A semiparametric estimation of liquidity effects on option pricing

Abstract. This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation. Eva Ferreira and Gonzalo Rubio acknowledge the financial support provided by Dirección Interministerial Científica y Técnica (DGICYT) grants PB98-0149 and PB97-0621 respectively. All three authors aknowledge the financial support provided by Universidad del País Vasco (UPV/EHU) grant UPV 038.321-HA129/99, and the BSI Gamma Foundation. We appreciate the helpful comments of two anonymous referees, ángel León, José M. Campa, Fernando Tusell and Javier Fernández Navas, seminar participants at the Bank of Spain and the European Financial Management Association (Athens), and the computational assistance of Gregorio Serna. We thank Juan Ayuso and MEFF for providing the data used in this article. The contents of this paper are the sole responsability of the authors.     

Foreign equity option pricing under stochastic volatility model with double jumps

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices.     

Modelling the dependency between currency and debt crises: An option based approach

The interrelation between currency and debt crises is considered in a model relying on option pricing theory. By capturing uncertainty and time aspects in this stochastic and dynamic framework we analyze parameters that determine the probabilities and dependencies of these crises.     

The double exponential jump diffusion model for pricing European options under fuzzy environments

The interest rate and volatility may have different values in the different commercial banks and financial institutions. Moreover, the fluctuations of the underlying assets are rare events, and there are not enough historical data to estimate the jump intensity in a precise sense. This paper considers European option pricing problems with the fuzzy interest rate, fuzzy drift, fuzzy volatility and fuzzy jump intensity. We present the fuzzy pricing formula of European options based on the Kou's double exponential jump diffusion model. We also obtain the crisp possibilistic mean option pricing formula in fuzzy double exponential jump diffusion model by using the crisp possibilistic mean values of the fuzzy numbers. Comparing with B-S formula, numerical analysis and empirical results show that the fuzzy double exponential jump diffusion formula and the crisp possibilistic mean option pricing formula are reasonable and can be taken as reference pricing tools for the financial investors.     

基于Poisson跳跃的信用价差期权定价

信用价差是用以向投资者补偿参照资产违约风险的、高于无风险利率的利差。信用价差期权作为风险控制的重要手段之一,其定价也日益得到人们的关注。现有文献几乎是单纯地利用几何布朗运动来刻画资产的价格变化过程从而对信用价差期权进行定价。而在实际中会出现某些不寻常的事件导致资产价格出现不间断的跳跃现象,普通的定价方法对这种现象的解释力度不够。因此本文引入Poisson跳跃来描述信用价差变化过程中的异常情况,更好地解释当遇到金融危机等情况时资产价值的跳跃现象。由于Longstaff和Schwartz的模型引入了随机利率,可以给出定价公式的封闭解析解的优点,本文在此模型上进行进行研究,将刻画信用价差动态过程的O-U过程与Poisson跳跃结合,利用伊藤公式进行推导并引入了利率的平方根过程,得到了欧式信用价差期权的定价公式,更好地考虑了资产价格的跳跃情况。     

Applying the Model Order Reduction method to a European option pricing model

This paper presents a European option pricing model by applying the Model-Order-Reduction (MOR) method. A European option pricing theorem based on Black–Scholes' equation is implemented by the Finite-Difference Method (FDM). However, the numerical models generated by the FDM could be simplified through the MOR technique, which is based on the concept of an Arnoldi-based Model-Order Reduction algorithm. In terms of computational cost, the MOR models are at least 2 orders of magnitude faster than the original FDM models with a negligible compromise in accuracy.     

Analytical American Option Pricing: The Flat‐barrier Lower Bound*

In a Black and Scholes (1973) world, this paper studies the pricing performance of a closed‐form lower bound to American option values based on an exercise strategy corresponding to a flat‐exercise boundary. The lower bound has a simple two‐step implementation akin to Barone‐Adesi and Whaley (1987) formula and shows superior pricing performance in the out‐of‐the‐money region and for long maturities.     

