In an effort to bolster soundness standards in banking, the 2006 international regulatory agreement of Basel II requires globally active banks to include operational risk in estimating regulatory and economic capital to be held against major types of risk. This paper discusses practical issues faced by a bank in designing and implementing an operational risk capital model. Focusing on the use of the Loss Distribution Approach (LDA) in the context of the Basel Advanced Measurement Approach (AMA), pertinent topics of future research are suggested.
{"title":"Issues in Operational Risk Capital Modeling","authors":"Mo Chaudhury","doi":"10.2139/ssrn.1480378","DOIUrl":"https://doi.org/10.2139/ssrn.1480378","url":null,"abstract":"In an effort to bolster soundness standards in banking, the 2006 international regulatory agreement of Basel II requires globally active banks to include operational risk in estimating regulatory and economic capital to be held against major types of risk. This paper discusses practical issues faced by a bank in designing and implementing an operational risk capital model. Focusing on the use of the Loss Distribution Approach (LDA) in the context of the Basel Advanced Measurement Approach (AMA), pertinent topics of future research are suggested.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81667122","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}
We study the problem of pricing an Asian option using CUDA on a graphics processing unit. We demonstrate that it is possible to get accuracy of 2E-4 in less than a fiftieth of a second.
{"title":"Graphical Asian Options","authors":"M. Joshi","doi":"10.2139/ssrn.1473563","DOIUrl":"https://doi.org/10.2139/ssrn.1473563","url":null,"abstract":"We study the problem of pricing an Asian option using CUDA on a graphics processing unit. We demonstrate that it is possible to get accuracy of 2E-4 in less than a fiftieth of a second.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"104 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75937952","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}
There is strong evidence that on-the-run U.S. Treasury securities trade much more liquidly and at significantly higher prices than their off-the-run counterparts. We examine if the same phenomenon is present in the German government bond market whose market structure differ markedly from that of the U.S. Treasury market. In sharp contrast to the U.S. evidence, we find that on-the-run status has only a negligible effect on the liquidity and pricing once other factors have been controlled for. Instead, the highly liquid German bond futures market, whose turnover is many times larger than in the cash market, leads to significant liquidity spillovers. Specifically, we find that bonds which are deliverable into futures contracts are both trading more liquidly and commanding a significant price premium, and that this effect became more pronounced during the recent financial crisis.
{"title":"Liquidity Premia in German Government Bonds","authors":"J. Ejsing, Jukka Sihvonen","doi":"10.2139/ssrn.1456858","DOIUrl":"https://doi.org/10.2139/ssrn.1456858","url":null,"abstract":"There is strong evidence that on-the-run U.S. Treasury securities trade much more liquidly and at significantly higher prices than their off-the-run counterparts. We examine if the same phenomenon is present in the German government bond market whose market structure differ markedly from that of the U.S. Treasury market. In sharp contrast to the U.S. evidence, we find that on-the-run status has only a negligible effect on the liquidity and pricing once other factors have been controlled for. Instead, the highly liquid German bond futures market, whose turnover is many times larger than in the cash market, leads to significant liquidity spillovers. Specifically, we find that bonds which are deliverable into futures contracts are both trading more liquidly and commanding a significant price premium, and that this effect became more pronounced during the recent financial crisis.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"33 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83882753","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 article analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.
{"title":"American Option Valuation: Implied Calibration of GARCH Pricing-Models","authors":"Michael Weber, Marcel Prokopczuk","doi":"10.2139/ssrn.1470686","DOIUrl":"https://doi.org/10.2139/ssrn.1470686","url":null,"abstract":"This article analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"35 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90153743","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 the second part of a series of articles on the pricing of interest rate contingent claims in the multifactor Quadratic Gaussian model, we concentrate on the pricing of swaptions. Assuming the zero-coupon bond volatility to be a deterministic function of some Markov processes, we derive the true volatility of the coupon-bond as a weighted sum of some zero-coupon bond volatility with different maturities. Bounding the stochastic weights such that the misspecified volatility dominates the true one, we obtain bounds and hedges to the true price which are solved with approximate solutions of the Black type to the prices of call option and binary option when volatility, rates and dividends are function of the Markov processes.
