A counter-example to an option pricing formula under transaction costs

In the paper by Melnikov and Petrachenko (Finance Stoch. 9: 141–149, 2005), a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counter-example to show that the option pricing formula stated in that paper can in fact lead to arbitrage. This is related to the fact that under transaction costs a superreplicating strategy may be less expensive to set up than a strictly replicating one.     

An endogenous volatility approach to pricing and hedging call options with transaction costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland [J. Finance, 1985 Leland, HE. 1985. Option pricing and replication with transaction costs. J. Finance, 40: 1283–1301. [Crossref], [Web of Science ®] , [Google Scholar], 40, 1283–1301] heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black–Scholes option prices when transaction costs are zero. Data on S&P 500 index cash options from January to June 2008 illustrate the model.     

On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case.Received: March 2004, Mathematics Subject Classification (2000): 62P05JEL Classification: G11, G13The authors are grateful to an anonymous referee for numerous helpful comments and to Yulia Romaniuk for final corrections. The paper was partially supported by grant NSERC 264186.     

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.     

Heterogeneous time varying transaction costs and asset pricing in international equity markets

In this paper, we examine the time variation in transaction costs relative to excess returns, in a panel consisting of 10 international equity indices over the time period 1984–2005. This is undertaken by extending the consumption CAPM (CCAPM) model proposed by Campbell and Shiller (Rev. Financ. Stud. 1:195–228, 1988) to incorporate time varying proportional transaction costs. We rigorously address both the cross-country heterogeneity in the estimated model and endogeneity. We find strong evidence that suggests transaction costs should be included as an additional explanatory variable in the CCAPM. This leads to the conclusion that transaction costs should be included in asset pricing models as their stochastic process impacts directly on private consumption expenditure.

Risk sensitive asset management with transaction costs

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska. Mansucript received: July 1998; final version received: January 1999     

No-arbitrage criteria for financial markets with transaction costs and incomplete information

This note deals with criteria of absence of arbitrage opportunities for an investor acting in a market with frictions and having a limited access to the information flow. We develop a mathematical scheme covering major models of financial markets with transaction costs and prove several results including a criterion for the robust no-arbitrage property and a hedging theorem.      

Portfolio optimisation with strictly positive transaction costs and impulse control

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a nontrivial asymptotically optimal solution for the problem of exponential utility maximisation.     

Trends and determinants of Australian managed fund transaction costs

The present paper examines the often-overlooked managed fund fee that is incurred when investors enter and exit managed fund products. The present paper documents that transaction costs for investors, measured by the application-redemption spread, are above stock market brokerage rates although they have declined since 1995. The study analyses the relationship between this transaction fee and several variables. In summary, retail fund transaction costs are positively related to retail funds’ assets under management, whilst this relationship is negative for larger wholesale funds, consistent with economies of scale. Direct entry and exit fees and initial commissions are positively related to transaction costs which raises the possibility that the commissions are used to levy soft-dollar payments. The paper also documents a relationship between transaction costs and fund flows which differs between retail and wholesale funds. Overall, the findings are consistent with the proposition that the various fees are used by managers as interchangeable and the different fee regimes reflect different products and markets.     

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.     

Transaction costs and competition among audit firms in local markets

We develop a measure to capture an audit firm's competitive position in a local audit market based on the transaction costs of changing audit firms included in DeAngelo's (1981) multi-period audit pricing model. Our competition measure reflects the size difference between the largest audit firm in a market specified by client industry at the city level and the other audit firms operating in that market. We find that audit fees of a client decrease as this size difference increases. This result suggests that smaller audit firms charge lower audit fees because of their competitive disadvantage to the local largest firm.     

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.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Legal constraints,transaction costs and the evaluation of mutual funds

The paper considers the legal restrictions on investment and the transaction costs related to optimal turnover that affect mutual funds. A method is developed for mutual fund performance evaluation when both these factors are included in the reference portfolios, and it is applied to a sample of available Spanish mutual funds. The poor performance results reflected in previous studies are not significantly modified. However, when net returns on the reference portfolios are used in the evaluation the performance is clearly improved.     

Unifying Black–Scholes Type Formulae Which Involve Brownian Last Passage Times up to a Finite Horizon

The authors recently discovered some interesting relations between the Black–Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous results for last passage times up to a finite horizon. This is achieved in the present paper, where Yuri’s formula, as originally presented in Akahori et al. (On the pricing of options written on the last exit time, 2008), is also derived.