Spanning with indexes

This paper presents several approximation theorems of a general contingent claim in terms of index options. We demonstrate that any contingent claim on the primitive securities in an infinite state economy can be approximated arbitrarily close by a portfolio of index options. In addition, these index options are associated with the same payout function, which belongs to a large and explicit class of one-variable measurable functions. I also characterize the layer structure of a general contingent claim.     

On the use of semimartingales and stochastic integrals to model continuous trading

The continuous-time contingent claim valuation model is generalized to stopping times (random trading dates), giving substance to the question of what it means to have unlimited opportunities to trade while trading intercessions may occur only finitely, albeit arbitrarily, often. Robustness and stability of the contingent claim valuation formula are demonstrated, validating the use of continuous-time models for approximating discrete-time trading environments. The no-arbitrage value of a redundant contingent claim is shown to be a stochastic integral obtained as the limit of bounded arbitrage opportunities. As a corollary, we find that the hypothesis needed to value an American call option is significantly stronger than that sufficient to value a European call option.     

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.     

股票价格服从分数布朗运动的再装期权定价

未定权益的定价是金融工程研究的前沿与热点问题。本文在标的资产的价格服从分数布朗运动的假设下,在风险中性条件下,运用鞅方法,导出了再装期权的定价公式。     

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.     

基于无套利对冲原理的信用风险期权定价

文章拓展了Klein假设中关于固定违约门槛的假设,构造可变违约门槛,根据无套利对冲原理,通过偏微分方程这种数学工具,推导出含信用风险的欧式脆弱期权价格波动的偏微分方程组和期权定价模型,进而求其显示解,得到类似于Black-Scholes公式的定价公式,该公式的推导过程比使用鞅理论推导更加浅显易懂。     

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.     

Bounds for the utility-indifference prices of non-traded assets in incomplete markets

Abstract We consider a special class of financial models with both traded and non-traded assets and show that the utility indifference (bid) price of a contingent claim on a non-traded asset is bounded above by the expectation under the minimal martingale measure. This bound also represents the marginal bid price for the claim. The key conclusion is that the bound and the marginal bid price are independent of both the utility function and initial wealth of the agent. Thus all utility maximising agents charge the same marginal price for the claim. This conclusion is in some sense the opposite conclusion to that of Hubalek and Schachermayer (2001), who show that any price is consistent with some equivalent martingale measure. Mathematics Subject Classification (2000): 91B28, 91B16, 60J70 Journal of Economic Literature Classification: G13     

Essential supremum and essential maximum with respect to random preference relations

In the first part of the paper, we study concepts of supremum and maximum as subsets of a topological space X$X$ endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility representations. In the second part of the paper, we consider partial orders and preference relations “lifted” from a metric separable space X$X$ endowed by a random preference relation to the space L⁰(X)$L^0\left(X\right)$ of X$X$-valued random variables. We provide an example of application of the notion of essential maximum to the problem of the minimal portfolio super-replicating an American-type contingent claim under transaction costs.     

Collateral amplification under complete markets

This paper examines the robustness of the Kiyotaki–Moore collateral amplification mechanism to the existence of complete markets for aggregate risk. We show that, when borrowers can hedge against aggregate shocks at fair prices, the volatility of endogenous variables becomes identical to the first best in the absence of credit constraints. The collateral amplification mechanism disappears.To motivate the limited use of contingent contracts, we introduce costs of issuing contingent debt and calibrate them to match the liquidity and safety premia the data. We find that realistic costs of state contingent market participation can rationalize the predominant use of uncontingent debt. Amplification is restored in such an environment.     

Contingent work in the UK and Sweden: evidence from the construction industry

This article explores the use of contingent forms of employment in two diverse country contexts—the UK and Sweden—and investigates the influence of changing regulatory and economic conditions over a period that covers the current economic downturn. Drawing on quantitative and qualitative data for the construction sector, the article addresses three questions. How do employers balance their flexibility preferences in the context of regulatory constraints? How has the global recession influenced employer behaviour? And to what extent can the Swedish experience be explained by convergence on other country models? While the UK employment model encourages employers to externalise the risk of unpredictable market conditions through the use of contingent contracts, the more supportive welfare regime in Sweden underpins a resilient preference of employers for open‐ended employment contracts. Ongoing changes in labour market regulation pose challenges to the strongly regulated Swedish model, yet we find only a shared direction of travel with the UK rather than convergence in the use of contingent employment.     

