Pricing Discrete Barrier Options Under Stochastic Volatility

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To the best of our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and λ-SABR models.     

Persistence and Kurtosis in GARCH and Stochastic Volatility Models

This article shows that the relationship between kurtosis, persistenceof shocks to volatility, and first-order autocorrelation ofsquares is different in GARCH and ARSV models. This differencecan explain why, when these models are fitted to the same series,the persistence estimated is usually higher in GARCH than inARSV models, and, why gaussian ARSV models seem to be adequate,whereas GARCH models often require leptokurtic conditional distributions.We also show that introducing the asymmetric response of volatilityto positive and negative returns does not change the conclusions.These results are illustrated with the analysis of daily financialreturns.     

Pricing Options under Stochastic Interest Rates: A New Approach

We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton type) interest rate processes. We will show that an explicit solution, which is an extended Black-Scholes formula under stochastic interest rates in certain asymptotic sense, can be obtained by extending the asymptotic expansion approach when the interest rate volatility is small. This method, called the small-disturbance asymptotics for Itô processes, has recently been developed by Kunitomo and Takahashi (1995, 1998) and Takahashi (1997). We found that the extended Black-Scholes formula is decomposed into the original Black-Scholes formula under the deterministic interest rates and the adjustment term driven by the volatility of interest rates. We will illustrate the numerical accuracy of our new formula by using the Cox–Ingersoll–Ross model for the interest rates.     

Pricing Perpetual Options for Jump Processes

Abstract

We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition. In the second model in which the jumps are downwards, we show that the value of the strategy corresponding to a constant option-exercise boundary satisfies a certain renewal equation. Then the optimal exercise strategy is obtained from the continuous junction condition. Furthermore, the same model can be used to price certain reset options. Finally, we show how the classical model of geometric Brownian motion can be obtained as a limit and also how it can be integrated in the two models.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.     

An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.     

The Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.     

Option Prices, Implied Price Processes, and Stochastic Volatility

This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994), Dupire (1994, 1997), and Rubinstein (1994), who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adjusted to fit current option prices exactly, just as interest rate processes can be adjusted to fit bond prices exactly. The procedure works with many volatility models, is fast to calibrate, and can price exotic options efficiently using familiar lattice techniques.     

基于随机波动率假设的权证定价理论评述

随机波动率(SV)模型在衍生品定价和风险管理中的应用开始发挥越来越重要的作用,但是,由于很难得到似然函数的闭型表达式,SV模型的参数估计问题严重限制了它在金融实践领域的普及应用.不过,近年来,学者们提出了许多旨在解决SV模型参数估计问题的有效且可行的新方法,大大推进了SV模型的应用化进程.本文将在权证定价分析的框架内,重点评述SV模型的参数估计方法,并从理论和实证的角度对它们的优点和不足进行简要评介和比较.     

基于随机波动率假设的权证定价理论评述

随机波动率(SV)模型在衍生品定价和风险管理中的应用开始发挥越来越重要的作用,但是,由于很难得到似然函数的闭型表达式,SV模型的参数估计问题严重限制了它在金融实践领域的普及应用。不过,近年来,学者们提出了许多旨在解决SV模型参数估计问题的有效且可行的新方法,大大推进了SV模型的应用化进程。本文将在权证定价分析的框架内,重点评述SV模型的参数估计方法,并从理论和实证的角度对它们的优点和不足进行简要评介和比较。     

Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (PartialIntegro-Differential Equation) and demonstrates how this equationcan be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples fromthe S&P500 market. This revised version was published online in November 2006 with corrections to the Cover Date.     

A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options

We set up a new kind of model to price the multi-asset options. A square root process fluctuating around its mean value is introduced to describe the random evolution of correlation between two assets. In this stochastic correlation model with mean reversion term, the correlation is a random walk within the region from −1 to 1, and it is centered around its equilibrium value. The trading strategy to hedge the correlation risk is discussed. Since a solution of high-dimensional partial differential equation may be impossible, the Quasi-Monte Carlo and Monte Carlo methods are introduced to compute the multi-asset option price as well. Taking a better-of two asset rainbow as an example, we compare our results with the price obtained by the Black–Scholes model with constant correlation.     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

广义欧式加权算术平均价格一揽子期权定价

本文在一揽子期权（Basket Options）定价理论的基础上，对期权的标的价格引入跳跃一扩散过程进行建模，用几何布朗运动描述其动态变化过程，用Possion过程刻画资产价格受新的信息和稀有偶发时间的冲击所发生跳跃的计数过程，用对数正态随机变量描述跳跃对应的跳跃幅度，有模型限定下，运用Ito-Skorohod微分公式和等价鞅测度变换，得出加权算术平均价格一揽子期权的一个推广的解析定价公式。     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

The Valuation of Volatility Options

This paper examines the valuation of European- and American-style volatilityoptions based on a general equilibrium stochastic volatility framework.Properties of the optimal exercise region and of the option price areprovided when volatility follows a general diffusion process. Explicitvaluation formulas are derived in four particular cases. Emphasis is placedon the MRLP (mean-reverting in the log) volatility model which has receivedconsiderable empirical support. In this context we examine the propertiesand hedging behavior of volatility options. Unlike American options,European call options on volatility are found to display concavity at highlevels of volatility.     

优礼与管控之间：清代错案责任“双轨制”之形成及其原因探析

清代错案责任追究制度呈现出以《吏部处分则例》为主、以《大清律例》为辅的"双轨制"法律体系。从对官员管控和优礼的政策视角出发,可以发现,中国古代错案责任制度的发展脉络,呈现出从单一适用律文到以律为主、以单行条文为修正的律例并用状态,再到清代"双轨制"模式的发展过程。结合对当时官僚政治态势的观察,可发现清代错案责任"双轨制"是管控与优礼政策相互作用发展到新阶段的产物。     

中国在全球工业机器人贸易网络中的拓扑特征与地位变迁

《国务院办公厅关于完善反洗钱、反恐怖融资、反逃税监管体制机制的意见》（国办函［2017］84号）中提出修改惩治洗钱犯罪相关规定,将上游犯罪本犯纳入洗钱罪主体范围,但是否要对自洗钱进行立法一直是我国法律学术界的一个争议焦点。本文在整体视角下提出自洗钱行为的认识框架,对自洗钱行为的危害进行分析,构造了自洗钱和协助洗钱刑事立法的统一理论基础。本文基于这一理论基础,对我国现行洗钱罪相关规定进行全面审视和系统分析,提出自洗钱立法建议。