INDEM - Working Paper Business Economic Series

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Golden options in financial mathematics
(2018-11) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto para el Desarrollo de Empresas y Mercados (INDEM)
This paper deals with the construction of smooth good deals (SGD), i.e., sequences of self- nancing strategies whose global risk diverges to ∞ and such that every security in every strategy of the sequence is a smooth derivative with a bounded delta. If the selected risk measure is the value at risk then these sequences exist under quite weak conditions, since one can involve risks with both bounded and unbounded expectation, as well as non-friction-free pricing rules. Moreover, every strategy in the sequence is composed of an European option plus a position in a riskless asset. The strike of the option is easily computed in practice, and the ideas may also apply in some actuarial problems such as the selection of an optimal reinsurance contract. If the chosen risk measure is a coherent one then the general setting is more limited. Indeed, though frictions are still accepted, expectations and variances must remain nite. The existence of SGDs will be characterized, and computational issues will be properly addressed as well. It will be shown that SGDs often exist, and for the conditional value at risk they are composed of the riskless asset plus easily replicable European puts. Numerical experiments will be presented in all of the studied cases.
CIFRA: Challenging the ICT Patent Framework for Responsible Innovation. D4.4: Policy Paper on potential new framings, identifying needs for changing the current IPR regime relevant for ICT industries
(2017-10-01) Fullea Carrera, Eduardo; López-Carrasco, Antonio; Blind, Knut; Florez Ramos, Esmeralda; Fosfuri, Andrea; Martínez-Ros, Ester; Álvarez Iturri, Silvana Valeria; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
Relationships between the stochastic discount factor and the optimal omega ratio
(2018-02-01) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
The omega ratio is an interesting performance measure because it fo- cuses on both downside losses and upside gains, and nancial markets are re ecting more and more asymmetry and heavy tails. This paper focuses on the omega ratio optimization in general Banach spaces, which applies for both in nite dimensional approaches related to continuous time stochastic pricing models (Black and Scholes, stochastic volatility, etc.) and more classical problems in portfolio selection. New algorithms will be provided, as well as Fritz John-like and Karush-Kuhn-Tucker-like optimality conditions and duality results, despite the fact that omega is neither di¤er- entiable nor convex. The optimality conditions will be applied to the most important pricing models of Financial Mathematics, and it will be shown that the optimal value of omega only depends on the upper and lower bounds of the pricing model stochastic discount factor. In particular, if the stochastic discount factor is unbounded (Black and Scholes, Heston, etc.) then the optimal omega ratio becomes unbounded too (it may tend to in nity), and the introduction of several nancial constraints does not overcome this caveat. The new algorithms and optimality conditions will also apply to optimize omega in static frameworks, and it will be illustrated that both in nite- and nite-dimensional approaches may be useful to this purpose.
Interest Rate Future Quality Options and Negative Interest Rates
(2017-07-10) Balbás, Alejandro; Laborda Herrero, Ricardo; Universidad Carlos III. Instituto para el Desarrollo Empresarial;
This paper verifies the existence of diversification gains from considering the "quality option asset strategy", which adds the portfolio replicating the interest rate future quality option, as proposed by Balbás and Reichardt (2010), and a portfolio comprised of stock and bonds. The empirical results show that the gains are statistically and economically significant, especially in the negative one-month Euribor rate period. The out-of-sample optimal tangency portfolio, which includes "quality option replicas", delivers an increase in the Sharpe ratio of around 40%, as well as a positive returnHloss oIseJng the costs of higher turnover. The main source of the diversiKcaLon gains emanates from the very low correlation between quality options and stocks. Furthermore, the (at least theoretical) existence of sequential arbitrage under negative rates magnifies the low correlation effect.
Pricing the quality of an innovative idea
(2017-02-09) Alvarez Iturri, Silvana Valeria; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial;
This paper aims to analyze whether the quality of an innovative idea can spur the patent's price. From an economic perspective, we address the question of how the quality of an innovative idea increases the patent's price. We examine the problem for the case of a single innovation rather than patent´s families. Therefore, we follow the assumption that innovative ideas have patents. Nevertheless, the analysis is divided into two stages; first we estimated the quality of the innovation by quantifying information of the patent documents from the patent portfolios of firms of the ICT sector over the period 1996 to 2015. By providing new empirical evidence, we showed that the patent´s quality can be estimate with multiple observed patents' characteristics which are significant related to the utility of the patent in the market and its impact on the follow-on innovation. The analyses also estimate the patent's price in the market for technologies based on the quality index. In the same way, we used information of the patent´s transaction in the ICT sector over the period of 2012- 2015 and review the main costs of the American, European and the international patent system. Our finale results indicate the possibility to reduce the asymmetric information of the quality in the patent´s transactions by using public information.