{"title":"Fast Calibration of Interest Rate Claims in the Quadratic Gaussian Model : 2 the Swaptions","authors":"D. Bloch","doi":"10.2139/ssrn.1441187","DOIUrl":"https://doi.org/10.2139/ssrn.1441187","url":null,"abstract":"In the second part of a series of articles on the pricing of interest rate contingent claims in the multifactor Quadratic Gaussian model, we concentrate on the pricing of swaptions. Assuming the zero-coupon bond volatility to be a deterministic function of some Markov processes, we derive the true volatility of the coupon-bond as a weighted sum of some zero-coupon bond volatility with different maturities. Bounding the stochastic weights such that the misspecified volatility dominates the true one, we obtain bounds and hedges to the true price which are solved with approximate solutions of the Black type to the prices of call option and binary option when volatility, rates and dividends are function of the Markov processes.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80890786","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}
We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the method to efficiently compute Vegas in those market models.
{"title":"Efficient Greek Estimation in Generic Market Models","authors":"M. Joshi, Chao Yang","doi":"10.2139/ssrn.1437847","DOIUrl":"https://doi.org/10.2139/ssrn.1437847","url":null,"abstract":"We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the method to efficiently compute Vegas in those market models.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73778970","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}
Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and investigates its performance by using the Standard and Poor’s 500 index returns and cross-sectional European option data. The fractionally integrated GARCH model significantly outperforms the simple GARCH(1, 1) model by generating 37% less option pricing errors. With stronger volatility persistence, it also dominates a component volatility model, who has enjoyed a reputation for its outstanding option pricing performance, by generating 15% less option pricing errors. We also confirm the fractionally integrated GARCH model’s robustness with the latest option prices. This paper indicates that capturing volatility persistence represents a very promising direction for future study.
{"title":"Volatility Long Memory on Option Valuation: Component Garch versus Fractionally Integrated GARCH","authors":"Yintian Wang","doi":"10.2139/ssrn.1438001","DOIUrl":"https://doi.org/10.2139/ssrn.1438001","url":null,"abstract":"Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and investigates its performance by using the Standard and Poor’s 500 index returns and cross-sectional European option data. The fractionally integrated GARCH model significantly outperforms the simple GARCH(1, 1) model by generating 37% less option pricing errors. With stronger volatility persistence, it also dominates a component volatility model, who has enjoyed a reputation for its outstanding option pricing performance, by generating 15% less option pricing errors. We also confirm the fractionally integrated GARCH model’s robustness with the latest option prices. This paper indicates that capturing volatility persistence represents a very promising direction for future study.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84998283","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 article presents a simple yet powerful simulation-based approach for approximating the values of prices and Greeks (i.e. derivatives with respect to the underlying spot prices, such as delta, gamma, etc) for American-style options. This approach is primarily based upon the Least Squares Monte Carlo (LSM) algorithm and is thus termed the Modified LSM (MLSM) algorithm. The key to this approach is that with initial asset prices randomly generated from a carefully chosen distribution, we obtain a regression equation for the initial value function, which can be differentiated analytically to generate estimates for the Greeks. Our approach is intuitive, easy to apply, computationally efficient and most importantly, provides a unified framework for estimating risk sensitivities of the option price to underlying spot prices. We demonstrate the effectiveness of this technique with a series of increasingly complex but realistic examples.
