the face of competition for talent. When the job benefits that workers value are non-contractible, retention cannot be achieved by a sequence of spot contracts, but must be based on self-enforcing long-term agreements, which we call relational retention contracts. Retention then is successful only if workers trust their employers' promises. We demonstrate that relational contracts are valuable even if there are no incentive problems inside firms and that firms with a relatively low valuation for talent may be able to retain talented workers.     

Contract employment policy and research productivity of knowledge workers: an analysis of Spanish universities

Abstract

This article investigates how contract employment practices adopted by universities—fixed-term contracts and permanent contracts—impact research productivity measured in terms of publications in scholarly journals. The empirical application considers the Spanish public higher education system for the period 2002–2008. We report an inverse U-shaped relationship between the rate fixed-term contracts and the research productivity of Spanish universities. That is, contract policies based on fixed-term contracts are conducive to research productivity; however, beyond a critical threshold value increases in the proportion of fixed-term contracts are associated with declining research productivity. These findings reveal that contract employment policies shape research productivity, and that flexible and balanced contract practices are critical for enhancing universities’ research productivity. The results suggest that the excessive use of fixed-term contracts might create an unstable working environment that limits the universities’ capacity to capitalize on their knowledge workers. Policy implications and future research avenues are discussed.     

Path dependent volatility

We propose a general class of non-constant volatility models with dependence on the past. The framework includes path-dependent volatility models such as that by Hobson and Rogers and also path dependent contracts such as options of Asian style. A key feature of the model is that market completeness is preserved. Some empirical analysis, based on the comparison with standard local volatility and Heston models, shows the effectiveness of the path dependent volatility. In particular, it turns out that, when large market movements occur, the tracking errors of Heston minimum-variance hedging are up to twice the hedging errors of a path dependent volatility model.      

Availability and settlement of individual stock futures and options expiration-day effects: evidence from high-frequency data

This study examines whether the expiration-day effects of stock options traded in Australian Stock Exchange on return, volatility, trading volume, and temporary price changes of individual stocks vary with the availability and the settlement method of individual stock futures contracts. Using transaction data of the stocks that have both options and futures contacts from 1993 to 1997, we find that options expiration has significant effects on return and volatility of the underlying stocks in absence of individual stock futures. After introduction of a cash-settled stock futures contract, the effects decrease notably. However, the switch of a futures contract from cash settlement to physical delivery promotes the expiration effects on return and volatility and boosts temporary price changes on expiration days. Finally, options expiration has little effect on trading volume. Trading activity tends to behave normally regardless whether stock futures contracts are available or not.