含权债券定价的统一框架及其数值分析

本文从理论上推导了一般债券定价的偏微分方程,详细分析了包含欧式和美式看涨和看跌期权的4类债券,并给出了4类含权债券定价的边界条件。利用隐性差分法数值求解了偏微分方程,针对4类期权对不同利率参数的敏感性进行了分析。     

The Liquidity Premium in the Money Market: A Comparison of the German Mark Period and the Euro Area

Abstract. This paper investigates to what extent the expectations hypothesis of the term structure (EHTS) of interest rates receives some support since the launch of the European single currency. Empirical evidence shows that in general this theory applies to most European countries, and to Germany in particular. The objective of this paper thus is twofold. First, the EHTS for the German money market and for a larger sample including the German mark period and the euro money market is tested in order to check whether the results for the former are affected by the new financial environment since January 1999. Second, the implications of the results for the monetary policy assessment are discussed. We estimate cointegrating vector autoregressive models in order to quantify the level of the liquidity premium. The results suggest that financial markets do not consider the monetary policy of the European Central Bank simply as the one prevailing during the German period.     

Pricing to market in European automobile exports to OECD countries: a panel data approach

This paper investigates pricing to market behaviour using data for European auto exports. The empirical analysis uses forward instead of spot exchange rates. Cross-country and cross-product analyses reveal that pricing behaviour depends mainly on the class of product, while the country of origin and destination appears as less important. Furthermore, the data do not usually reject the hypothesis of a symmetric response of export prices to depreciations and appreciations of the exporter's currency. Finally, although the point estimates confirm the combined influence of the business cycle and the direction of the exchange rate movements on pricing to market in most cases, formal tests seldom provide statistical significance for this result.     

Time-varying global and local sources of market and currency risks in Russian stock market

In this paper we study international asset pricing models and the pricing of global and local market risks as well as currency risk in the Russian stock market from an international investors' point of view using weekly data from 1999 to 2009. In our empirical specification, we utilize the multivariate GARCH-M framework of De Santis and Gérard (1998). We find currency risk to be priced in the Russian market. The price of currency risk is found to be time-varying and affected for example by the price of oil. Moreover, our results suggest that the Russian market is partially segmented and the local market risk is priced in the market. Our model implies in-sample risk premium for the Russian equity market that is, on average, almost ten times higher than that of the US and that the Russian risk premium is on average caused mostly by the local and currency risk components.     

基于复合期权的创业板上市公司IPO定价研究

指出传统IPO定价方法用于具有高风险、高成长性等特征的高新技术企业IPO定价的缺陷,将实物期权概念引入IPO定价研究中。根据高新技术企业项目投资的特征,引入复合期权建立相应的数学模型,采用复合期权方法建立高新技术企业的IPO定价模型。最后,通过算例分析说明该模型在实践运用中具有一定的借鉴意义。     

Warrant pricing under GARCH diffusion model

The GARCH diffusion model has attracted a great deal of attention in recent years, as it is able to describe financial time series better, when comparing to many other models. This paper considers the problem of warrant pricing when the underlying asset follows the GARCH diffusion model. An analytical approximate solution for European option prices is derived by means of Fourier transform. The approximate solution can be quickly computed by the fast Fourier transform (FFT) algorithm. Monte Carlo simulations show that this approximate solution is correct and the FFT is accurate and efficient, and hence it enables us to investigate the volatility smile implied by the GARCH diffusion model. Then a method is developed to provide the maximum likelihood (ML) estimation of the GARCH diffusion model based on the efficient importance sampling (EIS) procedure. Furthermore, the empirical performance of the GARCH diffusion model applied to the valuation of Hang Seng Index (HSI) warrants traded on the Hong Kong Stock Exchange (HKEx) is investigated. Empirical results show that the GARCH diffusion model outperforms the Black–Scholes (B–S) model in terms of the pricing accuracy, indicating that the pricing model incorporated with stochastic volatility can improve the pricing of warrants.     

Pricing bond options under a Markovian regime-switching Hull–White model

In this paper, we investigate the valuation of bond options under a Markovian regime-switching Hull–White model, where both the mean-reverting level and the volatility of the interest rate are modulated by a continuous-time, finite-state Markov chain. Using techniques of measure changes and the inverse Fourier transform, we obtain an integral representation for the pricing formula of a standard European option on a zero-coupon bond. Numerical results for the prices and implied volatilities of bond options arising in our model are given in a two-regime case.     