Differential equations connecting VaR and CVaR
(2017-01-09) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial;
The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while super- visors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither differentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satis es all of these properties, and this simpli es many ana- lytical studies if VaR is replaced by CVaR. In this paper several differential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very efficient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent differentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given.
The newsvendor problem with convex risk
(2016-12-12) Charron, Jean Philippe; Balbás, Alejandro; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
The newsvendor problem is a classical topic in Management Science and Operations Research. It deals with purchases and price strategies when a least one deadline is involved. In this paper we will assume that the decision is driven by an optimization problem involving both expected pro ts and risks. As a main novelty, risks will be given by a convex risk measure, including the usual utility functions. This approach will allow us to nd necessary and su¢ cient optimality conditions under very general frameworks, since we will not need any speci c assumption about the demand distribution.
Must an optimal buy and hold strategy contain any derivative?
(2016-11-21) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial;
Consider a portfolio choice problem maximizing the expected return and simultaneously minimizing a general (and frequently coherent) risk measure. This paper shows that every stock (or stock index) is often outperformed by a buy and hold strategy containing some of its derivatives and the underlying stock itself. As a consequence, every investment only containing international benchmarks will not be efficient, and the investors must properly add some derivatives. Though there is still a controversy, this finding had been pointed out in dynamic frameworks, but the novelty is that one does not need to rebalance the portfolio of derivatives before their expiration date. This is very important in practice because transaction costs are sometimes significant when trading derivatives.
Good deal measurement in asset pricing: Actuarial and financial implications
(2016-09-12) Balbás, Alejandro; Garrido, José; Okhrati, Ramin
We will integrate in a single optimization problem a risk measure beyond the variance and either arbitrage free real market quotations or financial pricing rules generated by an arbitrage free stochastic pricing model. A sequence of investment strategies such that the couple (risk; price) diverges to (-∞, -∞) will be called good deal. We will see that good deals often exist in practice, and the paper main objective will be to measure the good deal size. The provided good deal measures will equal an optimal ratio between both risk and price, and there will exist alternative interpretations of these measures. They will also provide the minimum relative (per dollar) price modification that prevents the good deal existence. Moreover, they will be a crucial instrument to detect those securities or marketed claims which are over or under-priced. Many classical actuarial and financial optimization problems may generate wrong solutions if the used market quotations or stochastic pricing models do not prevent the good deal existence. This fact will be illustrated in the paper, and it will be pointed out how the provided good deal measurement may be useful to overcome this caveat. Numerical experiments will be yielded as well.
Dificultades en la aplicación de las deducciones fiscales por actividades de I+D+i
(2016-05-09) Fernández Sánchez, Inés; Martínez-Ros, Ester; Universidad Carlos III de Madrid. Instituto par el Desarrollo Empresarial (INDEM)
A pesar de que los incentivos fiscales, y dentro de ellos las deducciones fiscales, son uno de los principales mecanismos que el sector público en España utiliza para fomentar las actividades de investigación, desarrollo e innovación (en adelante I+D+i), es constatable el hecho de que las empresas innovadoras no aplican esta deducción tanto como se esperaría. El objetivo de nuestro estudio busca ampliar el conocimiento y entendimiento de las dificultades que las empresas tienen a la hora de aplicar las deducciones fiscales, lo que es una cuestión novedosa ya que hasta el momento no existe un análisis cuantificado del peso de los obstáculos percibidos en la aplicación de este tipo de incentivos. Para ello analizaremos los datos extraídos de la Encuesta sobre Innovación en las Empresas, concretamente en el año 2008 ya que es el primer y, de momento, único año para el que se dispone de información en relación con estas cuestiones. Los resultados del análisis muestran que la mayoría de las empresas conoce la deducción y su normativa y que las principales razones por las que las empresas (tanto grandes empresas como PYMES) no aplican deducciones por actividades de I+D+i están relacionadas con el gasto en estas actividades: por un lado las empresas que pese a innovar no aplican deducciones por actividades de I+D+i consideran tener un gasto muy pequeño en esas actividades (lo que entendemos unido a que el procedimiento de aplicación suele ser largo y costoso puede ser un motivo por el que no les compense su aplicación) y, por otro lado, que el concepto de gasto recogido en la normativa &- y por el cual cabría aplicar la deducción &- no siempre coincide con el concepto de gasto realizado por las empresas. Por último, podemos afirmar que la no aplicación de la deducción fiscal para actividades de I+D+i no se debe ni al desconocimiento de la normativa que la regula ni a la consideración de que ésta sea ambigua.
