Profil du chercheur

Publications de Yves RAKOTONDRATSIMBA

1. « Hedging option contracts with locally weighted regression, functional data analysis, and Markov chain Monte Carlo techniques »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   The delta-gamma Approximation (DGA) is a technique that is often used for hedging options in practice. For its simplicity, it is widely used because it can immediately indicate the number of shares of the underlying assets to be reinvested to hedge the original investments. However, the DGA requires that the change of the underlying asset price to be small for an acceptable performance. Therefore, when this change of the underlying asset price is large, then the hedging performance is not acceptable implying losses, and frequent rebalancing operations of the portfolio may be needed. But, a rebalancing operation has an associated transaction fee and a high frequency of rebalancing operations imply high additional costs. Hence, there is a trade-off between losses due to low performance of the DGA (when the change of the underlying asset price is large) and additional costs due to rebalancing operations to compensate the low performance of the DGA. In the present work, we propose a hedging framework that improves its performance with the purpose to reduce losses by improving the quality of approximating the option prices. This framework consists of estimating the implied volatility using the Markov chain Monte Carlo, predicting the change of the underlying asset price using the functional data analysis, and approximating the option price using the locally weighted regression.

   
   
   

2. « A reinforcement-learning-based automated trading system with nonlinear variation of transaction fees »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   The automated trading systems (ATS) are highly interested by traders for their abilities to automatically adapt the embedded decision-making mechanism considering both endogenous and exogenous changes in the financial and economic environments. Their abilities depend greatly on both the choice of the decision-making algorithm and the aspects of the trading environment that are taken into account in the algorithm to make decisions. One of the aspects that significantly influences on the actual profitability obtained using the ATS is the transaction fee. Often, this aspect is neglected or (if considered) is simply modeled as proportional to the trade amount, where this proportionality is maintained constant (that is, linear with respect to the trade amount). However, in reality, a transaction fee is composed by different components such as the flat trade fee, trade fee per share, broker-assisted trade fee, among others. In particular, the trade fee per share often varies nonlinearly with respect to the trade amount and on the trade frequency. In this work, we study how the fact of including this nonlinear variation of the transaction fees (with respect to the transaction amount) affects on the decisions made by the ATS. In particular, we implement the ATS' decision algorithm using a reinforcement learning (RL) such as the Q-learning. The advantage of such an algorithm is that it considers the decision-making problem as a stochastic control problem, and it suggests a sequence of optimal (present and future) actions in order to maximize the expected value of the discounted cumulative rewards. Finally, with the purpose to illustrate the impact of considering the nonlinear variation of transaction fees in the decision-making model, we compare the corresponding results to those that are obtained using the linear variation of transaction fees.

   
   
   

3. « Learning to hedge derivatives for risk management »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   In risk management, the delta-gamma approximation is extensively used, for instance, for derivatives portfolio hedging (such as options). However, this approximation usually works well locally for small changes of the underlying asset price. When these changes become large, then the derivatives prices estimated by the delta-gamma approximation can be significantly different from those that are estimated using the Black-Scholes formula. In this work, we propose a method that allows us to hedge derivatives such as options even for large changes of their underlying asset prices. While the delta-gamma approximation uses the first- and second-order Greeks for derivatives portfolio hedging, our method is based on hedging with a linear combination of some kernel functions. These kernel functions depend in turn on the implied asset price, which in turn is forecasted using the functional data analysis (FDA) approach. Then, both these instances of option prices and the corresponding asset prices are used to find the weights for the linear combination of the kernel functions that allow us to hedge the considered derivative. We then compare the hedging performance of our approach to that obtained using the delta-gamma approximation and other techniques.

   
   
   

4. « Delta-Gamma approximation for the Credit Valuation Adjustment of a vanilla option »

   par Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
   
   
   

5. « Bond sensitivities under large shifts of the interest rates »

   par Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
   
   
   

6. « Forecasting the stock price with no standard volatility model »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   In this work, we provide an approach to derive a distribution forecast for the stock price, without resorting to any presumed (complex) parametric model. The representation learning approach presented in this work can be seen as a nonlinear autoregressive (NAR) model that takes into account the volatility, skewness and kurtosis of the underlying asset price distribution. Aside from the forecasting aspect, we explore a way to represent the asset price that avoids the recourse to any well-established volatility model, such as the GARCH family. Finally, this work is realized with the intention to provide various formulas that can empower the reader to implement an immediately usable stock price forecasting tool.

