A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Un modelo de riesgo de crédito basado en opciones compuestas con barrera. Aplicación al mercado continuo español

In this work the valuation methodology of compound option written on a downand-out call option, developed by Ericsson and Reneby (2003), has been applied to deduce a credit risk model. It is supposed that the firm has a debt structure with two maturity dates and that the credit event takes place when the assets firm value falls under a determined level called barrier. An empirical application of the model for 105 firms of Spanish continuous market is carried out. For each one of them its value in the date of analysis, the volatility and the critical value are obtained and from these, the default probability to short and long-term and the implicit probability in the two previous probabilities are deduced. The results are compared with the ones obtained from the Geskemodel (1977).

Un modelo de riesgo de crédito basado en opciones compuestas con barrera. Aplicación al mercado continuo español

In this work the valuation methodology of compound option written on a downand-out call option, developed by Ericsson and Reneby (2003), has been applied to deduce a credit risk model. It is supposed that the firm has a debt structure with two maturity dates and that the credit event takes place when the assets firm value falls under a determined level called barrier. An empirical application of the model for 105 firms of Spanish continuous market is carried out. For each one of them its value in the date of analysis, the volatility and the critical value are obtained and from these, the default probability to short and long-term and the implicit probability in the two previous probabilities are deduced. The results are compared with the ones obtained from the Geskemodel (1977).

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

On the term structure of Interbank interest rates: Jump-diffusion processes and option pricing

In this paper we study the dynamic behavior of the term structureof Interbank interest rates and the pricing of options on interest ratesensitive securities. We posit a generalized single factor model withjumps to take into account external influences in the market. Daily datais used to test for jump effects. Qualitative examination of the linkagebetween Monetary Authorities' interventions and jumps are studied. Pricingresults suggests a systematic underpricing in bonds and call options ifthe jumps component is not included. However, the pricing of put optionson bonds presents indeterminacies.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

Australian Asian options

We study European options on the ratio of the stock price to its averageand viceversa. Some of these options are traded in the Australian StockExchange since 1992, thus we call them Australian Asian options. Forgeometric averages, we obtain closed-form expressions for option prices.For arithmetic means, we use dierent approximations that produce verysimilar results.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

Environment conditions and biological innovations in the european agrarian growth, 1819-1939

The circumstances that were the driving forces behind Europe's economic growth beginning in the 19th century are diverse, and not easily prioritized. Until the 1970's, specifically, in Economy and Economic History, attention was focused on different institutional and technological variables, and various regularities were proposed. Nevertheless, new studies also underlined that the evolution of economic activity could not be understood considering only the new production possibilities offered by market economies. As a result, today it is also accepted that those processes can not be explained without considering two additional circumstances: the energy flows that sustained them, and the changes undergone in their transformation In this context, a question arises that takes on special importance. Which was the influence of the biological change in the economic growth?. A part of the flows of energy must be made into food, and this transformation can only happen with the participation.