Spectral calibration of exponential Lévy models

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation.     

On the Upper Bound of a Call Option

Using only a weak set of assumptions, Merton (1973) shows that the upper bound of a European or American call option on a non-dividend paying stock is the underlying stock price: a result which is often extended to options on dividend paying stocks. In this short technical piece we show that the underlying stock price is in fact not the least upper bound of either a European or an American call option on a stock that pays one or more known dividends prior to maturity. Based on Merton's (1973) original framework, new upper bounds are established which depend on the size(s) of the dividend(s) compared to the size of the strike. JEL Classification: G12, G13     

A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

The Effect of Mortgage Price and Default Risk on Mortgage Spreads

Variations over time in mortgage yield spreads should reflect changes in the underlying prepayment option value; moreover, the relationship between mortgage yield spreads and interest rate dynamics should weaken as the value of the borrowers prepayment option declines. We verify this hypothesis through an empirical analysis of residential mortgage yield spread behavior, and we also present evidence that the strength of the relationship between mortgage spreads and interest rate dynamics weakens (strengthens) as the level of default risk increases (decreases). This result is consistent with the competing risks effect between a borrowers option to prepay or default. Our results demonstrate the importance of accounting for mortgage price discount to par as well as default risk when developing time series of mortgage yields.     

Pricing derivatives of American and game type in incomplete markets

In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively.On the technical level, an important role is played by -sub- and -supermartingales. We characterize these processes in terms of semimartingale characteristics.Received: June 2003, Mathematics Subject Classification (2000):   91B24, 60G48, 91B16, 91A15, 60G40JEL Classification:   G13, D52, C73The authors want to thank PD Dr. Martin Beibel for the idea leading to the proof of Proposition A.4 and both anonymous referees for many valuable comments. The second author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg Angewandte Algorithmische Mathematik at Munich University of Technology and by the Fonds zur Förderung der wissenschaftlichen Forschung at Vienna University of Technology.     

A Complete-Market Generalization of the Black-Scholes Model

The author proposes a new single-stock generalization of the Black-Scholes model. The stock price process is Markovian, the volatility is time-varying, and the market is complete. We also consider the option pricing based on our model and a connection with the equilibrium theory.     

Option pricing when correlations are stochastic: an analytical framework

In this paper we develop a novel market model where asset variances–covariances evolve stochastically. In addition shocks on asset return dynamics are assumed to be linearly correlated with shocks driving the variance–covariance matrix. Analytical tractability is preserved since the model is linear-affine and the conditional characteristic function can be determined explicitly. Quite remarkably, the model provides prices for vanilla options consistent with observed smile and skew effects, while making it possible to detect and quantify the correlation risk in multiple-asset derivatives like basket options. In particular, it can reproduce and quantify the asymmetric conditional correlations observed on historical data for equity markets. As an illustrative example, we provide explicit pricing formulas for rainbow “Best-of” options.     

基于价值权力的战略管理方法和模型

实物期权方法近年来在战略投资领域得到了广泛应用,但在战略管理领域中的应用却没有得到更进一步的发展。本文试图找到实现实物期权思想在战略管理领域更广泛应用的途径。通过扩展实物期权概念的内涵,本文引申出价值权力的概念,提出了基于价值权力进行战略分析和管理的思路,并进一步构建了进行价值权力分析和管理的直观工具,为在变化日益加速的不确定性环境下对企业战略进行全面的分析和管理提供了一个新的视角和相关模型。     

美式累计订单询价机制的运作及启示

IPO发售机制对一国的股票发行及上市公司具有重要的影响，而世界范围内越来越多的国家已开始果用美式累计订单询价这一IPO发售机制。本文首先对美式累计订单询价机制的一般询价过程进行了介绍，并对美式累计订单询价机制的信息收集过程进行了阐述，随后分析了美式累计订单询价机制相对其他IPO发售机制所具有的优点，最后对新服发行询价制下我国证券公司及监管当局提出了相应的对策建议。     

亚式期权定价的模拟方法研究

由于算术平均价格亚式期权的定价没有解析公式，所以文章用Monte Carlo模拟方法通过Matlab软件编写程序对亚式期权进行了定价。发现在某些情况下，亚式期权的价值并不是国内外一些研究者所认为的低于相应的欧式期权的价值。