   
   
   

7. « Bond valuation under lower and upper bounds for the Short Rate »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   We address here to the issue related to the bond valuation when the associated underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is the case when dealing with the zero lower bound for the interest rate or with the negative interest rates situation. The model considered here is referred to as LUB (Lower and Upper Bound) model and, for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model representation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. As for the Black’s approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristic(s), the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Then we provide the definitive closed formula approximation which is the expected solution, at least from the theoretical point of view. To overcome the difficulty linked to the practical implementation of the multidimensional integral associated with this solution, by using a cubature approach, we finally derive another approximated closed form for the zero-coupon price. This last may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

   
   
   

8. « Bond valuation under lower and upper bounds for the short rate »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   We address here to the issue related to the bond valuation when the associated underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is the case when dealing with the zero lower bound for the interest rate or with the negative interest rates situation. The model considered here is referred to as LUB (Lower and Upper Bound) model and, for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model representation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. As for the Black’s approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristic(s), the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Then we provide the definitive closed formula approximation which is the expected solution, at least from the theoretical point of view. To overcome the difficulty linked to the practical implementation of the multidimensional integral associated with this solution, by using a cubature approach, we finally derive another approximated closed form for the zero-coupon price. This last may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

   
   
   

9. « The Delta-Gamma approximation under a large change of the underlying asset »

   par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
   
   

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   Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

   Abstract

   The Delta-Gamma Approximation (DGA) for the option price is a well-known concept, on which the practical hedging is based on. However, the usage of this tool requires that the underlying asset change should be of a small size. Consequently, there is the need to make a very frequent re-balancing of the portfolio made by the hedging instruments. This situation, unfortunately, induces transaction costs, which may be untenable at last. We contribute here by showing that the DGA can be extended in order to handle large variations of the underlying asset price (as for example between -20 % to -10 % or 10 % to 20 %). A first extension is the local version of a DGA suitable for the situation of large asset changes, in some interval with a moderated size and whose the center is far from the origin. A second possible extension, referred to EDGA, is an approximation-based regression. On one hand, the need for full revaluation in risk measurement and stress testing can be circumvented by using a suitable high order EDGA. On the other hand, for various situations, either the local DGA or a low order EDGA can provide a good replication of the option price change. This has the consequence of enabling to replace the (possibly costly) frequent re-balancing hedging operations by probably just a single (or very few) step operation(s).

   
   
   

10. « Learning to hedge derivatives »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    In risk management, the delta-gamma approximation is extensively used, for instance, for derivatives portfolio hedging (such as options). However, this approximation usually works well locally for small changes of the underlying asset price. When these changes become large, then the derivatives prices estimated by the delta-gamma approximation can be significantly different from those that are estimated using the Black-Scholes formula. In this work, we propose a method that allows us to hedge derivatives such as options even for large changes of their underlying asset prices. While the delta-gamma approximation uses the first- and second-order Greeks for derivatives portfolio hedging, our method is based on hedging with a linear combination of some kernel functions of higher orders. These kernel functions depend in turn on the implied asset price, which in turn is forecasted using the functional data analysis (FDA) approach. On the other hand, the implied volatility term used in the Black-Scholes model to estimate an option price is often considered as constant, while this is not the case in reality. This issue can be addressed by considering a model for the implied volatility such as the Malz model and its variants. In this work, we propose a Machine Learning algorithm (such as the neural network) to learn the implied volatility of the option price and compare its performance to that of the Malz model. Hence, once the implied volatility is learned, we estimate a number of option prices of an asset using the Black-Scholes model for various times-to-maturities. Then, both these instances of option prices and the corresponding asset prices are used to find the weights for the linear combination of the kernel functions that allow us to hedge the considered derivative. We then compare the hedging performance of our approach to that obtained using the delta-gamma approximation with the Malz model that is used to estimate the implied volatility.