Coherent Pricing
(2016-05-09) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto par el Desarrollo Empresarial (INDEM)
Recent literature proved the existence of an unbounded market price of risk (MPR) or maximum generalized Sharpe ratio (GSR) if one combines the most important Brownian-motion-linked arbitrage free pricing models with a coherent and expectation bounded risk measure. Furthermore, explicit sequences of portfolios with a theoretical (risk, return) diverging to (��1;+1) were constructed and their performance tested. The empirical evidence revealed that the divergence to (��1;+1) is only theoretical (not real), but the MPR is much larger than the GSR of the most important international stock indices. The natural question is how to modify the available pricing models so as to prevent the caveat above. The theoretical MPR cannot equal inf nity but must be large enough (consistent with the empirical findings) and this will be the focus of this paper. It will be shown that every arbitrage free pricing model can be improved in such a manner that the new stochastic discount factor (SDF) satisfie the two requirements above, and the newMPR becomes bounded but large enough. This is important for several reasons; Firstly, if the existent models predict unrealistic price evolutions then these mistakes may imply important capital losses to practitioners and theoretical errors to researchers. Secondly, the lack of an unbounded MPR is much more coherent and consistent with equilibrium. Finally, the major discrepancies between the initial pricing model and the modifie one will affect the tails of their SDF, which seems to justify several empirical caveats of previous literature. For instance, it has been pointed out that it is not easy to explain the real quotes of many deeply OTM options with the existing pricing models.
VaR as the CVaR sensitivity : applications in risk optimization
(2016-02-01) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto par el Desarrollo Empresarial (INDEM)
VaR minimization is a complex problem playing a critical role in many actuarial and financial applications of mathematical programming. The usual methods of convex programming do not apply due to the lack of sub-additivity. The usual methods of differentiable programming do not apply either, due to the lack of continuity. Taking into account that the CVaR may be given as an integral of VaR, one has that VaR becomes a first order mathematical derivative of CVaR. This property will enable us to give accurate approximations in VaR optimization, since the optimization VaR and CVaR will become quite closely related topics. Applications in both finance and insurance will be given.
Sequential arbitrage measurement in bond markets : theory and empirical applications in the Euro-zone
(2015-01-14) Balbás, Alejandro; Peng, Yao; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
We develop a mathematical programing approach in order to measure the arbitrage size in bond markets. Transaction costs may be incorporated. The obtained arbitrage measures have two interesting interpretations: On the one hand they provide the highest available arbitrage profit with respect to the price of the sold (bought) securities. On the other hand they give the minimum relative (per dollar) bid (ask) price modification leading to an arbitrage free market. Moreover, some primal problems lead to optimal arbitrage strategies (if available), while their dual problems generate proxies for the Term Structure of Interest Rates. The developed methodology permits us to implement an empirical test in the Euro-zone during the Euro crisis. Classical literature justifies the relevance of empirical analyses verifying the degree of efficiency during market turmoils. Our empirical study of the German, French and Spanish sovereign bonds markets finds that the main arbitrage opportunities come from the price differences between maturity-matched strips or "On-The-Run Premium" for zero-coupon bonds. When we remove the strips and the zero-coupon bonds the arbitrage still exists in the Spanish market.
Optimal reinsurance under risk and uncertainty
(2014-06-01) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Rodríguez de las Heras Pérez, Antonio; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated. Three main contributions seem to be reached. Firstly, necessary and sufficient opti- mality conditions are given. Secondly, the optimal contract is often a bang-bang solution, i:e:, the sensitivity between the retained risk and the total claims saturates the imposed constraints. For some special cases the optimal contract might not be bang-bang, but there is always a bang-bang contract as close as desired to the optimal one. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be impor- tant because linear problems are easy to solve in practice, since there are very efficient algorithms.
Bank Competition, Borrower Competition and Interest Rates
(2014-06-16) Bellón, Carlos; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
The effect bank competition has on interest rates should depend on the fact that borrowers compete against each other. The borrowing rate of a firm affects its ability to compete in the industrial marketplace, and ultimately, its ability to repay its loans. Thus, competition amongst borrowers acts as a limit to the amount of rents financial oligopolists can extract. I find evidence that firms that operate within areas of limited bank competition face higher rates than their peers. I also identify an innovative control group that can be used in tests of bank market structure.
Information disclosure in optimal auctions
(2014-03) Ganuza, Juan-José; Penalva, José; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
A celebrated result in auction theory is that the optimal reserve price in the standard private value setting does not depend on the number of bidders. We modify the framework by considering that the seller controls the accuracy with which bidders learn their valuations, and show that in such a case, the greater the number of bidders the more restrictive the reserve price. We also show that the auctioneer provides more information when using an optimal auction mechanism than when the object is always sold.