{"title":"Pricing and Hedging American-Style Options: A Simple Simulation-Based Approach","authors":"Yang Wang, R. Caflisch","doi":"10.21314/JCF.2010.220","DOIUrl":"https://doi.org/10.21314/JCF.2010.220","url":null,"abstract":"This article presents a simple yet powerful simulation-based approach for approximating the values of prices and Greeks (i.e. derivatives with respect to the underlying spot prices, such as delta, gamma, etc) for American-style options. This approach is primarily based upon the Least Squares Monte Carlo (LSM) algorithm and is thus termed the Modified LSM (MLSM) algorithm. The key to this approach is that with initial asset prices randomly generated from a carefully chosen distribution, we obtain a regression equation for the initial value function, which can be differentiated analytically to generate estimates for the Greeks. Our approach is intuitive, easy to apply, computationally efficient and most importantly, provides a unified framework for estimating risk sensitivities of the option price to underlying spot prices. We demonstrate the effectiveness of this technique with a series of increasingly complex but realistic examples.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89135613","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}
Affine models are very popular in modeling financial time series as they allow for analytical calculation of prices of financial derivatives like treasury bonds and options. The main property of affine models is that the conditional cumulant function, defined as the logarithmic of the conditional characteristic function, is affine in the state variable. Consequently, an affine model is Markovian, like an autoregressive process, which is an empirical limitation. The paper generalizes affine models by adding in the current conditional cumulant function the lagged conditional cumulant function. Hence, generalized affine models are non-Markovian, such as ARMA and GARCH processes, allowing one to disentangle the short term and long-run dynamics of the process. Importantly, the new model keeps the tractability of prices of financial derivatives. This paper studies the statistical properties of the new model, derives its conditional and unconditional moments, as well as the conditional cumulant function of future aggregated values of the state variable, which is critical for pricing financial derivatives. It derives the analytical formulas of the term structure of interest rates and option prices. Different estimating methods are discussed including MLE, QML, GMM, and characteristic function based estimation methods. In a term structure of interest rate out-of-sample forecasting exercise, our results suggest that for a many horizons, a simple multivariate generalized affine model on observed yields predicts the whole term structure of the interest rate better than the VAR and the Nelson-Siegel’s model with AR(1) factor dynamic.
{"title":"Generalized Affine Models","authors":"Bruno Feunou, Nour Meddahi","doi":"10.2139/ssrn.1367033","DOIUrl":"https://doi.org/10.2139/ssrn.1367033","url":null,"abstract":"Affine models are very popular in modeling financial time series as they allow for analytical calculation of prices of financial derivatives like treasury bonds and options. The main property of affine models is that the conditional cumulant function, defined as the logarithmic of the conditional characteristic function, is affine in the state variable. Consequently, an affine model is Markovian, like an autoregressive process, which is an empirical limitation. The paper generalizes affine models by adding in the current conditional cumulant function the lagged conditional cumulant function. Hence, generalized affine models are non-Markovian, such as ARMA and GARCH processes, allowing one to disentangle the short term and long-run dynamics of the process. Importantly, the new model keeps the tractability of prices of financial derivatives. This paper studies the statistical properties of the new model, derives its conditional and unconditional moments, as well as the conditional cumulant function of future aggregated values of the state variable, which is critical for pricing financial derivatives. It derives the analytical formulas of the term structure of interest rates and option prices. Different estimating methods are discussed including MLE, QML, GMM, and characteristic function based estimation methods. In a term structure of interest rate out-of-sample forecasting exercise, our results suggest that for a many horizons, a simple multivariate generalized affine model on observed yields predicts the whole term structure of the interest rate better than the VAR and the Nelson-Siegel’s model with AR(1) factor dynamic.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78569540","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}
Abstract: The coincident rise in crude oil prices and increased numbers of financial participants in the crude oil futures market from 2000-2008 has led to allegations that "speculators" drive crude oil prices. As crude oil futures peaked at $147/bbl in July 2008, the role of speculators came under heated debate. In this paper, we employ unique data from the U.S. Commodity Futures Trading Commission (CFTC) to test the relation between crude oil prices and the trading positions of various types of traders in the crude oil futures market. We employ Granger Causality tests to analyze lead and lag relations between price and position data at daily and multiple day intervals. We find little evidence that hedge funds and other non-commercial (speculator) position changes Granger-cause price changes;–the results instead suggest that price changes do precede their position changes.
{"title":"The Role of Speculators in the Crude Oil Futures Market","authors":"J. Harris, Bahattin Buyuksahin","doi":"10.2139/ssrn.1435042","DOIUrl":"https://doi.org/10.2139/ssrn.1435042","url":null,"abstract":"Abstract: The coincident rise in crude oil prices and increased numbers of financial participants in the crude oil futures market from 2000-2008 has led to allegations that \"speculators\" drive crude oil prices. As crude oil futures peaked at $147/bbl in July 2008, the role of speculators came under heated debate. In this paper, we employ unique data from the U.S. Commodity Futures Trading Commission (CFTC) to test the relation between crude oil prices and the trading positions of various types of traders in the crude oil futures market. We employ Granger Causality tests to analyze lead and lag relations between price and position data at daily and multiple day intervals. We find little evidence that hedge funds and other non-commercial (speculator) position changes Granger-cause price changes;–the results instead suggest that price changes do precede their position changes.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"48 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76561292","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}
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