    
    
    

11. « La gestion des risques liés aux produits dérivés suivant l’approche en Machine Learning »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    La couverture d’une option financière de type Européen, utilisée par les praticiens et analysée/étudiée par le monde académique, se base essentiellement sur une approximation que l’on réfère dans la suite par DGA (Delta-Gamma-Approximation). Cette dernière est d’autant plus viable que la variation de l’actif sous-jacent est assez faible. Ce qui justifie le fait que la couverture s’effectue en général de manière journalière. Cependant un nombre élevé d’opérations engendre des coûts qui deviennent à la fin économiquement non viable. Espacer les opérations de couverture permet de limiter les coûts mais pourrait faire exposer de pertes conséquentes sur la position du fait que le sous-jacent aurait subi un décalage important, puisque la DGA utilisée ne s’applique plus. Considérer une approximation du changement de prix d’une option dans le cadre d’une variation conséquente de l’actif sous-jacent devient ainsi un problème capital (encore ouvert) pour les couverture et mesures de risque associées à une position isolée ou sur portefeuille. Cette considération est aussi utile actuellement avec les exigences de stress Test selon les directives réglementaires Bâle 3 pour la Banque et Solvabilité 2 pour l’Assurance. Nous avons apporté au moins trois types de solutions à ce problème de DGA sous de large variations du sous-jacent à l’option que l’on peut noter par DGA-mod, DGA-loc et EDGA que l’on peut comprendre respectivement par « DGA modifiée », « DGA locale » et « Extended DGA ». D’amples « What-If-Else-Analyses » ont été effectuées pour faire comprendre à l’utilisateur les forces et limites de ces solutions. D’abord la DGA-mod a été introduite pour corriger une mauvaise utilisation de la DGA classique faîte par beaucoup (à la fois en pratique et en théorie). Ensuite face à l’impossibilité de la DGA classique (même étendue avec un développement d’ordre élevé) pour de large variations des cours du sous-jacent nous avons proposé la notion de DGA-loc. Ce dernier donne de résultats assez spectaculaires et ouvre ainsi de nouvelles voies, à la fois en stress-test et tout aussi bien dans le cadre de gestion d’option à la fois financière ou réelle. Cependant la DGA-loc nécessite une certaine vue de la part de l’utilisateur. Face à cette limitation, nous avons enfin proposé la EDGA qui permet d’atteindre de résultats comparables à ceux obtenus avec la DGA-loc, mais dont le résultat peut être moins satisfaisant que celui obtenu avec la DGA-mod si jamais la variation relative avérée de l’actif sous-jacent est trop faible. La DGA classique est seulement basée sur une utilisation d’une fonction polynôme du second degré pour remplacer la variation de prix (hautement non linéaire) de l’option. Contrairement aux usages connus à travers la littérature et en cohérence avec les pratiques dans l’industrie financière, nous pensons qu’il est utile d’inclure des vues dans l’outil de base même pour établir un remplacement convenable de la DGA classique. C’est ainsi la raison pour laquelle nous faisons appels à une technique de ML. Cette dernière intervient d’abord pour la prédiction des variations possibles et raisonnables du sous-jacent à l’horizon considéré. Ensuite un nouvel appel à une technique de ML est utilisé pour trouver une substitution convenable de la variation de prix de l’option, qui par la suite nous permet de faire une réplication, en vue d’une finalité de couverture ou juste pour parvenir de manière économique (à la fois en moyen et temps de calcul) des mesures de la position sous divers scénarios d’évolutions du cours du sous-jacent.