Market orientation and academic spin-off firms
(2014-01) Abbate, Tindara; Cesaroni, Fabrizio; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
Purpose: Academic spin-off firms are considered an important mechanism to transfer technological knowledge from university to industry, although they often show a low growth rate. One possible cause is the lack of proper marketing capabilities, since spin-off managers tend to reduce the role of marketing to the implementation of mere tactical activities. This study analyses whether spin-off firms adopt a market orientation and the effect it produces on firms' economic and innovation performance. Design/methodology/approach: The empirical analysis is based on both quantitative survey data and in-depth interviews, referring to a unique sample including Italian and Spanish spin-off companies. Findings: Results highlight that MKTOR and MARKOR measurement scales show different abilities to capture the implementation of market orientation by sampled firms. We find that the generation and dissemination of information on customers and competitors directly affect firms' ability to develop technological innovations and gain profits. Nevertheless, market orientation also constitutes a challenge to spin-offs, and may eventually generate inefficiencies when external technological conditions require firms to respond quickly to environmental stimuli. Practical implications: The findings of this study are relevant to academic spin-off managers who are responsible for adopting, implementing and maintaining market orientation strategies under different environmental conditions. Limitations: The characteristics of sample used for the quantitative analysis may limit the generalization of results. Originality/value: Even though the market orientation concept has been largely analyzed, no previous study has examined its application by academic spin-offs. By employing qualitative and quantitative analyses we provide novel insights in this respect.
Equity, commodity and interest rate volatility derivatives
(2013) Balbás, Alejandro; Blanco, Iván; Navarro, Eliseo; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
A new methodology to construct synthetic volatility derivatives is presented. The underlying asset price process is very general, since equity, commodities and interest rates are included. The focus is on volatility swaps and volatility swap options, but much more derivatives may be considered. The proposed methods optimize the conditional value at risk of the non-hedged risk, and yields both bid and ask prices, as well as optimal hedging strategies for both purchases and sales. Upper bounds for the broker capital losses under very negative scenarios are given. Numerical experiments are presented so as to illustrate the performance in practice of this new approach.
On the inefficiency of Brownian motions and heavier tailed price processes
(2013) Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
Recent literature has shown the existence of pathologies if one combines the most important models for pricing and hedging derivatives and coherent risk measures. There may exist portfolios (good deals) whose (return; risk) is as close as desired to (1; 􀀀1). This paper goes beyond existence properties and looks for explicit constructions and empirical tests. It will be shown that the good deal above may be a combination of European and digital options, very easy to replicate in practice. This theoretical nding will enable us to implement empirical experiments involving three international stock indices (S&P_500, Eurostoxx_50 and DAX) and three commodity futures (Gold, Brent and DJ 􀀀 UBSCI). According to the empirical results, the good deal always outperforms the underlying index/commodity. The good deal is built in full compliance with the standard Derivative Pricing Theory. Properties of classical pricing models totally inspire and lead the good deal construction. This is a very interesting di¤erence with respect to previous literature attempting to outperform a benchmark. Besides, the selected pricing models satisfy the existence of risk neutral probabilities such that self- nancing price processes become martingales. According to recent results, while local martin- gales characterize the absence of arbitrage, martingales characterize the existence of equilibrium. However, this equilibrium is di¢ cult to imagine, because for every portfolio traders can build a new one with identical price, higher return and lower risk. Perhaps dynamic arbitrage free pricing models contradict other important achievements of Financial Economics related to e¢ ciency and equilibrium, and further research is required to recover consistency.
The Role of Connections in Academic Promotions
(2012-09-07) Zinovyeva, Natalia; Bagues, Manuel F.; Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial (INDEM)
This paper analyzes the role of connections in academic promotions. We exploit evidence from centralized evaluations in Spain, where evaluators are randomly as- signed to promotion committees. We nd that prior connections between candidates and evaluators have a dramatic impact on candidates' success. For instance, the presence of a co-author or an advisor in the committee is equivalent to a standard deviation increase in candidates' research output. The e ect of a weaker link, such as a member of candidate's doctoral thesis committee, is one fourth as large. The source of the premium enjoyed by connected candidates depends on the nature of their relationship with committee members. In the case of weak links, informa- tional gains tend to dominate evaluation biases. Candidates promoted by a weak link turn out to be more productive in the future relative to other promoted candi- dates. However, consistently with the potential existence of favoritism, candidates promoted by a strong connection exhibit a signi cantly worse research record both before and after the evaluation.

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