Game contingent claims in complete and incomplete markets

A game contingent claim is a contract which enables both the buyer and the seller to terminate it before maturity. For complete markets Kifer [Finance and Stochastics 4 (2000) 443–463] shows a connection to a (zero-sum) Dynkin game whose value is the unique no-arbitrage price of the claim. But, for incomplete markets one needs a more general approach. We interpret the contract as a generalized non-zero-sum stopping game. For the complete case this leads to the same results as in Kifer [Finance and Stochastics 4 (2000) 443–463]. For the general case we show the existence of an equilibrium point under the condition that both the seller and the buyer have an exponential utility function. For other utility functions such a point need not exist in the context of incomplete markets.     

科技创业企业现金流量权相机性分配的经验分析

科技创业企业在进行外源融资时,投资者和创业者之间的现金流量权分配是这类企业产权结构的一项主要内容。这类企业现金流量很小,创业者的工资收入往往很低,他们的收入主要采用股份的形式。因此,现金流量权的相机分配是投资者激励作为经营管理者的创业者积极性的一个重要手段。     

Pricing European continuous-installment currency options with mean-reversion

In this paper, we consider European continuous-installment currency option under the mean-reversion environment. Specifically, we provide efficient pricing formula of installment currency put option via a partial differential equation (PDE) approach when the exchange rate follows the mean reverting lognormal model. Using the Mellin transform techniques, we derive the integral equation representation for the optimal stopping boundary from the PDE for pricing of the option. To verify the efficiency and accuracy of our approach, we provide computational results with the least square Monte Carlo method proposed by Longstaff and Schwartz (2001). We also present some numerical examples to examine the characteristics of the optimal boundaries and prices.     

Contingent capital,capital structure and investment

We examine the interaction between investment and financing policies in a dynamic model for a firm with existing assets-in-place and a growth option, of which investment cost is financed with equity and contingent convertible bonds (CoCos). We attempt to clarify how CoCos impact on investment timing, capital structure and inefficiencies arising from debt overhang and asset substitution. We show that there is a conversion ratio (the fraction of equity allocated to CoCo holders upon conversion) to eliminate the inefficiencies. Our conclusions predict that debt leverage decreases with investment option payoff factor and the average appreciation rate of the cash flow. In contrast to traditional corporate finance theory saying that a firm's value decreases globally with business risk, our model indicates that it might first decrease and then increase with asset volatility.     

Economics,Darwinism, and the Case of Disciplinary Imports

The problem of causality in economics is still contended by various epistemological alternatives. The article builds on the received view of Darwinism in economics and examines the way in which economics and biology find common ground in concepts and assumptions that reflect causal commonalities of the natural and the social world. We claim that the role the contingent pattern plays in understanding socioeconomic change provides reasons to concede corrections to a rule‐based causal mechanism. The article concludes on the merits of advancing the ontological equivalent of interdisciplinary studies as one possible standard in reference to which to judge the epistemic adequacy of any import.     

Option pricing with stochastic volatility models

A general class of models for derivative pricing with stochastic volatility is analyzed. We include the possibility of jumps for the paths of the asset's price and for those of its volatility. We also consider the case of correlation between the process of the asset's price and that of its volatility. In this way we are able to give a unifying view on most of the models studied in the literature. We will examine theoretical issues related to the market price of volatility risk, the equivalent martingale measures and the possibility of obtaining a numerically tractable formula for contingent claim pricing. Finally, we propose some methodologies to test the behavior of stochastic volatility models when applied to market data.     

Portfolio constraints,differences in beliefs and bubbles

I propose an arbitrage-based theory of bubbles in economies with general portfolio constraints and differences in beliefs. I find that, in general, bubbles cannot exist unless the constraints restrict the demand for credit sufficiently to induce low interest rates. Speculation due to heterogeneous beliefs does not cause bubbles. Ruling out bubbles under asymmetric information requires stronger assumptions: the presence of some uninformed agents and mild portfolio restrictions (debt or borrowing constraints), or alternatively, the existence of some impatient and fully informed agents.     

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.     

财务契约理论文献综述

本文回顾了财务契约理论的演变过程,重点分析了财务约束、重新协商、控制权配置和索取权多样化等主要模型。认为保护投资者权益的根本机制是财务约束,即投资者要求企业给以足够的投资回报,否则就夺取企业的控制权从而使当前的控制人失去控制权利益。债务在公司治理中的作用一是迫使管理者支出自由现金,减少在职消费和低效投资;二是作为一种控制权转移机制,在股东和债权人之间转移企业的控制权,以实现最高经济效率。