Large traders and illiquid options: Hedging vs. manipulation

In this article, we study the effects on derivative pricing arising from price impacts by large traders. When a large trader issues a derivative and (partially) hedges his risk by trading in the underlying, he influences both his hedge portfolio and the derivative's payoff. In a Black–Scholes model with a price impact on the drift, we analyze the resulting trade-off by explicitly solving the utility maximization problem of a large investor endowed with an illiquid contingent claim. We find several interesting phenomena which cannot occur in frictionless markets. First, the indifference price is a convex function of the contingent claim – and not concave as in frictionless markets – implying that for any claim the buyer's indifference price is larger than the seller's indifference price. Second, the seller's indifference prices of large positions in derivatives are smaller than the Black–Scholes replication costs. Therefore, a large trader might have an incentive to issue options if they are traded at Black–Scholes prices. Furthermore, he hedges option positions only partly if he has a negative price impact and thus exploits his ability to manipulate the option's payoff. For a positive price impact he overhedges the option position leading to an extra profit from the stock position exceeding a perfect hedge. Finally, we also study a model where the large shareholder has a price impact on both drift and volatility.     

江苏碳排放期权价格测算及清洁发展机制对策——基于B-S模型的定价分析

发展低碳经济,提升碳交易与清洁发展能力已是大势所趋。文章通过对CDM项目进展、经济基础与资源禀赋等方面对江苏省内企业发展碳交易市场进行潜力分析后发现,该地区存在巨大的节能减排空间。实证研究中将实物期权理论引入碳交易机制,借助B-S模型及欧盟碳交易市场相关数据构造出碳排放期权定价模型,根据欧盟与江苏经济发展的相似性折扣给出江苏地区碳交易的市场定价,同时,围绕技术、管理及政策三个层面提出该地区CDM机制的新型思路建议,旨在为江苏企业在清洁发展机制下逐步开发完善碳交易市场提供有利依据与参考。     

不同约束条件下的股指期货价格区间研究

在股指期货持有成本定价模型的基础上,结合中国沪深300股指期货合约的特点,根据无套利原理,给出了考虑交易成本、期货保证金和不同借贷利率等限制条件下的股指期货定价区间和相应的交易策略,为从事沪深300股指期货套期保值、套利和投机交易的相关人员提供借鉴意义。     

Link-save trading

Transaction costs involved while trading several assets may be described using bid-ask spread of the asset prices. We assume that the prices of several assets may be linked, so that transactions involving several assets have prices that are not necessarily equal to the sums of (bid or ask) prices of the individual assets. The family of possible price combinations forms a convex (random) set which changes in time and is called the set-valued price process. It is shown that the necessary and sufficient condition for no-arbitrage is the existence of a martingale selection, i.e. a martingale that takes values in the set-valued price process. Examples and applications to option pricing are discussed.     

Profit opportunities with the American put-call parity when dividends are not expected

The objective of this research is to study borrowing and lending profit opportunities with the put-call parity of American options when dividends on the stock are not expected. Studying profit opportunities embedded in the put-call parity is intriguing because of their relative simplicity. The only assumptions necessary for the parity to hold are that option markets are frictionless and generate efficient prices of puts and calls around the underlying stock price. For this reason alone (parsimony of postulates) the put-call parity is a tempting vehicle for studying option market efficiency. In this work it is shown that both synthetic lending and borrowing parities (before and after transaction costs), on average and ex post, have negative expected profits (i.e. put-call parity implied rates are inferior to the observed riskless rate). When certain trading rules are established, however, empirical evidence of substantial profit opportunities with both lending and borrowing with the American parity (even after considering transaction costs) is observed. It is also shown that these opportunities are greater for some stocks than for others. The existence of these disparities might be an indication that the pricing mechanism of the respective options is not always in sync. The duration of disequilibrium between the options market and the stock market suggests that such occurrences are not just random bursts.     