    
    
    

12. « Forecasting yield-curve distribution under the Negative Interest Rate Policy »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

    
    
    

13. « Bond valuation under lower and upper bounds for the short rate »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    We address in this paper the issue of a bond valuation when the underlying shadow rate is assumed to stay inside a given tunnel, but not only above a lower bound as is considered by various authors when dealing with the zero-lower bound for the interest rate or as with the negative interest rates situation arisen after the policy adopted by the European Central Bank from 2014. The model considered here is referred to as LUB (Lower and Upper Bound) model, and for the simplicity, the underlying shadow rate is assumed to follow the one-factor Vasicek model for the interest rate. Our consideration of the LUB model is not only done under the willing to deal with a model epresentation consistent with market situations observed both in developed and emerging countries, but it is also performed with the intention to provide a helping tool when structuring bespoke financial products linked to interest rates. Indeed, discarding the ranges of interest rate levels not attainable under the market regime may mildly/drastically lower or rise zero-coupon prices. As is well-known for the Black's approach in the context of interest rate zero-lower bound, the LUB restriction on the shadow rate level leads to technical complications in the bond valuation such that getting tractable zero-coupon bond prices is challenging. We first provide a Monte-Carlo explicit based expression for the zero-coupon price, in the sense that this last is given as a deterministic function of the bond characteristics, the model parameters, the underlying state variable and independent realizations of the standard normal Gaussian random variable. Not only the obtained price is helping from the pricing audit point of view, but it has also the advantage to provide a starting point for the derivation of the zero-coupon price sensitivities. Next, using a cubature approach, we derive an approximate closed form for the zero-coupon price which has the advantage to be free of any standard Gaussian random variable realizations and may serve as a quick tool for the LUB model parameter calibration and the underlying shadow rate estimation.

    
    
    

14. « Bond sensitivities when the interest-rates are near the zero lower bound »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

15. « Approximate Closed Formulae for Zero-Coupon Bond Pricing in the Zero Lower Bound Framework »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Since the 2007 financial crisis, many central banks adopted policies to lower their interest rates, whose dynamics can not be captured using classical models. Recently, Meucci and Loregian (2016) proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite the fact that their work distinguishes from others in the literature by their consideration of practical aspects, some technical difficulties still remain, such as the lack of the analytic expression for the zero-coupon bond (ZCB) price. In this work, we provide approximate closed formulae for the ZCB price in the zero lower bound (ZLB) framework, when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Then, a filtering procedure is performed using the Unscented Kalman Filter (UKF) to estimate the unobservable state variable (the shadow rate), and the model calibration is proceeded by estimating the model parameters using the Particle Swarm Optimization (PSO) algorithm. Lastly, empirical illustrations are given and discussed using (as input data) the interest rates of the AAA-rated bonds compiled by the European Central Bank ranging from September 6, 2004 to June 21, 2012.

    
    
    

16. « Forecasting Negative Yield-Curve Distributions »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Negative interest rates are present in various marketplaces since mid-2014, following the negative interest rate policy (NIRP) adopted by the European Central Bank in order to lift the economic growth (and, therefore, the inflation). However, this policy involves difficulties for market practitioners as there is no model that enables to forecast negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable models, the well-known Historical Approach (HA) appears to be a good resource. By tweaking the HA, we derive a data-driven and very tractable tool that allows practitioners to generate yield-curve distribution at future discrete time horizons. So, we provide a robust and easy-to-understand forecasting model, suitable for the NIRP context, allowing to appreciate its prediction power. Besides the methodology development that we present in this work, various numerical illustrations are reported in order to shed light on the benefit (and the limit) of our forecasting approach.

    
    
    

17. « Forecasting yield-curve distribution under the Negative Interest Rate Policy »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

    The nomrevue field is not defined as a custom field. , pages The pages field is not defined as a custom field. , Milan, Italy , The anneedepublication field is not defined as a custom field.
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

    
    
    

18. « Generation of scenarios for the interest rates under the arbitrage-free dynamic Nelson-Siegel model »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

19. « Forecasting Yield-Curve Distribution under the Negative Interest Rate Policy »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

    
    
    

20. « Sensitivities under the G2++ model of yield curve »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

21. « Forecasting yield-curve distribution under the Negative Interest Rate Policy »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Negative interest rates are present in various market places since mid-2014, following the Negative Interest Rate Policy (NIRP) adopted by the European Central Bank in order to lift growth or inflation. This spans difficulties for many market practitioners as there is not yet any model which enables to handle negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable model, the well-known Historical Approach (HA) appears to be a good recourse. By tweaking the HA, we derive a data-driven and very tractable tool allowing various users to generate a distribution forecast of the yield curves at future discrete time horizon. So we provide here a robust and easy-to-understand reference forecasting model, suitable for the NIRP context, allowing to appreciate the prediction power of any ongoing alternative parametric model. Besides the methodology development, various experiments are also reported here in order to shed light in depth on the benefit and limit of our forecasting approach.

