Auto-static for the people: risk-minimizing hedges of barrier options

We present and test a method for computing risk-minimizing static hedge strategies. The method is straightforward, yet flexible with respect to the type of contingent claim being hedged, the underlying asset dynamics, and the choice of risk-measure and hedge instruments. Extensive numerical comparisons for barrier options in a model with stochastic volatility and jumps show that the resulting hedges outperform previous suggestions in the literature. We also demonstrate that the risk-minimizing static hedges work in an infinite intensity Levy-driven model, and a number of controlled experiments illustrate that hedge performance is robust to model risk.     

Static versus dynamic hedges: an empirical comparison for barrier options

We conduct an empirical comparison of static versus dynamic hedges of barrier options. Using more than five years of data, we compare a number of static hedges from the literature with dynamic hedges based on the local volatility model. The main result is that the variability of profit-and-loss distributions from certain static hedges is significantly smaller than that of dynamic hedges and robust to changing market scenarios. Furthermore, these static hedges are able to provide a robust tracking of barrier options’ sensitivities. This article reflects the authors’ personal opinion and not necessarily the opinion of their employers.     

Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview

In this paper an overview of inference methods for continuous-time stochastic volatility models observed at discrete times is presented. It includes estimation methods for both parametric and nonparametric models that are completely or partially observed in a variety of situations where the data might be nonlinear functions of the components of the model and/or contaminated with observation noise. In each case, the main reported methods are presented, making emphasis on underlying ideas, theoretical properties of the estimators (bias, consistency, efficient, etc.), and the viability of their implementation to solve actual problems in finance.     

The risk adjusted uncovered equity parity

This paper explores the risk adjusted uncovered equity parity model to investigate a degree of market integration for four Asian emerging markets relative to the U.S., Japan and the U.K. from January 1994 to July 2008. The uncovered equity parity is revised to take into account of market risk in a framework of a portfolio rebalancing model. Evidence was found to strongly support our hypotheses; Market risk is significant in international capital flows between the Asian emerging markets and the developed economies, and it can help explain the failure of a traditional uncovered equity (or interest) parity model. The relationship between returns and an appreciation of the exchange rate are divided between the Asian emerging markets and the developed economies, depending on the direction of capital flows.     

CAPM option pricing

This paper extends the option pricing equations of [Black and Scholes, 1973] , [Jarrow and Madan, 1997] and [Husmann and Stephan, 2007] . In particular, we show that the length of the individual planning horizon is a determinant of an option’s value. The derived pricing equations can be presented in terms of the Black and Scholes [1973. Journal of Political Economy 81, 637–654] option values which ensures an easy application in practice.     

中国外汇交易中心提供多渠道技术支持服务

中国外汇交易中心的技术支持服务人员在约定的服务时间内,通过电话、邮件、MSN等多种方式受理客户技术服务请求和服务满意度反馈。     

世行调整支持中国的援助计划

1980年中华人民共和国恢复世界银行（以下简称世行）成员国席位以来,世行积极与中国开展合作,共同应对中国面临的发展挑战。30年来,中国在推进改革、发展经济和减少贫困方面取得了举世瞩目的成就,     

Double-sided Parisian option pricing

In this paper we derive Fourier transforms for double-sided Parisian option contracts. The double-sided Parisian option contract is triggered by the stock price process spending some time above an upper level or below some lower level. The double-sided Parisian knock-in call contract is the general type of Parisian contract from which also the single-sided contract types follow. The paper gives an overview of the different types of contracts that can be derived from the double-sided Parisian knock-in calls, and, after discussing the Fourier inversion, it concludes with various numerical examples, explaining the, sometimes peculiar, behavior of the Parisian option. The paper also yields a nice result on standard Brownian motion. The Fourier transform for the double-sided Parisian option is derived from the Laplace transform of the double-sided Parisian stopping time. The probability that a standard Brownian motion makes an excursion of a given length above zero before it makes an excursion of another length below zero follows from this Laplace transform and is not very well known in the literature. In order to arrive at the Laplace transform, a very careful application of the strong Markov property is needed, together with a non-intuitive lemma that gives a bound on the value of Brownian motion in the excursion.      

