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Bertil Naslund - One of the best experts on this subject based on the ideXlab platform.
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Currency Option pricing with mean reversion and uncovered interest parity a revision of the garman kohlhagen model
European Journal of Operational Research, 1997Co-Authors: Niklas Ekvall, Peter L Jennergren, Bertil NaslundAbstract:Abstract We consider a model for the pricing of Currency Options where the logarithm of the exchange rate exhibits mean reversion, i.e. follows the Omstein-Uhlenbeck process. We mention reasons why exchange rates could exhibit mean reversion. The domestic and foreign short interest rates are related to the logarithm of the exchange rate through Uncovered Interest Parity. Under these assumptions, we derive formulas for the value of a European Currency Option, from the point of view of both domestic and foreign investors. We also derive formulas for Options on forward and futures contracts. We compare Option values computed by means of the Garman-Kohlhagen model with corresponding results from our model. It appears that our model cannot explain all instances of mispricing of Currency Options by the Garman-Kohlhagen model which have been reported by previous authors. The main virtue of our paper, however, is that we derive a simple model which incorporates clear theoretical relationship between the exchange rate and the domestic and foreign interest rates.
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Siegel's paradox and the pricing of Currency Options
Journal of International Money and Finance, 1995Co-Authors: Bernard Dumas, L. Peter Jennergren, Bertil NaslundAbstract:Abstract It is an important property of a Currency Option that its value does not depend on whose point of view is taken, that of the domestic or foreign investor. Option values obtained from the Garman-Kohlhagen model do satisfy this property. The Merton jump-diffusion model has been proposed as a more realistic Currency Option model, to eliminate pricing biases inherent in the Garman-Kohlhagen model. The jump-diffusion model assumes that the jump risk is non-priced, ie , can be diversified away. If both the domestic and foreign investor make that assumption, then the jump-diffusion model produces Option values which are different for the two investors, thus violating the law of one price. This is an instance of the Siegel paradox. The extent to which computed Option values may differ between the two investors is indicated through numerical examples.
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Currency Option pricing in credible target zones
1993Co-Authors: Bernard Dumas, L. Peter Jennergren, Bertil NaslundAbstract:This paper develops a model for valuing Options on a Currency which is maintained within a band. The starting point of our model is the well known Krugman model for exchange-rate behavior within a target zone. Results from model runs provide insight into evidence reported by other authors of mispricing of Currency Options by extensions of the Black-Scholes model.
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realignment risk and Currency Option pricing in target zones
National Bureau of Economic Research, 1993Co-Authors: Bernard Dumas, Peter L Jennergren, Bertil NaslundAbstract:This paper extends the Krugman target zone model by including a realignment mechanism. Various properties of that realignment mechanism are discussed. The movement of the exchange rate is governed both by a Wiener process on fundamental and by a Poisson jump process with endogenous realignment size. The realignment mechanism is such that (except in cases where a speculative attack occurs) no jump in fundamental is needed to accompany the jump in the exchange rate. A risk neutral valuation of Currency Options is constructed. Some properties of Option values under realignment risk are illustrated by numerical results.
Bernard Dumas - One of the best experts on this subject based on the ideXlab platform.
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Siegel's paradox and the pricing of Currency Options
Journal of International Money and Finance, 1995Co-Authors: Bernard Dumas, L. Peter Jennergren, Bertil NaslundAbstract:Abstract It is an important property of a Currency Option that its value does not depend on whose point of view is taken, that of the domestic or foreign investor. Option values obtained from the Garman-Kohlhagen model do satisfy this property. The Merton jump-diffusion model has been proposed as a more realistic Currency Option model, to eliminate pricing biases inherent in the Garman-Kohlhagen model. The jump-diffusion model assumes that the jump risk is non-priced, ie , can be diversified away. If both the domestic and foreign investor make that assumption, then the jump-diffusion model produces Option values which are different for the two investors, thus violating the law of one price. This is an instance of the Siegel paradox. The extent to which computed Option values may differ between the two investors is indicated through numerical examples.