集体建设用地定级与估价在培育地票交易市场中的作用探讨

本文对重庆市地票价格的定价进行了探讨,分析了现有定价方式无法为市场双方提供合理价值基础,对地票交易市场的培育和完善不能起到很好的促进作用,在此基础上作者提出了以现有的价格为基础,开展重庆市集体建设用地定级与基准地价研究工作,出台集体建设用地评估的技术规范,培育中介机构专门从事评估等建议,以期对保障农民权益,培育和完善城乡统一的建设用地市场的发展提供有益借鉴。     

沪深300股指期货在现货交易和非交易时段交易特征的比较研究

我国沪深300股指期货交易2010年4月16日正式推出,但沪深300股指期货市场与沪深300现货市场的交易时间存在显著的差异,即相对于股票现货市场,沪深300股指期货市场提前15分钟开盘,延迟15分钟收盘。运用日内分笔数据和分钟数据,对沪深300股指期货不同交易时段的交易特征进行比较。研究表明,不同交易时段知情交易者市场参与度存在明显差异,提前交易时段知情交易的概率最高,现货交易时段次之,延迟交易时段最低;沪深300股指期货在开盘时段的交易提供了较大的价格发现,特别是开盘的第一笔交易包含有大量的私有信息,价格贡献最大;提前交易时段私有信息的价格发现贡献度最高;尽管提前交易时段的交易提供了较大的价格发现,但定价效率较低。     

Production theory,uncertain prices and investment portfolios

This paper examines the allocative decisions of a competitive firm where input and output prices are uncertain and where the capital asset pricing model prevails. The firm behaves much as a profit maximizer under certainty, except that certainty equivalent prices formally replace the known prices. These certainty equivalent prices are composed of the expected price, the covariance of the price with the market (a measure of systematic risk) and a measure of risk aversion in the economy. Both static and comparative static propositions emerge in a natural way as extensions of standard, competitive and profit maximizing behavior. In addition, the model contains both the certainty case and the risk-neutral case as limiting examples.     

European quanto option pricing in presence of liquidity risk

In this paper, we study the pricing problems of the European quanto options in which the underlying foreign asset is in imperfectly liquid markets. First, we assume that the dynamics of the underlying foreign asset price are affected by market liquidity and propose a liquidity-adjusted quanto model. This allows for the effects of market liquidity on European quanto option pricing. And then we derive the analytical pricing formulas for four different types of European quanto options. Finally, we empirically investigate the pricing performance of our proposed model with a European quanto construction involving the SSE 50 ETF, as the underlying asset, and the CNY/HKD exchange rate. Empirical results demonstrate that the pricing accuracy of the proposed model is markedly superior to that of the Black-Scholes quanto model. In other words, allowing for liquidity risk in the framework of European quanto option pricing can make markedly improvements in fitting the real market data. Particularly, the improvement rate is high for medium-term and out-of-the-money options. Moreover, these results are robust for different liquidity measures.     

Option pricing with stochastic volatility models

A general class of models for derivative pricing with stochastic volatility is analyzed. We include the possibility of jumps for the paths of the asset's price and for those of its volatility. We also consider the case of correlation between the process of the asset's price and that of its volatility. In this way we are able to give a unifying view on most of the models studied in the literature. We will examine theoretical issues related to the market price of volatility risk, the equivalent martingale measures and the possibility of obtaining a numerically tractable formula for contingent claim pricing. Finally, we propose some methodologies to test the behavior of stochastic volatility models when applied to market data.     

Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps

This paper presents an equilibrium formulation of asset pricing in an environment of mixed Poisson–Brownian information with recursive utility. The optimal portfolio choice problem is studied together with a derivation of Euler equation as necessary condition for optimality. It is further shown that the price processes governed by the Euler equation, together with the market clearing conditions, constitute the equilibrium price processes. Closed form formulas are derived for European call options and for other derivative securities in a particular parameterization of the economy. The derived option pricing formula contain many existing models as special cases, and is potentially useful in explaining the moneyness biasedness associated with Black–Scholes model.     

The valuation of American barrier options using the decomposition technique

In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call ‘symmetry’ relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.     