Robust stock option plans

The main purpose of this paper is to address the issue of robustness of stock option plans, which is essential for reliable accounting valuations. The introduction of the accounting standards SFAS 123R and IFRS 2 for executive stock options has led to an important change. As companies are now forced to value their stock options at grant date for accounting purposes, the robustness of prices against the choice of certain valuation models and input parameters has become a very important issue. We address this issue by first analyzing certain building blocks of existing stock option plans with regard to their robustness properties. Based on our analysis, we then show how robustness of stock option plans can be achieved. The resulting stock option plans are both transparent in structure and reasonable in respect to the incentives they provide in order to increase shareholder value. We therefore conclude that stock options can be reliably expensed, if the corresponding plans are properly designed.     

Information and option pricings

How can one relate stock fluctuations and information-based human activities? We present a model of an incomplete market by adjoining the Black-Scholes exponential Brownian motion model for stock fluctuations with a hidden Markov process, which represents the state of information in the investors' community. The drift and volatility parameters take different values depending on the state of this hidden Markov process. Standard option pricing procedure under this model becomes problematic. Yet, with an additional economic assumption, we provide an explicit closed-form formula for the arbitrage-free price of the European call option. Our model can be discretized via a Skorohod embedding technique. We conclude with an example of a simulation of IBM stock, which shows that, not surprisingly, information does affect the market.     

Reducing reporting risk: Designating foreign currency forward contracts as cash flow hedges

We present an example that compares the effects on earnings of designating a foreign currency forward contract as either a cash-flow or fair-value hedge of a foreign currency denominated receivable. Entities engaging in exchange transactions not denominated in their functional currency frequently enter into foreign currency forward contracts in order to mitigate their foreign exchange rate risk exposure. The aggregate effect on earnings of the transaction gain or loss on the foreign currency receivable and the gain or loss on the forward contract is known on the date the forward contract is initiated. The effect on each period’s earnings during the term of a forward contract designated as a cash-flow hedge is also known on the date the contract is initiated; whereas the effect on each periods’ earnings from a fair-value hedge cannot be determined until the respective balance sheet dates. Therefore, designating forward contracts as cash-flow hedges may suppress volatility in reported earnings compared to designating forward contracts as fair-value hedges. In addition, the reporting risk (the amount of uncertainty surrounding the pending measure of an item to be reported in the financial statements) is lower when a forward contract is designated as a cash-flow hedge relative to designating it as a fair-value hedge. This suggests foreign currency forward contracts designated as cash-flow hedges are more consistent with the purpose of hedge accounting: to mitigate the effects on earnings of applying different measurement criteria for the hedge and the hedged item.     

Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature.     

An adjusted binomial model for pricing Asian options

We propose a model for pricing both European and American Asian options based on the arithmetic average of the underlying asset prices. Our approach relies on a binomial tree describing the underlying asset evolution. At each node of the tree we associate a set of representative averages chosen among all the effective averages realized at that node. Then, we use backward recursion and linear interpolation to compute the option price.     

Owner-occupied homes,income-producing properties,and REITs as inflation hedges: Empirical findings

New evidence on the correlation patterns of various real estate returns with inflation is presented. Returns on a wide array of real estate, nonresidential as well as residential, are investigated. Stock and bond returns are also analyzed for comparison purposes. Extensive heterogeneity is found in real estate return correlations with inflation. Nonresidential property returns are most strongly positively correlated with inflation, although the appreciation in owner-occupied homes is also positively associated with inflation. However, REIT returns tend to be strongly negatively correlated with inflation. In this respect, they look more like traditional stocks and bonds than any other type of real estate. Finally, new evidence on return correlations with energy prices is also presented. Nonresidential real estate performs best here, too, although no real estate asset fully compensates investors for adverse energy price shocks.     

Stochastic volatility and option pricing

Through a simple Monte Carlo experiment, Dimitrios Gkamas documents the effects that stochastic volatility has on the distribution of returns and the inability of the normal distribution utilized by the Black–Scholes model to fit empirical returns. He goes on to investigate the implied volatility patterns that stochastic volatility models can generate and potentially explain.     

Risk-neutral compatibility with option prices

A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.     

Information revelation through option exercise

In many real-world situations, agents must formulate optionexercise strategies with imperfect information. In such a setting,agents may infer the private signals of other agents throughtheir observed exercise strategies. The building of an officebuilding, the drilling of an exploratory oil well, and the commitmentof a pharmaceutical company toward the research of a new drugall convey private information to other market participants.This article develops an equilibrium framework for option exercisegames with asymmetric private information. Many interestingaspects of the patterns of equilibrium exercise are analyzed.In particular, informational cascades, where agents ignore theirprivate information and jump on the exercise bandwagon, mayarise endogenously.