Option Pricing and Replication with Transactions Costs

Transactions costs invalidate the Black-Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black-Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.     

Efficient Option Replication in the Presence of Transactions Costs

In the presence of transaction costs, a risk-return trade-off exists between the quality and the cost of a replicating strategy. In that context, I show how to expand the set of all possible time-based strategies through the introduction of a multi-scale class of strategies, which consist in rebalancing different fractions of an option portfolio at different time frequencies. The method, based on time-scale diversification, is to dynamic replication what investment in diversified portfoliosis to static portfolio selection: in a dynamic context, one may enjoy the benefits of diversification by using different time scales in trading the same asset. This revised version was published online in November 2006 with corrections to the Cover Date.     

Option Pricing Bounds in Discrete Time

Upper and lower bounds are derived for call options traded at discrete intervals. These bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being “non-negative beta.” The development of the bounds relies on the single-price law and arbitrage arguments. Both single-period and multiperiod results are produced, and put option bounds follow by extension. The bounds exist as equilibrium values given a consensus on stock price distribution; they are also valid for empirical studies, being adjustable for dividends and commissions.     

Jump Diffusion Option Valuation in Discrete Time

We develop a simple, discrete time model to value options when the underlying process follows a jump diffusion process. Multivariate jumps are superimposed on the binomial model of Cox, Ross, and Rubinstein (1979) to obtain a model with a limiting jump diffusion process. This model incorporates the early exercise feature of American options as well as arbitrary jump distributions. It yields an efficient computational procedure that can be implemented in practice. As an application of the model, we illustrate some characteristics of the early exercise boundary of American options with certain types of jump distributions.     

Analysis of the Nonlinear Option Pricing Model Under Variable Transaction Costs

In this paper we analyze a nonlinear Black–Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price V is assumed to be a function of the underlying asset price and the Gamma of the option. We show that the generalizations of the classical Black–Scholes model can be analyzed by means of transformation of the fully nonlinear parabolic equation into a quasilinear parabolic equation for the second derivative of the option price. We show existence of a classical smooth solution and prove useful bounds on the option prices. Furthermore, we construct an effective numerical scheme for approximation of the solution. The solutions are obtained by means of the efficient numerical discretization scheme of the Gamma equation. Several computational examples are presented.     

Model Comparison with Transaction Costs

Failing to account for transaction costs materially impacts inferences drawn when evaluating asset pricing models, biasing tests in favor of those employing high-cost factors. Ignoring transaction costs, Hou, Xue, and Zhang (2015, Review of Financial Studies, 28, 650–705) q-factor model and Barillas and Shanken (2018, The Journal of Finance, 73, 715–754) six-factor models have high maximum squared Sharpe ratios and small alphas across 205 anomalies. They do not, however, come close to spanning the achievable mean-variance efficient frontier. Accounting for transaction costs, the Fama and French (2015, Journal of Financial Economics, 116, 1–22; 2018, Journal of Financial Economics, 128, 234–252) five-factor model has a significantly higher squared Sharpe ratio than either of these alternative models, while variations employing cash profitability perform better still.     

Optimal Portfolio Selection with Transaction Costs

Abstract

This paper examines the lifetime portfolio-selection problem in the presence of transaction costs. Using a discrete time approach, we develop analytical expressions for the investor's indirect utility function and also for the boundaries of the no-transactions region. The economy consists of a single risky asset and a riskless asset. Transactions in the risky asset incur proportional transaction costs. The investor has a power utility function and is assumed to maximize expected utility of end-of-period wealth. We illustrate the solution procedure in the case in which the returns on the risky asset follow a multiplicative binomial process. Our paper both complements and extends the recent work by Gennotte and Jung (1994), which used numerical approximations to tackle this problem.     

Dynamic Trading with Predictable Returns and Transaction Costs

We derive a closed‐form optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean‐reversion speeds. The optimal strategy is characterized by two principles: (1) aim in front of the target, and (2) trade partially toward the current aim. Specifically, the optimal updated portfolio is a linear combination of the existing portfolio and an “aim portfolio,” which is a weighted average of the current Markowitz portfolio (the moving target) and the expected Markowitz portfolios on all future dates (where the target is moving). Intuitively, predictors with slower mean‐reversion (alpha decay) get more weight in the aim portfolio. We implement the optimal strategy for commodity futures and find superior net returns relative to more naive benchmarks.     

The Politics of Transaction Costs

This article aims to develop a model for analysing the operation and outcomes of the contracting process as it applies to public services, and to explore the politics of transaction costs involved in this process using a case study of Compulsory Competitive Tendering (CCT) in the UK. For this purpose the article deals with the policy outputs from two time periods, 1991 and 1994, which are regarded as the most dynamic years in terms of CCT policy implementation. The article also demonstrates how transaction costs may be manipulated in the contracting process by the interested parties. Finally, it suggests that the politics of transaction costs should be studied systematically in the future.     

