Global Business&Economic Review-Anthology 2002,371 (2002)
Using insights from real option theory, Abid (2001) developed a new financial instrument that he ... more Using insights from real option theory, Abid (2001) developed a new financial instrument that he called Zero inflation and interest credit opportunity (ZICO) where time is bartered and derived a series of models to value the payoffs of the ZICO’s buyer and seller.
ZICO is defined as a contract by which an investor lends funds to another investor for a certain predetermined period and acquires the right to borrow from the second investor the
same amount of funds and for the same length of time. To value the payoffs of the ZICO buyer, Abid (2001) considered three states of nature determined by the regularity of
investment opportunities. The first model explains how the one-ZICO period can be stated as two sub-periods of time referenced by three points of time. Each sub-period is governed by a set of investment opportunities entirely described by different rates of return. The ZICO buyer
lends funds to the ZICO seller for the first time sub-period and postpone his investment decision for the second ZICO sub-period. At the end of the first sub-period the ZICO seller
reimburses the borrowed funds and lends the same amount to the ZICO buyer for the same length of time. At the end of the second sub-period, which corresponds to the expiration date
of the ZICO contract, the ZICO buyer reimburses the funds he has borrowed. At this stage the
positions of the buyer and the seller are symmetric and ZICO may be seen as a zero sum game. For the payoffs of the buyer and the seller to be equal to zero, the expected return in the
second sub-period must be equal to the half of the expected return in the first sub-period. The second model is derived when the offered investment opportunities are not regular. In that case it is up to the buyer to invest in the second sub-period and wait for only the first subperiod or to continue lending and by the way continue postponing his investment waiting for the opportune moment to invest. The third model is set when investment opportunities are regular with an option to reinvest the payoff of the preceding ZICO contract (ZICO rollingover). The aim of this paper it to extend the discrete ZICO model to continuous time with stochastic returns. The ZICO two sub-periods are decomposed in infinitesimal periods. Returns generated by the first and second ZICO sub-periods respectively are assumed following a Geometrical Brownian motion described by a stochastically differential equation:
The payoff of the ZICO buyer is non linear. It evolutes proportionally to time squared and the difference between twice the instantaneous mean second sub-period return and the instantaneous mean of the first sub-period return. As the difference increases as the payoff of
the ZICO seller decreases and it becomes difficult for him to honour his commitment by reimbursing the buyer at the end of the ZICO first sub-period and lending him the same amount of funds that he borrowed from the ZICO buyer at the beginning of the first subperiod.
In ZICO economy, selection between efficient and inefficient investment decisions is accelerated compared to the standard economy. Acceleration may be measured by the difference of the two instantaneous means’ return . The payoff of the ZICO buyer is generated according to simultaneous effect of half time squared and the difference between twice the
instantaneous mean return that occur in the second sub-period and the instantaneous mean return or opportunity cost in the first sub-period. As selection in the ZICO investmentfinancing strategy is function of time squared this may lead to risk default.
To manage the default risk, velocity variation of the payoff must be reduced. There is a probability that investors will be unable to satisfy some or all of the indenture requirement
so the risk default must be introduce in the initial model to add guarantee and prudence to the fulfilment of the ZICO contract. The idea is to slow down the time quadratic evolution of the
investor’s payoff. To dissipate the velocity of payoff changes we introduce a guarantee term proportional to the return generated in the first ZICO sub-period.
The default risk is defined in the first ZICO sub-period. This risk is materialized by the fact
that the payoff of the seller is a quadratic function of time and if it is negative the seller go bankrupt. The guarantee mechanism allow to assess instantaneously the welfare of the seller as a measure of his ability to satisfy his agreement. With guarantee, return is no longer a linearly increasing function of time but it can be stated as a function that does not change for long term. Return is governed by a function that admit an asymptote determined by the instantaneous mean return over the grantee coefficient.
