We present a new method for reducing the bias present in Monte-Carlo estimators of the price of American-style contingent claims. At each exercise opportunity (in a time discretization), we assume there is an unbiased estimator of the claim value at the next exercise opportunity. We approximate the distribution of this statistic using the central limit theorem, and use this to derive an asymptotic expression for the bias. This expression is easily estimated in the context of a simulation, which allows for the straightforward computation of bias-reduced estimators of the claim value. We conclude by presenting a well-studied multivariate pricing example to show that this method offers significant improvements over the vanilla stochastic mesh technique, and that it is much more computationally efficient approach to reducing bias than nonparametric bootstrapping.
{"title":"A bias-reduction technique for Monte Carlo pricing of early-exercise options","authors":"Tyson Whitehead, R. Reesor, M. Davison","doi":"10.21314/JCF.2012.253","DOIUrl":"https://doi.org/10.21314/JCF.2012.253","url":null,"abstract":"We present a new method for reducing the bias present in Monte-Carlo estimators of the price of American-style contingent claims. At each exercise opportunity (in a time discretization), we assume there is an unbiased estimator of the claim value at the next exercise opportunity. We approximate the distribution of this statistic using the central limit theorem, and use this to derive an asymptotic expression for the bias. This expression is easily estimated in the context of a simulation, which allows for the straightforward computation of bias-reduced estimators of the claim value. We conclude by presenting a well-studied multivariate pricing example to show that this method offers significant improvements over the vanilla stochastic mesh technique, and that it is much more computationally efficient approach to reducing bias than nonparametric bootstrapping.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"33-69"},"PeriodicalIF":0.9,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67702119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a multivariate Sato model for multivariate option pricing where the asset log-returns are expressed as Sato time changed Brownian motions and where the time change is the weighted sum of a common and an idiosyncratic component. This model presents the main advantage that it allows to replicate univariate option prices in both the strike and time to maturity dimensions. In particular it is able to t both the univariate option surfaces and the asset log-return dependence structure with high precision for a period ranging from June 2008 until October 2009 including therefore the credit crisis period.
{"title":"Sato two factor models for multivariate option pricing","authors":"Florence Guillaume","doi":"10.21314/JCF.2012.248","DOIUrl":"https://doi.org/10.21314/JCF.2012.248","url":null,"abstract":"This paper provides a multivariate Sato model for multivariate option pricing where the asset log-returns are expressed as Sato time changed Brownian motions and where the time change is the weighted sum of a common and an idiosyncratic component. This model presents the main advantage that it allows to replicate univariate option prices in both the strike and time to maturity dimensions. In particular it is able to t both the univariate option surfaces and the asset log-return dependence structure with high precision for a period ranging from June 2008 until October 2009 including therefore the credit crisis period.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"17 1","pages":"159-192"},"PeriodicalIF":0.9,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we deal with the issue of pricing numerically by simulation convertible bonds. A convertible bond can be seen as a coupon-paying and callable American option. Moreover call times are typically subject to constraints, called call protections, preventing the issuer from calling the bond at certain sub-periods of time. The nature of the call protection may be very path-dependent, like a path dependence based on a ‘large’ number d of Boolean random variables, leading to high-dimensional pricing problems. Deterministic pricing schemes are then ruled out by the curse of dimensionality, and simulation methods appear to be the only viable alternative. We consider in this paper various possible clauses of call protection. We propose in each case a reference, but heavy, if practical, deterministic pricing scheme, as well as a more efficient (as soon as d exceeds a few units) and practical Monte Carlo simulation/regression pricing scheme. In each case we derive the pricing equation, study the convergence of the Monte Carlo simulation/regression scheme and illustrate our results by reports on numerical experiments. One thus gets a practical and mathematically justified approach to the problem of pricing by simulation convertible bonds with highly path-dependent call protection. More generally, this paper is an illustration of the real abilities of simulation/regression numerical schemes for high to very high-dimensional pricing problems, like systems of 2 scalar coupled partial differential equations that arise in the context of the application at hand in this paper.
