Hedging errors with Leland's option model in the presence of transaction costs

Nonzero transaction costs invalidate the Black–Scholes [1973. Journal of Political Economy 81, 637–654] arbitrage argument based on continuous trading. Leland [1985. Journal of Finance 40, 1283–1301] developed a hedging strategy which modifies the Black–Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Kabanov and Safarian [1997. Finance and Stochastics 1, 239–250] calculated the limiting hedging error of the Leland strategy and pointed out that it is nonzero for the approximate pricing of an European call option, in contradiction to Leland's claim. As a further contribution, we first identify the mathematical flaw in the argument of Leland's claim and then quantify the expected percentage of hedging losses in terms of the hedging frequency and the level of the option strike price.     

Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs

One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other well-known strategies and find that our strategy outperforms all the others.     

On the drivers of technical analysis profits in cryptocurrency markets: A Distributed Lag approach

The cryptocurrency literature on technical analysis has largely ignored drivers of technical analysis return adjusted by transaction costs (i.e., adjusted returns). To that end, we propose a Heterogeneous Autoregressive Distributed Lag Model of Returns (HARDL-R) to examine the impact from EPU, VIX, and SP500 returns to adjusted returns. We provide evidence that these three drivers matter during bubble periods compared to non-bubble periods. When not differentiating bubble periods, we find that VIX is the only driver influencing the dynamics of adjusted returns from 2016 to 2021. These findings remain relatively stable after controlling for the volume of transactions.     

A note on transaction costs and the interpretation of dividend drop‐off ratios

In a recent edition of this Journal, Bartholdy and Brown (1999) presented an analysis of the ex‐dividend share price behaviour of shares listed on the New Zealand Stock Exchange. The authors conclude that their results are consistent with the tax clientele effect (driven by long‐term investors) and that there is little or no support for the short‐term trading hypothesis. Our purpose is to highlight the importance of transaction costs in analyses such as Bartholdy and Brown's. We argue that their results have an alternative interpretation because their analysis excludes the impact of transaction costs. We extend their model to include transaction costs and show that their results are not necessarily inconsistent with the short‐term trading hypothesis. A critical point of our analysis is that, in the presence of transaction costs, the equilibrium drop‐off ratio for dividend strip traders will be less than one, and, in some cases, can be less than the equilibrium drop‐off ratio for long‐term investors.     

Optimal mean-reversion strategy in the presence of bid-ask spread and delays in capital allocations

A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of the investor's portfolio. I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.     

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.     

电子商务环境下中间商嬗变的经济学分析

中间商的出现和发展是社会分工和专业化的必然结果,并带来专业化收益和交易成本下降的双重效应。在电子商务环境下,中间商的传统功能被不断弱化,且随着电子商务的进一步发展,制造商与消费者直接交换所需的交易成本也在不断上升,从而迫切要求能够节约交易成本的各种新型中间商的协同配套发展。电子商务环境下,中间商依然有其存在的巨大意义和价值,新型中间商有着广阔的发展空间和前景。     

On Leland's strategy of option pricing with transactions costs

We compute the limiting hedging error of the Leland strategy for the approximate pricing of the European call option in a market with transactions costs. It is not equal to zero in the case when the level of transactions costs is a constant, in contradiction with the claim in Leland (1985).     

网络关注度对我国股票市场信息不对称程度的影响

以2013-2016年391支股票的360搜索指数中的投资者关注度和媒体关注度的指数作为网络关注度度量指标,同时基于股票市场交易数据采用多种信息不对称计算方法构建了信息不对称性度量指标,并进一步构造了信息不对称主成分综合指标。通过建立横截面回归模型,探究投资者和媒体关注度对我国股票市场的信息不对称程度的影响作用。实证分析及稳健性检验结果表明：投资者关注度的增加会减少知情交易及信息不透明程度,从而减少了股票市场的信息不对称程度,提高了股票市场的流动性;媒体关注度对不同的信息不对称性度量指标的影响存在着不一致性。本研究通过探索投资者关注度及媒体关注度在新兴市场中的应用,对于我国证券市场监管层制定政策以及对于普通投资者优化投资策略都具有重要的参考意义。     

On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs

The Hoggard–Whalley–Wilmott equation is introduced to model portfolios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation (PDE), whose nonlinearity reflects the presence of transaction costs. We show analytically the existence of solutions which are not necessarily convex nor concave. Numerical treatments are also given, which are devised to effectively handle an infinite domain and unbounded solutions.      

Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

Dynamic Hedging Effectiveness in South Korean Index Futures and the Impact of the Asian Financial Crisis

This paper focuses on the impact of the 1997 Asian financial market crisis upon hedging effectiveness within the KOSPI 200 stock index and index futures markets. The paper utilizes the inter-temporal relationship between the two markets to examine the characteristics of several minimum variance hedge ratios. It also examines the performances of alternative hedging strategies for dynamic portfolio management in the presence of cointegrated time-varying risks. The results show a decline in the persistence of conditional volatility within market prices after the crisis. This decline leads to the relative performance of utilizing constant hedge ratios to increase, though not significantly so to guarantee a superior performance over more sophisticated time-varying hedge ratio strategies.     

New entry,strategic diversity and efficiency in soccer betting markets: the creation and suppression of arbitrage opportunities

ABSTRACT

We find that prices offered by competing bookmakers within the same quote-driven soccer (football) betting market provide arbitrage opportunities. However, the management practices of bookmakers prevent informed bettors exploiting these in practice. We identify two groups of bookmakers, ‘position-takers’ and ‘book-balancers’. Position-takers alter their odds infrequently, while actively restricting informed traders. Book-balancers actively manage inventory by adjusting odds, and place few restrictions on their customers. We identify 545 arbitrage portfolios, and find that around 50% would require a bet on the favourite at the position-taking bookmaker. The management practices of position-takers generally prevent these opportunities being exploited in practice.     

Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model

The paper develops a general discrete-time framework for asset pricing and hedging in financial markets with proportional transaction costs and trading constraints. The framework is suggested by analogies between dynamic models of financial markets and (stochastic versions of) the von Neumann–Gale model of economic growth. The main results are hedging criteria stated in terms of “dual variables” – consistent prices and consistent discount factors. It is shown how these results can be applied to specialized models involving transaction costs and portfolio restrictions.     

An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs

We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the S&P500 index. We consider a delta-hedging strategy (DHS) for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM), assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (P&L) of the DHS under both models. We find that, under the log-normal model of Black–Scholes–Merton, the actual PDF of the P&L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the P&L volatility in the DM and JDM. We show that, under both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply mean–variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the P&L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the P&L volatility can be reduced by increasing the hedging frequency.     

Arbitrage and the Evaluation of Linear Factor Models in UK Stock Returns

I examine the impact of the no arbitrage restriction on the estimation and evaluation of linear factor models in UK stock returns. The no arbitrage restriction reduces volatility and eliminates most of the negative values of the fitted stochastic discount factor models. All of the factor models are rejected and there are significant differences in the pricing performance between models under the no arbitrage restriction. The no arbitrage restriction can have a significant impact on both the parameter estimates and pricing errors for some models.