The Quarterly Review of Economics and Finance, 2009
The crude oil price is generally considered as the fundamental factor in the valuation of undevel... more The crude oil price is generally considered as the fundamental factor in the valuation of undeveloped reserves but it is not the unique one. Undeveloped field value also depends on the uncertainty relating to the convenience yield and the risk-free interest rate. The purpose of this paper is to decide on the best continuous-time stochastic models for these risk factors. The Generalized Method of Moments and the Maximum Likelihood Estimation are implemented to fit the parameters of continuous-time stochastic processes. The results of unit root tests without breaks reveal a mean reversion in convenience yield series. Multiple structural change tests show that the risk-free interest rate can be considered constant. The simulation of continuous-time stochastic processes and the mean error between the simulated prices and the market ones show that the Geometric Brownian Motion with jumps is the best model for the oil price compared to the other commonly used processes.
Journal of Computational and Applied Mathematics, 2009
In this paper, we evaluate a multi-stage information technology investment project, by implementi... more In this paper, we evaluate a multi-stage information technology investment project, by implementing and resolving Berk, Green and Naik’s (2004) model, which takes into account specific features of IT projects and considers the real option to suspend investment at each stage. We present a particular case of the model where the project value is the solution of an optimal control problem with a single state variable. In this case, the model is more intuitive and tractable. The case study confirms the practical potential of the model and highlights the importance of the real-option approach compared to classical discounted cash flow techniques in the valuation of IT projects.
Purpose – The aim of this paper is to study the impact of equity returns volatility of reference ... more Purpose – The aim of this paper is to study the impact of equity returns volatility of reference entities on credit-default swap rates using a new dataset from the Japanese market. Design/methodology/approach – Using a copula approach, the paper models the different relationships that can exist in different ranges of behavior. It studies the bivariate distributions of credit-default swap rates
Global Business&Economic Review-Anthology 2002,371 (2002)
Using insights from real option theory, Abid (2001) developed a new financial instrument that he ... more Using insights from real option theory, Abid (2001) developed a new financial instrument that he called Zero inflation and interest credit opportunity (ZICO) where time is bartered and derived a series of models to value the payoffs of the ZICO’s buyer and seller.
ZICO is defined as a contract by which an investor lends funds to another investor for a certain predetermined period and acquires the right to borrow from the second investor the
same amount of funds and for the same length of time. To value the payoffs of the ZICO buyer, Abid (2001) considered three states of nature determined by the regularity of
investment opportunities. The first model explains how the one-ZICO period can be stated as two sub-periods of time referenced by three points of time. Each sub-period is governed by a set of investment opportunities entirely described by different rates of return. The ZICO buyer
lends funds to the ZICO seller for the first time sub-period and postpone his investment decision for the second ZICO sub-period. At the end of the first sub-period the ZICO seller
reimburses the borrowed funds and lends the same amount to the ZICO buyer for the same length of time. At the end of the second sub-period, which corresponds to the expiration date
of the ZICO contract, the ZICO buyer reimburses the funds he has borrowed. At this stage the
positions of the buyer and the seller are symmetric and ZICO may be seen as a zero sum game. For the payoffs of the buyer and the seller to be equal to zero, the expected return in the
second sub-period must be equal to the half of the expected return in the first sub-period. The second model is derived when the offered investment opportunities are not regular. In that case it is up to the buyer to invest in the second sub-period and wait for only the first subperiod or to continue lending and by the way continue postponing his investment waiting for the opportune moment to invest. The third model is set when investment opportunities are regular with an option to reinvest the payoff of the preceding ZICO contract (ZICO rollingover). The aim of this paper it to extend the discrete ZICO model to continuous time with stochastic returns. The ZICO two sub-periods are decomposed in infinitesimal periods. Returns generated by the first and second ZICO sub-periods respectively are assumed following a Geometrical Brownian motion described by a stochastically differential equation:
The payoff of the ZICO buyer is non linear. It evolutes proportionally to time squared and the difference between twice the instantaneous mean second sub-period return and the instantaneous mean of the first sub-period return. As the difference increases as the payoff of
the ZICO seller decreases and it becomes difficult for him to honour his commitment by reimbursing the buyer at the end of the ZICO first sub-period and lending him the same amount of funds that he borrowed from the ZICO buyer at the beginning of the first subperiod.