{"title":"Pricing convertible bonds with call protection","authors":"S. Crépey, Abdallah Rahal","doi":"10.21314/JCF.2011.258","DOIUrl":"https://doi.org/10.21314/JCF.2011.258","url":null,"abstract":"In this paper we deal with the issue of pricing numerically by simulation convertible bonds. A convertible bond can be seen as a coupon-paying and callable American option. Moreover call times are typically subject to constraints, called call protections, preventing the issuer from calling the bond at certain sub-periods of time. The nature of the call protection may be very path-dependent, like a path dependence based on a ‘large’ number d of Boolean random variables, leading to high-dimensional pricing problems. Deterministic pricing schemes are then ruled out by the curse of dimensionality, and simulation methods appear to be the only viable alternative. We consider in this paper various possible clauses of call protection. We propose in each case a reference, but heavy, if practical, deterministic pricing scheme, as well as a more efficient (as soon as d exceeds a few units) and practical Monte Carlo simulation/regression pricing scheme. In each case we derive the pricing equation, study the convergence of the Monte Carlo simulation/regression scheme and illustrate our results by reports on numerical experiments. One thus gets a practical and mathematically justified approach to the problem of pricing by simulation convertible bonds with highly path-dependent call protection. More generally, this paper is an illustration of the real abilities of simulation/regression numerical schemes for high to very high-dimensional pricing problems, like systems of 2 scalar coupled partial differential equations that arise in the context of the application at hand in this paper.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"37-75"},"PeriodicalIF":0.9,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pricing barrier and average options in a stochastic volatility environment.","authors":"Kenichiro Shiraya, Akihiko Takahashi, M. Toda","doi":"10.21314/JCF.2011.257","DOIUrl":"https://doi.org/10.21314/JCF.2011.257","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"111-148"},"PeriodicalIF":0.9,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raquel J. Fonseca, Steve Zymler, W. Wiesemann, B. Rustem
We study a currency investment strategy, where we maximize the return on a portfolio of foreign currencies relative to any appreciation of the corresponding foreign exchange rates. Given the uncertainty in the estimation of the future currency values, we employ robust optimization techniques to maximize the return on the portfolio for the worst-case foreign exchange rate scenario. Currency portfolios differ from stock only portfolios in that a triangular relationship exists among foreign exchange rates to avoid arbitrage. Although the inclusion of such a constraint in the model would lead to a nonconvex problem, we show that by choosing appropriate uncertainty sets for the exchange and the cross exchange rates, we obtain a convex model that can be solved efficiently. Alongside robust optimization, an additional guarantee is explored by investing in currency options to cover the eventuality that foreign exchange rates materialize outside the specified uncertainty sets. We present numerical results that show the relationship between the size of the uncertainty sets and the distribution of the investment among currencies and options, and the overall performance of the model in a series of backtesting experiments.
{"title":"Robust Optimization of Currency Portfolios","authors":"Raquel J. Fonseca, Steve Zymler, W. Wiesemann, B. Rustem","doi":"10.21314/JCF.2011.227","DOIUrl":"https://doi.org/10.21314/JCF.2011.227","url":null,"abstract":"We study a currency investment strategy, where we maximize the return on a portfolio of foreign currencies relative to any appreciation of the corresponding foreign exchange rates. Given the uncertainty in the estimation of the future currency values, we employ robust optimization techniques to maximize the return on the portfolio for the worst-case foreign exchange rate scenario. Currency portfolios differ from stock only portfolios in that a triangular relationship exists among foreign exchange rates to avoid arbitrage. Although the inclusion of such a constraint in the model would lead to a nonconvex problem, we show that by choosing appropriate uncertainty sets for the exchange and the cross exchange rates, we obtain a convex model that can be solved efficiently. Alongside robust optimization, an additional guarantee is explored by investing in currency options to cover the eventuality that foreign exchange rates materialize outside the specified uncertainty sets. We present numerical results that show the relationship between the size of the uncertainty sets and the distribution of the investment among currencies and options, and the overall performance of the model in a series of backtesting experiments.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"3-30"},"PeriodicalIF":0.9,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Ornstein-Uhlenbeck process is particularly useful for modeling stochastic processes in financial applications. Further, functions of such a process can be used to model random volatility of other processes, resulting in more flexible models for financial risk variables. The distribution of such a financial risk variable is of particular interest in Value at Risk analysis. As we know, the far quantiles of the distribution function provide information on the level of capital reserves required to accommodate extreme stress situations. This paper presents an approximation for the distribution function, which in some situations works surprisingly well for even the far tails of the distribution. While theoretically unjustified and strange, it may still be very useful in practice. keywords: log-normal approximation, high quantiles, VaR, capital reserve, random volatility model.
{"title":"Strange facts about the marginal distributions of processes based on the Ornstein-Uhlenbeck process","authors":"R. Brownrigg, E. Khmaladze","doi":"10.21314/JCF.2011.225","DOIUrl":"https://doi.org/10.21314/JCF.2011.225","url":null,"abstract":"The Ornstein-Uhlenbeck process is particularly useful for modeling stochastic processes in financial applications. Further, functions of such a process can be used to model random volatility of other processes, resulting in more flexible models for financial risk variables. The distribution of such a financial risk variable is of particular interest in Value at Risk analysis. As we know, the far quantiles of the distribution function provide information on the level of capital reserves required to accommodate extreme stress situations. This paper presents an approximation for the distribution function, which in some situations works surprisingly well for even the far tails of the distribution. While theoretically unjustified and strange, it may still be very useful in practice. keywords: log-normal approximation, high quantiles, VaR, capital reserve, random volatility model.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"111-148"},"PeriodicalIF":0.9,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67700928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast simplified approaches to Asian option pricing","authors":"D. Tangman, A. Peer, Nisha Rambeerich, M. Bhuruth","doi":"10.21314/JCF.2011.229","DOIUrl":"https://doi.org/10.21314/JCF.2011.229","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"14 1","pages":"3-36"},"PeriodicalIF":0.9,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67700864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：