Experimental evidence on trading behavior,market efficiency and price formation in double auctions with unknown trading duration

The reasons for the highly efficient market outcomes observed under the double auction remain unclear. This paper presents a series of experimental financial markets designed to investigate the importance of unknown trading period duration on trading behavior and the convergence tendencies of such markets. Using panel data techniques the results support the conclusions that individuals generally display more aggressive trading strategies, trading earlier in a period, and that markets exhibit reduced levels of informational efficiency when unknown duration is present. Markets with imperfect information structures are also studied and, in a unique result, are associated with significantly slower rates of trade, as traders become more cautious over their trading strategies. Investigation of the price formation process provides evidence that the pricing error varies over time and the estimation of a fixed effects model provides unique support that learning effects and unknown trading period duration influence the price formation process. Future refinement of theoretical models of the price formation process or institutions of exchange should recognize the effect of unknown trading period duration on market behavior, along with potential learning effects. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of American option prices in a path integral framework using Fourier–Hermite series expansions

In this paper we review the path integral technique which has wide applications in statistical physics and relate it to the backward recursion technique which is widely used for the evaluation of derivative securities. We formulate the pricing of equity options, both European and American, using the path integral framework. Discretising in the time variable and using expansions in Fourier–Hermite series for the continuous representation of the underlying asset price, we show how these options can be evaluated in the path integral framework. For American options, the solution technique facilitates the accurate determination of the early exercise boundary as part of the solution. Additionally, the continuous representation of the state variable allows the relatively accurate and efficient evaluation of the option prices and the delta hedge ratio.     

Arbitrage concepts under trading restrictions in discrete-time financial markets

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.     

Dynamics of state price densities

State price densities (SPDs) are an important element in applied quantitative finance. In a Black–Scholes world they are lognormal distributions, but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy no-arbitrage constraints and corrects for the intraday covariance structure in option prices. In contrast to existing methods, we do not use any parametric or smoothness assumptions.     

On pricing and hedging options in regime-switching models with feedback effect

We study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback effect depending on the economic condition. We adopt a pricing kernel which prices both financial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.     

Leverage and the price volatility of equity shares in equilibrium

The traditional valuation formulas for corporate debt, which are derived in a complete market setting and are based on the no-arbitrage principle, imply that equity prices become more volatile as leverage increases. If the asset structure is incomplete, the presence of corporate debt affects the linear subspace spanned by the payoffs of the existing assets, and the pricing of corporate debt and shares of levered firms becomes a simultaneous valuation problem. This paper characterizes the relationship between the price of corporate debt and the share price of a levered firm in an equilibrium framework where corporate debt is a non-redundant asset. While, in the absence of bankruptcy, higher leverage always implies riskier equity, it does not necessarily mean more volatile equity prices. In fact, the link between leverage and equity price volatility depends in a particular way on investors’ preferences towards risk.     

The impact of individual and institutional investor sentiment on the market price of risk

We examine the effect of individual and institutional investor sentiment on the market price of risk derived from DJIA and S&P500 index returns. Consistent with behavioral asset pricing models, we find significant positive response of rational sentiment suggesting greater incentive for rational investors to engage in arbitrage when the compensation for taking risk is greater. Further, an increase in irrational optimism leads to a significant downward movement, but an increase in rational sentiment does not lead to a significant change market price of risk. These results are robust for both market indexes, DJIA and S&P500 and for both individual and institutional investor sentiment.     

The role of an illiquidity risk factor in asset pricing: Empirical evidence from the Spanish stock market

The main purpose of this study is to construct an illiquidity risk factor for the Spanish stock market over the 1994–2002 period. Because of the absence of consensus in empirical research about the most appropriate liquidity measure, we applied the Amihud [Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets 5, 31–56] illiquidity ratio that shows the price response associated with one euro of trading volume. Moreover, we generated an illiquidity factor using the Fama and French [Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56] orthogonal approach and analyzed whether it enters the stochastic discount factor as an additional state variable. We conclude that systematic illiquidity should be a key ingredient of asset pricing.