    
    
    

22. « Generating joint forecast distributions for stock prices at multiple-time horizons »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Many approaches proposed in the literature to forecast stock prices are based on pointwise forecasts for a single-time horizon. Although the forecast performance obtained from these approaches might provide an acceptable guideline for buying or selling stocks, for the purpose of position management and risk management, one needs to have a notion of a confident range of possible forecasts of stock prices at multiple-time horizons. In this work, we show that the forecast performance can be improved from that of traditional approaches by working along two directions: by generating joint forecast distributions (instead of pointwise forecasts) and by forecasting for multiple-time horizons (instead of a single-time horizon). In particular, we formulate various types of historical-approach based methods (parametric and non-parametric), with various forecast methods (auto-regressive and recurrent neural networks) with various types of probability functions (exogenous and endogenous). Further, we compare the forecast performance achieved from each of these methods from their respective statistical results using real stock prices corresponding to various assets.

    
    
    

23. « Bond valuation when the interest-rates are near the zero lower bound »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Since the 2007 financial crisis, the levels of interest rates in many countries are time-to-time so low such that the common and classical models fail to be functional. Recently, Meucci A. and Loregian A. (2014) have proposed an interest rates approach, based on the inverse-call transformation, which is very transparent from the practical point of view, in comparison with other available models allowing to avoid negative interest rates. However, some technical difficulties remain as for example the non-availability of analytic expression for the zero-coupon bond (ZCB) price. Our purpose in this paper is to provide approximated closed formulas for the ZCB price when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Moreover we derive formulas allowing the user to filter the unobservable state variable involved in the ZCB price, as well as the model parameters.

    
    
    

24. « Bond valuation when the interest-rates are near the zero lower bound »

    par Jae Yun JUN KIM et Yves RAKOTONDRATSIMBA
    
    

    The nomrevue field is not defined as a custom field. , pages The pages field is not defined as a custom field. , Covilha, Portugal , The anneedepublication field is not defined as a custom field.
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur

    Abstract

    Since the 2007 financial crisis, the levels of interest rates in many countries are time-to-time so low such that the common and classical models fail to be functional. Recently, Meucci A. and Loregian A. (2014) have proposed an interest rates approach, based on the inverse-call transformation, which is very transparent from the practical point of view, in comparison with other available models allowing to avoid negative interest rates. However, some technical difficulties remain as for example the non-availability of analytic expression for the zero-coupon bond (ZCB) price. Our purpose in this paper is to provide approximated closed formulas for the ZCB price when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Moreover we derive formulas allowing the user to filter the unobservable state variable involved in the ZCB price, as well as the model parameters.

    
    
    

25. « Stock picking by probability-possibility approaches »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

26. « Control of the price acceptability under the univariate Vasicek model »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

27. « Valuing the probability of generating negative interest rates under the Vasicek one-factor model »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

28. « Correlation as a pricing factor for oil derivatives »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

29. « Commodity futures price under cointegration »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

30. « Valuation and sensitivities of a write-down CoCo »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

31. « Commodities derivatives sensitivities »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

32. « Black-Scholes option sensitivity using high order Greeks. »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

33. « Hedging with a portfolio of Interest rates »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

34. « Commodities Price Sensitivities under the Schwartz-Smith model »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

35. « Enhancement of the bond portfolio immunization under a parallel shift of the yield curve »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur
    
    
    

36. « Enhancement of the Bond Duration-Convexity Approximation »

    par Yves RAKOTONDRATSIMBA
    
    

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    Axe de recherche : Mathématiques pour les Sciences de l'Ingénieur