Ton C.f Vorst - Academia.edu (original) (raw)
Papers by Ton C.f Vorst
Journal of Pure and Applied Algebra, 1982
In this paper we examine the problem of managing portfolios consisting of both, stocks and option... more In this paper we examine the problem of managing portfolios consisting of both, stocks and options. Due to the resulting asymmetric portfolio return distribution we do not use mean variance analysis but represent the preferences of the investors in terms of confidence limits on down side risk measures. For the simultaneous optimization of the stock and option positions we derive portfolios with a maximum expected return under a given preference structure expressed by shortfall constraints. To identify the optimal optioned portfolio we derive an approximation of the return distribution. The solution identified by this procedure will dominate comparable portfolios derived by using mean variance analysis. On the basis of Monte Carlo Simulations we will illustrate our results and demonstrate the stochastic dominance of these solutions. R C U d Dans ce papier nous examinons le problbme d'arranger les portefeuilles qui portent des actions et des options. La rentabilitk esp6rke rksultante de la distribution de la portefeuille asymktrique nous n 'utilisons pas 1 'analyse moyenne-variance. Pour 1 'optimisation simultank des positions d 'action et d 'option nous derivons des portefeuilles avec une rentabilitk esp6rk maximale sous une structure prkferk exprim& par des restrictions des pertes. Pour identifier 1 'option-portefeuille optimale nous dkrivons une approximation de la distribution de rentabilit6. La solution identifike par cette procMure dominera des portefeuilles comparables dkrivkes en utilisant 1 'analyse moyenne-variance. Nous illustrons ces resultats avec des simulations de Monte Carlo et nous dkmontrerons la dominance stochastique de ces solutions.
European Journal of Operational Research, 1996
Some recent results for frictionless economies show that popular dynamic portfolio strategies suc... more Some recent results for frictionless economies show that popular dynamic portfolio strategies such as stop-loss and lock-in are inefficient. I.e. for each of these strategies there exists an alternative portfolio strategy that gives the same final payoff distribution at lower initial costs. However, the alternative strategies require considerably more active trading than the simple strategies. The results rely heavily on the assumption of no transaction costs. Under this assumption the initial investment required is a linear function of the prices of the contingent claims that build the final payoff distribution. In this paper we demonstrate that, even for modest levels of transaction costs, the efficient strategies are more costly than the simple strategies, i.e. a strategy that replicates the final payoff distribution of an efficient strategy is excessively costly due to the transaction costs and the heavy trading involved. Since the initial investment is no longer a linear function of the contingent claims, the optimization problems to find the most efficient strategy are complicated combinatorial optimization problems which can only be solved for trees with a small number of steps. In a world without transaction costs, options are redundant instuments, since all payoff distributions can be replicated by trading in stocks and bonds. In the second half of this paper we show that the use of options in a world with transaction costs enables investors to realize final value distributions at lower initial costs than would be possible with trades in stocks an bonds only. Hence, although in theory options do not give rise to other portfolio strategies, they do in a more restrictive setting with transaction costs.
CrossRef Listing of Deleted DOIs
Http Dx Doi Org 10 3905 Jod 2005 580517, Feb 22, 2009
In this paper we shall discuss a financial option of which the payoff depends on the average valu... more In this paper we shall discuss a financial option of which the payoff depends on the average value of the underlying security over some final time interval. After explaining what an option is about we will derive a partial differential equation for the option which is different from the partial differential equation of a simple European call option. From this we will get an expectation formula for the option value. We will give an economical as well as a mathematical argument for this expectation formula. CONTENTS 1. Introduction 2. A partial differential equation for the option price 3. The option price as an expectation 4. The black-scholes formula 5. Problems with an explicit formula 6. Conclusion 7. References 8. Index
Statistica Neerlandica, 1996
In this paper we give an introduction in option pricing theory and explicitly specify the Black-S... more In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.