Liquidity Premia and Transaction Costs

Standard literature concludes that transaction costs only have a second‐order effect on liquidity premia. We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime‐switching model in which the investment opportunity set varies over time, we explicitly characterize the optimal consumption and investment strategy. In contrast to the standard literature, we find that transaction costs can have a first‐order effect on liquidity premia. However, with reasonably calibrated parameters, the presence of transaction costs still cannot fully explain the equity premium puzzle.     

Optimal Portfolio Selection with Transaction Costs and Finite Horizons

We examine the optimal trading strategy for a CRRA investorwho maximizes the expected utility of wealth on a finite dateand faces transaction costs. Closed-form solutions are obtainedwhen this date is uncertain. We then show a sequence of analyticalsolutions converge to the solution to the problem with a deterministicfinite horizon. Consistent with the common life-cycle investmentadvice, the optimal trading strategy is found to be horizondependent and largely buy and hold. Moreover, it might be optimalfor the investor in our model not to buy any stock, even whenthe risk premium is positive. Further analysis of the optimalpolicy is also provided.     

Option Valuation with Information Costs: Theory and Tests

In this paper, the valuation of stock and index options is analyzed in the context of Merton's model of capital market equilibrium with incomplete information. It is possible to derive a partial differential equation for options in such a context. The derivation gives more understanding of the way an option's future payoff is discounted to the present. In order to estimate some of its parameters, the model is calibrated to market prices. It is tested using market prices and the authors' valuation formula. It is found that model prices are not significantly different from market prices, especially when out-of-the-money and deep-in-the-money options are considered. The model gives an explanation to the “strike bias” and the “smile effect.” Simulations of models based respectively on stochastic volatilities and gamma processes, are in accordance with the findings in this paper concerning biases in the Black and Scholes model, especially for pricing deep-in-the-money and out-of-the-money options. Even if the estimation method has its drawbacks, the costs of gathering and processing information regarding the option and its underlying asset play a central role in explaining the biases observed in the Black and Scholes model and help also the understanding of the U-shaped curve known as the smile of volatilities.     

交易成本理论的现实意义

科斯的交易成本理论包括交易成本和科斯定理.交易成本的本质是与交易有关的制度的运行成本,科斯定理最根本的是明确产权对减少交易成本的决定性作用.体制的创新、企业的改革、外部效应所产生的污染问题及政府的职能转变等充分诠释了交易成本理论的现实意义.     

The Effects of Transaction Costs and Different Borrowing and Lending Rates on the Option Pricing Model: A Note

This paper modifies the Black-Scholes option pricing model to include the effects of transaction costs and different borrowing and lending rates. The paper demonstrates that these market imperfections tend to offset each other yielding a bounded range of prices for each option. The paper also shows that under some conditions the option pricing hedge may be society's lowest cost financial intermediary.     

Trading Volume and Transaction Costs in Specialist Markets

Prior work with competitive rational expectations equilibrium models indicates that there should be a positive relation between trading volume and differences in beliefs or information among traders. We show that this result is sensitive to whether and how transaction costs are modeled. In a specialist market with endogenous transaction costs we show that trading volume can be negatively related to the degree of informational asymmetry in the market. Our analysis highlights the dependence of volume on market structure, and our results suggest that the “volume effects” of corporate or macroeconomic events reflect a decrease, rather than an increase, in heterogeneity of beliefs or asymmetry of information.     

Corporate Bond Market Transaction Costs and Transparency

Using a complete record of U.S. over‐the‐counter (OTC) secondary trades in corporate bonds, we estimate average transaction costs as a function of trade size for each bond that traded more than nine times between January 2003 and January 2005. We find that transaction costs decrease significantly with trade size. Highly rated bonds, recently issued bonds, and bonds close to maturity have lower transaction costs than do other bonds. Costs are lower for bonds with transparent trade prices, and they drop when the TRACE system starts to publicly disseminate their prices. The results suggest that public traders benefit significantly from price transparency.     

经济政策的制定及其交易成本

正经济政策制定的目的在于纠正市场失灵,但是任何政府干预的行为,都需付出交易成本的代价。在经济政策制定的过程中,交易成本常常表现为决策成本、规模成本、摩擦成本等,降低交易成本有赖于政府角色的匡正和制度对政府行为的限定与规范。在现代社会中,政治制度就像市场制度,政治家就像企业家,公民(选民)就像消费者,选举制度就像交易制度,选票就像货币。在政治市场里,人们建立起契约交换关系,一切活动都     

Transaction Costs and the Pricing of Assets

The existence of transaction costs explains why investors do not fully diversify their portfolios. This paper examines the implications of such limited diversification on equilibrium asset prices in the framework of the capital asset pricing model. In the pricing equation obtained here an asset's risk premium depends on a weighted average of its covariance with the market and its own variance.