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Currency Option pricing in credible target zones
1993Co-Authors: Bernard Dumas, L. Peter Jennergren, Bertil NaslundAbstract:This paper develops a model for valuing Options on a Currency which is maintained within a band. The starting point of our model is the well known Krugman model for exchange-rate behavior within a target zone. Results from model runs provide insight into evidence reported by other authors of mispricing of Currency Options by extensions of the Black-Scholes model.
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realignment risk and Currency Option pricing in target zones
National Bureau of Economic Research, 1993Co-Authors: Bernard Dumas, Peter L Jennergren, Bertil NaslundAbstract:This paper extends the Krugman target zone model by including a realignment mechanism. Various properties of that realignment mechanism are discussed. The movement of the exchange rate is governed both by a Wiener process on fundamental and by a Poisson jump process with endogenous realignment size. The realignment mechanism is such that (except in cases where a speculative attack occurs) no jump in fundamental is needed to accompany the jump in the exchange rate. A risk neutral valuation of Currency Options is constructed. Some properties of Option values under realignment risk are illustrated by numerical results.
Fan-yong Liu - One of the best experts on this subject based on the ideXlab platform.
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Pricing Currency Options based on fuzzy techniques
European Journal of Operational Research, 2009Co-Authors: Fan-yong LiuAbstract:Owing to the fluctuation of financial markets from time to time, some financial variables can always be observed with perturbations and be expected in the imprecise sense. Therefore, this paper starts from the fuzzy environments of Currency Options markets, introduces fuzzy techniques, and gives a fuzzy Currency Options pricing model. By turning exchange rate, interest rates and volatility into triangular fuzzy numbers, the Currency Option price will turn into a fuzzy number. This makes the financial investors who can pick any Currency Option price with an acceptable belief degree for their later use. In order to obtain the belief degree, an optimization procedure has been applied. An empirical study is performed based on daily foreign exchange market data. The empirical study results indicate that the fuzzy Currency Options pricing method is a useful tool for modeling the imprecise problem in the real world.
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Bounds Pricing Method of Currency Options Based on Triangular Fuzzy Numbers, Fuzzy Programming and Fuzzy Regression
2009 International Association of Computer Science and Information Technology - Spring Conference, 2009Co-Authors: Fan-yong LiuAbstract:Some financial variables can always be observed with perturbations and be expected in the imprecise sense because of the fluctuation of financial markets. Therefore, this paper introduces fuzzy techniques, and gives a fuzzy Currency Options bounds pricing model. By denoting four input variables in the Garman-Kohlhagen model as triangular fuzzy numbers, the Currency Option price will turn into afuzzy number. In order to construct easily the membership function of this fuzzy number, a triangular fuzzy number is used to approximate it. Then a fuzzy programming procedure is proposed to determine its lower bound and upper bound. Finally, the proposed fuzzy Currency Options bounds pricing model is tested with the daily market data of the EUR/USD Currency Option. The empirical study results indicate that the proposed method is a useful tool for modelling the imprecise problems in the foreign exchange derivativemarkets.
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ICANNGA (1) - Pricing the Foreign Currency Options with the Fuzzy Numbers Based on the Garman-Kohlhagen Model
Adaptive and Natural Computing Algorithms, 1Co-Authors: Fan-yong LiuAbstract:This paper starts from the fuzzy environments of foreign Currency Options markets, introduces fuzzy sets theory, and gives a fuzzy version of Garman-Kohlhagen Currency Options pricing model. By taking exchange rate, domestic interest rate, foreign interest rate, and volatility as triangular fuzzy numbers, the Currency Option price will turn into a fuzzy number. This makes the financial investors who can pick any Currency Option price with an acceptable belief degree for the later use. In order to obtain the belief degree, an optimization procedure has been applied. An empirical study is performed based on market data. The study result indicates the fuzzy Currency Options pricing method is a useful tool for modeling the imprecise problem in the real world.
Foad Shokrollahi - One of the best experts on this subject based on the ideXlab platform.
