THE NORMALIZING TRANSFORMATION OF THE IMPLIED VOLATILITY SMILE

We study specific nonlinear transformations of the Black–Scholes implied volatility to show remarkable properties of the volatility surface. No arbitrage bounds on the implied volatility skew are given. Pricing formulas for European payoffs are given in terms of the implied volatility smile.     

STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q-OPTIMAL MEASURE

The aim of this paper is to study the minimal entropy and variance-optimal martingale measures for stochastic volatility models. In particular, for a diffusion model where the asset price and volatility are correlated, we show that the problem of determining the q -optimal measure can be reduced to finding a solution to a representation equation. The minimal entropy measure and variance-optimal measure are seen as the special cases   q = 1  and   q = 2  respectively. In the case where the volatility is an autonomous diffusion we give a stochastic representation for the solution of this equation. If the correlation ρ between the traded asset and the autonomous volatility satisfies  ρ² < 1/ q   , and if certain smoothness and boundedness conditions on the parameters are satisfied, then the q -optimal measure exists. If  ρ²≥ 1/ q   , then the q -optimal measure may cease to exist beyond a certain time horizon. As an example we calculate the q -optimal measure explicitly for the Heston model.     

我国期货市场的波动性与有效性--基于三大交易市场的实证分析

通过对中国三大期货市场的铜、黄豆和小麦三种主要期货品种收益率的分布与波动性的实证分析 ,论证了其时间序列存在ARCH效应 ;运用GARCH模型对这三种期货品种进行了拟合分析和统计检验 ,检验结果表明这三个期货品种的波动性均具有很高的持续性 ,但大连黄豆的波动持续性弱于上海铜和郑州小麦 ,其波动性受各种外部冲击的影响较大 ;通过GARCH( 1 ,1 )的市场有效性检验 ,论证了中国期货市场尚未达到弱式有效 ,市场风险较大。     

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF‐NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non‐Gaussian stochastic volatility model of Barndorff‐Nielsen and Shephard for the exponential mean‐reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log‐spot prices possess a stationary distribution defined as a normal variance‐mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean‐reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff‐Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.     

基于因子分析的套利定价模型及实证研究

众所周知,建立套利定价模型的关键在于因素的筛选,计算量很大。而因子分析能将为数众多的原始指标变量经过分析综合为少数几个公共因子变量,从而大大减少计算的复杂度。本文利用因子分析的方法对11个因素进行筛选,确定四个能够很好地反映所有因素包含的信息但又互不相关的公共因子变量,并建立套利定价模型,实证检验说明,通过该方法进行因素筛选建立的套利定价模型具有较好的定价效果。     

NO MARGINAL ARBITRAGE OF THE SECOND KIND FOR HIGH PRODUCTION REGIMES IN DISCRETE TIME PRODUCTION–INVESTMENT MODELS WITH PROPORTIONAL TRANSACTION COSTS

We consider a class of production–investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no‐arbitrage of the second kind condition introduced by Rásonyi. We show that this condition implies the closedness of the set of attainable claims and is equivalent to the existence of a strictly consistent price system under which the evaluation of future production profits is strictly negative. This allows us to discuss the closedness of the set of terminal wealth in models with nonlinear production, functions which may admit arbitrages of the second kind for low production regimes but not marginally for high production regimes.     

THE MEANING OF MARKET EFFICIENCY

Fama defined an efficient market as one in which prices always “fully reflect” available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, we overcome a well‐known limitation in tests for market efficiency, i.e., the need to assume a particular equilibrium asset pricing model, called the joint‐hypothesis or bad‐model problem. Indeed, we show that an efficient market is completely characterized by the absence of both arbitrage opportunities and dominated securities, an insight that provides tests for efficiency that are devoid of the bad‐model problem. Other theorems useful for both the testing of market efficiency and the pricing of derivatives are also provided.     

TERM STRUCTURES OF IMPLIED VOLATILITIES: ABSENCE OF ARBITRAGE AND EXISTENCE RESULTS

This paper studies modeling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account, and a family of European options for all maturities with a fixed payoff function h . We first characterize absence of arbitrage in terms of drift conditions for the forward implied volatilities corresponding to a general convex h . For the resulting infinite system of SDEs for the stock and all the forward implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We do this for two examples of h , namely, calls with a fixed strike and a fixed power of the terminal stock price, and we give explicit examples of volatility coefficients satisfying the required assumptions.     

A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory.