HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET

This paper presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor’s theorem, dynamic hedging portfolios are constructed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk‐free bank account, the underlying asset, and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.     

BLACK–SCHOLES REPRESENTATION FOR ASIAN OPTIONS

Asian options are securities with a payoff that depends on the average of the underlying stock price over a certain time interval. We identify three natural assets that appear in pricing of the Asian options, namely a stock S, a zero coupon bond B^T with maturity T, and an abstract asset A (an “average asset”) that pays off a weighted average of the stock price number of units of a dollar at time T. It turns out that each of these assets has its own martingale measure, allowing us to obtain Black–Scholes type formulas for the fixed strike and the floating strike Asian options. The model independent formulas are analogous to the Black–Scholes formula for the plain vanilla options; they are expressed in terms of probabilities under the corresponding martingale measures that the Asian option will end up in the money. Computation of these probabilities is relevant for hedging. In contrast to the plain vanilla options, the probabilities for the Asian options do not admit a simple closed form solution. However, we show that it is possible to obtain the numerical values in the geometric Brownian motion model efficiently, either by solving a partial differential equation numerically, or by computing the Laplace transform. Models with stochastic volatility or pure jump models can be also priced within the Black–Scholes framework for the Asian options.     

论全球碳市场机制的完善及中国的对策选择

本文在全球气候变化的大背景下提出一个可以将世界各国都纳入到减排体系的金融创新方法,在对全球碳市场现状和问题进行分析的基础上,通过引入碳期权来完善碳市场机制,并进一步探讨碳期权的定价策略,提出中国融入全球碳市场机制以及参加国际气候谈判的对策建议。     

Housing-Price Cycles and Prepayment Rates of U.S. Mortgage Pools

Empirical mortgage prepayment models generally have trouble explaining differences in mortgage-prepayment speeds among pools with similar interest rates on the underlying mortgages. In this article, we model some of the sources of termination heterogeneity across mortgage pools, particularly the role of regional variations in housing prices in generating atypical prepayment speeds. Using a sample of Freddie Mac mortgage pools from 1991 to 1998, we compare two classes of empirical models: a rational option-pricing model using a backward-solving pricing algorithm and an empirical hazard model. In both empirical estimation strategies, we find evidence that differences in house-price dynamics across regions are an important source of between-pool heterogeneity. This finding is then shown to be robust to alternative ways of parameterizing pool heterogeneity in mortgage termination models.     

PASSPORT OPTIONS

We relate the theory of passport options with general principles from martingale theory as well as with the theory of Bessel processcs. The calculation of the price of a passport option leads to an equality between two norms on continuous martingales. We also solve the discrete time case for passport options.     

期权理论在IT项目风险管理中的应用

本文简要介绍了金融期权和IT项目期权的含义,以及期权定价模型,详细分析了IT项目期权的类型和IT项目期权的套期保值,其中对比分析了NPV方法和期权方法(B-S模型)在评估IT项目中的差异。     

The Value of the Rent Control Option

In this paper, we combine direct arbitrage arguments and an option-pricing approach to develop a method of pricing the option for rent control. For a lump-sum payment of key money, a tenant acquires the right to rent a real estate unit for an exogenously determined controlled rent, as opposed to paying the free-market rent. The tenant may continue exercising this right as long as he or she lives. Alternatively, the tenant may sell the right to occupy the controlled rent unit and receive a fraction of the key money paid by the subsequent tenant. We value the equilibrium key money, in a representative agents partial equilibrium, while endogenously determining the expected tenure duration in a controlled rent unit. We propose a procedure for valuing rent control options different from the representative agents. Our analysis shows that under real-world levels of conditional life expectancy, the level of the fraction of the key money retained by a departing tenant has an insignificant effect on the expected tenure duration in a controlled rent unit and on the level of key money.     

A Note on the Joint Distribution of α, β-Percentiles and Its Application to the Option Pricing

In this paper, using Laplace transform, we will calculate the joint density of twopercentiles of stock prices in the Black–Sholes model and make the price of exchange options of such twopercentiles.     

Optimal dividend policy and growth option

We analyse the interaction between the dividend policy and the decision on investment in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly by establishing a connection with an optimal stopping problem. We characterize situations where it is optimal to postpone the distribution of dividends in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have an ambiguous effect on the investment decision.      

The association between employee stock option disclosures and corporate governance: Evidence from an enhanced disclosure regime

This study examines the role of corporate governance in employee stock option (ESO) disclosures following the revision of AASB 1028 Employee Benefits in 2001. We find that, while firms do not fully comply with AASB 1028 ESO disclosures, they voluntarily provide other ESO disclosures. In relation to corporate governance measures that have a role in the financial reporting process, we find two corporate governance measures dominate our results—the quality of auditor and duality of the role of CEO and Chair of the Board of Directors. We show that, in general, external auditor quality has positive incremental association with both mandatory and voluntary ESO disclosures while the dual role of CEO and chairperson of the board is associated with lower levels of mandatory disclosure.