Uncertainty in currency mispricing

Declaring a currency to be mispriced is fraught with uncertainties. In this article, these uncertainties are explicitly recognized in a model of pricing a homogeneous commodity around the world. This allows for a common driver of prices, due to a base-currency effect, and country-specific factors that lead to departures from absolute PPP on account of income differences, local taxes and charges, etc. This approach leads to estimates of currency mispricing whose significance can be tested in the usual way. Using Big Mac prices, we show that the approach has advantages over the popular Big Mac Index to currency valuation.     

碳排放权交易定价研究综述

《京都议定书》的问世使碳排放权在低碳经济时代成为一种稀缺商品,而该"商品"的定价问题就是碳排放权交易体系的核心关注点。文章对排放权定价的研究现状进行了系统综述,内容主要包括:碳排放权交易的基本定义、碳排放权定价理论以及国外和国内对碳排放权定价的研究现状。其中,国外对碳排放权定价的研究主要集中在碳排放权价格影响因素和定价模型两方面;国内的研究除影响因素和定价模型外,还对碳排放权的定价基础—碳货币和中国碳排放权的定价策略展开过讨论。文章拟通过较为系统的介绍,以期为未来碳交易定价的相关研究提供一定的参考。     

Currency substitution, portfolio diversification, and money demand

Abstract .  We extend the Thomas (1985) dynamic optimizing model of money demand and currency substitution to the case in which the individual has restricted or no access to foreign currency denominated bonds. In this case currency substitution decisions and asset substitution decisions are not separable. The results obtained suggest that the significance of an expected exchange rate depreciation term in the demand for domestic money provides a valid test for the presence of currency substitution. Applying this approach to six Latin-American countries, we find evidence of currency substitution in Colombia, Dominican Republic, and Venezuela, but not in Brazil and Chile.     

State-uncertainty preferences and the risk premium in the exchange rate market

This paper shows that state-uncertainty preferences help to explain the observed exchange rate risk premium. In the framework of Lucas (1982) economy, state-uncertainty preferences amount to assuming that a given level of consumption will yield a higher level of utility the lower is the level of uncertainty perceived by consumers. Under these preferences we can distinguish between two factors driving the exchange rate risk premium: “macroeconomic risk” and “the risk associated with variation in the private agents' perception on the level of uncertainty”. Empirical evidence from three main European economies in the transition period to the euro provides empirical support for the model. The model is more successful in accounting for the observed currency risk premium than models with more standard preferences, and the general perception of risk by private agents is shown to be a more important determinant of risk premium than macroeconomic uncertainty.     

Open-Economy Macroeconomics: Developments in Theory and Policy

This paper views developments in open-economy macroeconomics through the lens of the debate over European monetary unification. The empirical tendency for nominal exchange rate regimes to affect the variability of nominal and real exchange rates alike can be rationalized by sticky-price theories or models of asset-market liquidity effects. But plausible liquidity models have difficulty generating enough persistence to match the data. Thus, the macroeconomic stabilization costs of forgoing the exchange-rate realignment option seem pertinent. It is argued that our theories of efficiencies due to a common currency remain unsatisfactory, despite recent advances. The paper concludes by reviewing theories of currency crisis     

An analysis of East Asian currency area: Bayesian dynamic factor model approach

There has recently been an increasing interest in the establishment of a common currency area in East Asia in the aftermath of the East Asian financial crisis. In this article I examine the desirability and feasibility of forming a currency area in the region by checking the symmetry of shocks as an important criterion of the theory of Optimum Currency Area. I employ a dynamic factor model to decompose aggregate output into world, regional and country‐specific components and estimate the model using a Gibbs sampling simulation. Persistent properties of those components are examined and variance decomposition analysis is performed to investigate the role of each component in output variance. The European Monetary Union, with the successful launch of the euro, is the natural benchmark for comparison. Based on variance analysis, it is found that East Asian countries, on average, are less plausible candidates for a currency area than European counterparts. However, a subgroup of countries in East Asia is as qualified as those in Europe. Given the ongoing integration in East Asia, it is not premature to prepare for such a currency area in this region.