关于Shibor利率期权波动率定价机制的研究

Shibor自2007年发布以来,已成为人民币利率市场的一个重要定价基准,对金融衍生品、债券的定价起着十分重要的作用,由于人民币利率衍生品市场尚处于发展的初期,与美元Libor利率期权等较为成熟市场相比,目前Shibor利率期权缺少成熟的市场报价。本文通过风险中性的定价方程反解参数的方法,利用Shibor利率掉期曲线对Shibor利率上下限期权的隐含波动率进行计算,从而探讨对Shibor利率期权的定价。     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

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.     

Realizing smiles: Options pricing with realized volatility

We develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.     

A reduced PDE method for European option pricing under multi-scale,multi-factor stochastic volatility

The number of tailor-made hybrid structured products has risen more prominently to fit each investor’s preferences and requirements as they become more diversified. The structured products entail synthetic derivatives such as combinations of bonds and/or stocks conditional on how they are backed up by underlying securities, stochastic volatility, stochastic interest rates or exchanges rates. The complexity of these multi-asset structures yields lots of difficulties of pricing the products. Because of the complexity, Monte-Carlo simulation is a possible choice to price them but it may not produce stable Greeks leading to a trouble in hedging against risks. In this light, it is desirable to use partial differential equations with relevant analytic and numerical techniques. Even if the partial differential equation method would generate stable security prices and Greeks for single asset options, however, it may result in the curse of dimensionality when pricing multi-asset derivatives. In this study, we make the best use of multi-scale nature of stochastic volatility to lift the curse of dimensionality for up to three asset cases. Also, we present a transformation formula by which the pricing group parameters required for the multi-asset options in illiquid market can be calculated from the underlying market parameters.     

Multivariate option pricing with time varying volatility and correlations

In this paper we consider option pricing using multivariate models for asset returns. Specifically, we demonstrate the existence of an equivalent martingale measure, we characterize the risk neutral dynamics, and we provide a feasible way for pricing options in this framework. Our application confirms the importance of allowing for dynamic correlation, and it shows that accommodating correlation risk and modeling non-Gaussian features with multivariate mixtures of normals substantially changes the estimated option prices.     

Asset pricing under information with stochastic volatility

Based on a general specification of the asset specific pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong downward movements. The resulting option pricing formula is consistent with the strong negative skewness and high levels of kurtosis observed in empirical studies. Furthermore, we determine credit spreads in a simple structural model.      

Paramater estimation bias and volatility scaling in Black-Scholes option prices

When asset returns conform to a Gaussian distribution, the moments of the distribution over long return intervals may be estimated by scaling the moments of shorter return intervals. While it is well known that asset returns are not normally distributed, a key empirical question concerns the effect that scaling the volatility of dependent processes will have on the pricing of related financial assets. This study investigates the return properties of the most important currencies traded in spot markets against the U.S. dollar: the Japanese yen, the British pound, and the Swiss franc during the period November 1983 to April 2004. The novelty of this paper is that the volatility properties of the series are tested utilising statistical procedures developed from fractal geometry, with the economic impact determined within an option-pricing framework.     

Index-option pricing with stochastic volatility and the value of accurate variance forecasts

In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, pricing of options provides the appropriate test of forecasts of asset volatility. NYSE index returns over the period of 1968–1991 suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in the Black and Scholes formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed. (JEL C22, C53, C10, G11, G12)     

Choice of exchange rate system and macroeconomic volatility of three Asian emerging economies

This study highlights the importance of choice of exchange rate system to macroeconomic stability of small-open emerging economies based on the outcomes of the recent exchange rate regime switches of three Asian countries – Indonesia, Malaysia, and Thailand. These countries have high similarities in their economic structures, but have reacted very differently in mitigating the economic distortion of the 1997 financial crisis, in particular in the adoption of exchange rate system. The empirical results of this study show that the amplified instability of macro-variables in Thailand and Indonesia, which was due to the crisis, were not stabilized by switching the exchange rate system to a flexible regime. The volatilities, however, were effectively stabilized after the countries made the second switch – from the independent float to the managed float with no pre-announcement. For Malaysia, a switch from the managed float to the pegged system successfully reduced the volatilities. The exchange rate misalignments of the countries, except Indonesia, were also reduced when the countries switched from a flexible to a more fixed managed float system. These empirical findings thus strongly support central banks of small-open emerging economies to adopt a more fixed, rather than a more flexible system. However, the managed float system needs to couple with efficient management to ensure a smooth and stable regime.     

Exchange option pricing under stochastic volatility: a correlation expansion

Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269–303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito’s diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper.     

Cross section of option returns and idiosyncratic stock volatility

This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.     

Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach

Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate.     

The relationship between implied and realized volatility: evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Analytical pricing of single barrier options under local volatility models

This paper considers a single barrier option under a local volatility model and shows that any down-and-in option can be priced by a combination of three standard European options whose volatility functions are connected through symmetrization. The symmetrized volatility function is approximated by a sequence of smooth functions that converges to the original one. An approximation formula is developed to price the standard European options with the approximated volatility functions. Finally, we apply the Aitken convergence accelerator to obtain an approximate price of the down-and-in option. Other single barrier options are priced in a similar fashion.     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

The anticipated and concurring effects of the EMU: exchange rate volatility, institutions and growth

Reduced exchange rate volatility and higher and less heterogeneous quality of institutional rules and macroeconomic policies are two of the main (anticipated and concurring) effects expected from a currency union.In this paper, we measure the magnitude of these two effects for the Eurozone countries looking at real effective exchange rates (REER) and at different indicators of quality of institutional rules and macroeconomic policies (QIRMP). We find that the first effect is much stronger than the second when we compare relative changes for Eurozone countries and the rest of the world in the relevant period.We further evaluate the impact of both effects on economic growth on a larger sample of countries. Our findings show that both have significant impact on levels (more robust) and on rates of growth (weaker) of per capita GDP.     

American stochastic volatility call option pricing: A lattice based approach

This study presents a new method of pricing options on assets with stochastic volatility that is lattice based, and can easily accommodate early exercise for American options. Unlike traditional lattice methods, recombination is not a problem in the new model, and it is easily adapted to alternative volatility processes. Approximations are developed for European C.E.V. calls and American stochastic volatility calls. The application of the pricing model to exchange traded calls is also illustrated using a sample of market prices. Modifying the model to price American puts is straightforward, and the approach can easily be extended to other non-recombining lattices.