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Subdiffusive fractional Black–Scholes model for pricing Currency Options under transaction costs
Taylor & Francis Group, 2018Co-Authors: Foad ShokrollahiAbstract:A new framework for pricing European Currency Option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European Currency call Option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a Currency Option under transaction costs is obtained as time-step $$\Delta t = {\left({{{{t^{\alpha - 1}}} \over {\Gamma (\alpha )}}} \right)^{ - 1}}{\left({{2 \over \pi }} \right)^{{1 \over {2H}}}}{\left({{k \over \sigma }} \right)^{{1 \over H}}}$$, which can be used as the actual price of an Option. In addition, we also show that time-step and long-range dependence have a significant impact on Option pricing
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Currency Option pricing in the time-changed fractional Brownian motion under transaction costs
arXiv: Pricing of Securities, 2016Co-Authors: Foad ShokrollahiAbstract:A new framework for pricing the European Currency Option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign Currency Option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a Currency Option under transaction costs is obtained as time-step $\Delta t=\left(\frac{t^{\beta-1}}{\Gamma(\beta)}\right)^{-1}\left(\frac{2}{\pi}\right)^{\frac{1}{2H}}\left(\frac{\alpha}{\sigma}\right)^{\frac{1}{H}}$ , which can be used as the actual price of an Option. In addition, we also show that time-step and long-range dependence have a significant impact on Option pricing.
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Subdiffusive fractional Brownian motion regime for pricing Currency Options under transaction costs
arXiv: Pricing of Securities, 2016Co-Authors: Foad ShokrollahiAbstract:A new framework for pricing the European Currency Option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign Currency Option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a Currency Option under transaction costs is obtained as time-step $\Delta t=\left(\frac{t^{\beta-1}}{\Gamma(\beta)}\right)^{-1}\left(\frac{2}{\pi}\right)^{\frac{1}{2H}}\left(\frac{\alpha}{\sigma}\right)^{\frac{1}{H}}$ , which can be used as the actual price of an Option. In addition, we also show that time-step and long-range dependence have a significant impact on Option pricing.
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Actuarial approach in a mixed fractional Brownian motion with jumps environment for pricing Currency Option
Advances in Difference Equations, 2015Co-Authors: Foad Shokrollahi, Adem KilicmanAbstract:This research aims to investigate the strategy of fair insurance premium actuarial approach for pricing Currency Option, when the value of foreign Currency Option follows the mixed fractional Brownian motion with jumps and the European call and put Currency Option are presented. It has certain reference significance to avoiding foreign exchange risk.
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pricing Currency Option in a mixed fractional brownian motion with jumps environment
Mathematical Problems in Engineering, 2014Co-Authors: Foad Shokrollahi, Adem KilicmanAbstract:A new framework for pricing the European Currency Option is developed in the case where the spot exchange rate fellows a mixed fractional Brownian motion with jumps. The jump mixed fractional partial differential equation is obtained. Some Greeks and properties volatility are discussed. Finally the numerical simulations illustrate that our model is flexible and easy to implement.
Yufu Ning - One of the best experts on this subject based on the ideXlab platform.
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put Currency Option pricing under uncertain environments
International Conference on Natural Computation, 2017Co-Authors: Xiao Wang, Yufu NingAbstract:Based on an uncertain Currency model, put Currency Option pricing problem is discussed. Furthermore, we derive the pricing formulas of European and American put Currency Option. Meanwhile, this paper analyzes the relationship between pricing formulas and the relevant parameters. At last, two numerical examples presented in this paper illustrate the pricing formulas.
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ICNC-FSKD - Put Currency Option pricing under uncertain environments
2017 13th International Conference on Natural Computation Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2017Co-Authors: Xiao Wang, Yufu NingAbstract:Based on an uncertain Currency model, put Currency Option pricing problem is discussed. Furthermore, we derive the pricing formulas of European and American put Currency Option. Meanwhile, this paper analyzes the relationship between pricing formulas and the relevant parameters. At last, two numerical examples presented in this paper illustrate the pricing formulas.