Operations Research, 1991
Communications in Algebra, 1981
Applied Mathematical Finance, 1996
We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein m... more We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein model, in the sense that hedging is only allowed at some fixed trading dates. As a consequence, the financial market is incomplete in both modified models. Applying Schweizer's (and Schäl's) variance-optimal criterion for pricing and hedging general claims, we first analyse the dynamic consistency of the strategies which
Report Econometric Institute Erasmus University Rotterdam, Jan 22, 2002
Journal of Pure and Applied Algebra, 1982
In this paper we examine the problem of managing portfolios consisting of both, stocks and option... more In this paper we examine the problem of managing portfolios consisting of both, stocks and options. Due to the resulting asymmetric portfolio return distribution we do not use mean variance analysis but represent the preferences of the investors in terms of confidence limits on down side risk measures. For the simultaneous optimization of the stock and option positions we derive portfolios with a maximum expected return under a given preference structure expressed by shortfall constraints. To identify the optimal optioned portfolio we derive an approximation of the return distribution. The solution identified by this procedure will dominate comparable portfolios derived by using mean variance analysis. On the basis of Monte Carlo Simulations we will illustrate our results and demonstrate the stochastic dominance of these solutions. R C U d Dans ce papier nous examinons le problbme d'arranger les portefeuilles qui portent des actions et des options. La rentabilitk esp6rke rksultante de la distribution de la portefeuille asymktrique nous n 'utilisons pas 1 'analyse moyenne-variance. Pour 1 'optimisation simultank des positions d 'action et d 'option nous derivons des portefeuilles avec une rentabilitk esp6rk maximale sous une structure prkferk exprim& par des restrictions des pertes. Pour identifier 1 'option-portefeuille optimale nous dkrivons une approximation de la distribution de rentabilit6. La solution identifike par cette procMure dominera des portefeuilles comparables dkrivkes en utilisant 1 'analyse moyenne-variance. Nous illustrons ces resultats avec des simulations de Monte Carlo et nous dkmontrerons la dominance stochastique de ces solutions.
European Journal of Operational Research, 1996
Some recent results for frictionless economies show that popular dynamic portfolio strategies suc... more Some recent results for frictionless economies show that popular dynamic portfolio strategies such as stop-loss and lock-in are inefficient. I.e. for each of these strategies there exists an alternative portfolio strategy that gives the same final payoff distribution at lower initial costs. However, the alternative strategies require considerably more active trading than the simple strategies. The results rely heavily on the assumption of no transaction costs. Under this assumption the initial investment required is a linear function of the prices of the contingent claims that build the final payoff distribution. In this paper we demonstrate that, even for modest levels of transaction costs, the efficient strategies are more costly than the simple strategies, i.e. a strategy that replicates the final payoff distribution of an efficient strategy is excessively costly due to the transaction costs and the heavy trading involved. Since the initial investment is no longer a linear function of the contingent claims, the optimization problems to find the most efficient strategy are complicated combinatorial optimization problems which can only be solved for trees with a small number of steps. In a world without transaction costs, options are redundant instuments, since all payoff distributions can be replicated by trading in stocks and bonds. In the second half of this paper we show that the use of options in a world with transaction costs enables investors to realize final value distributions at lower initial costs than would be possible with trades in stocks an bonds only. Hence, although in theory options do not give rise to other portfolio strategies, they do in a more restrictive setting with transaction costs.
CrossRef Listing of Deleted DOIs
Http Dx Doi Org 10 3905 Jod 2005 580517, Feb 22, 2009
In this paper we shall discuss a financial option of which the payoff depends on the average valu... more In this paper we shall discuss a financial option of which the payoff depends on the average value of the underlying security over some final time interval. After explaining what an option is about we will derive a partial differential equation for the option which is different from the partial differential equation of a simple European call option. From this we will get an expectation formula for the option value. We will give an economical as well as a mathematical argument for this expectation formula. CONTENTS 1. Introduction 2. A partial differential equation for the option price 3. The option price as an expectation 4. The black-scholes formula 5. Problems with an explicit formula 6. Conclusion 7. References 8. Index
Statistica Neerlandica, 1996
In this paper we give an introduction in option pricing theory and explicitly specify the Black-S... more In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.
Operations Research, 1991
Communications in Algebra, 1981
Applied Mathematical Finance, 1996
We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein m... more We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein model, in the sense that hedging is only allowed at some fixed trading dates. As a consequence, the financial market is incomplete in both modified models. Applying Schweizer's (and Schäl's) variance-optimal criterion for pricing and hedging general claims, we first analyse the dynamic consistency of the strategies which
Report Econometric Institute Erasmus University Rotterdam, Jan 22, 2002