In ZICO economy, selection between efficient and inefficient investment decisions is accelerated compared to the standard economy. Acceleration may be measured by the difference of the two instantaneous means’ return . The payoff of the ZICO buyer is generated according to simultaneous effect of half time squared and the difference between twice the
instantaneous mean return that occur in the second sub-period and the instantaneous mean return or opportunity cost in the first sub-period. As selection in the ZICO investmentfinancing strategy is function of time squared this may lead to risk default.
To manage the default risk, velocity variation of the payoff must be reduced. There is a probability that investors will be unable to satisfy some or all of the indenture requirement
so the risk default must be introduce in the initial model to add guarantee and prudence to the fulfilment of the ZICO contract. The idea is to slow down the time quadratic evolution of the
investor’s payoff. To dissipate the velocity of payoff changes we introduce a guarantee term proportional to the return generated in the first ZICO sub-period.
The default risk is defined in the first ZICO sub-period. This risk is materialized by the fact
that the payoff of the seller is a quadratic function of time and if it is negative the seller go bankrupt. The guarantee mechanism allow to assess instantaneously the welfare of the seller as a measure of his ability to satisfy his agreement. With guarantee, return is no longer a linearly increasing function of time but it can be stated as a function that does not change for long term. Return is governed by a function that admit an asymptote determined by the instantaneous mean return over the grantee coefficient.
The Quarterly Review of Economics and Finance, 2009
The crude oil price is generally considered as the fundamental factor in the valuation of undevel... more The crude oil price is generally considered as the fundamental factor in the valuation of undeveloped reserves but it is not the unique one. Undeveloped field value also depends on the uncertainty relating to the convenience yield and the risk-free interest rate. The purpose of this paper is to decide on the best continuous-time stochastic models for these risk factors. The Generalized Method of Moments and the Maximum Likelihood Estimation are implemented to fit the parameters of continuous-time stochastic processes. The results of unit root tests without breaks reveal a mean reversion in convenience yield series. Multiple structural change tests show that the risk-free interest rate can be considered constant. The simulation of continuous-time stochastic processes and the mean error between the simulated prices and the market ones show that the Geometric Brownian Motion with jumps is the best model for the oil price compared to the other commonly used processes.
Journal of Computational and Applied Mathematics, 2009
In this paper, we evaluate a multi-stage information technology investment project, by implementi... more In this paper, we evaluate a multi-stage information technology investment project, by implementing and resolving Berk, Green and Naik’s (2004) model, which takes into account specific features of IT projects and considers the real option to suspend investment at each stage. We present a particular case of the model where the project value is the solution of an optimal control problem with a single state variable. In this case, the model is more intuitive and tractable. The case study confirms the practical potential of the model and highlights the importance of the real-option approach compared to classical discounted cash flow techniques in the valuation of IT projects.
Purpose – The aim of this paper is to study the impact of equity returns volatility of reference ... more Purpose – The aim of this paper is to study the impact of equity returns volatility of reference entities on credit-default swap rates using a new dataset from the Japanese market. Design/methodology/approach – Using a copula approach, the paper models the different relationships that can exist in different ranges of behavior. It studies the bivariate distributions of credit-default swap rates
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Papers by Fathi Abid
ZICO is defined as a contract by which an investor lends funds to another investor for a certain predetermined period and acquires the right to borrow from the second investor the
same amount of funds and for the same length of time. To value the payoffs of the ZICO buyer, Abid (2001) considered three states of nature determined by the regularity of
investment opportunities. The first model explains how the one-ZICO period can be stated as two sub-periods of time referenced by three points of time. Each sub-period is governed by a set of investment opportunities entirely described by different rates of return. The ZICO buyer
lends funds to the ZICO seller for the first time sub-period and postpone his investment decision for the second ZICO sub-period. At the end of the first sub-period the ZICO seller
reimburses the borrowed funds and lends the same amount to the ZICO buyer for the same length of time. At the end of the second sub-period, which corresponds to the expiration date
of the ZICO contract, the ZICO buyer reimburses the funds he has borrowed. At this stage the
positions of the buyer and the seller are symmetric and ZICO may be seen as a zero sum game. For the payoffs of the buyer and the seller to be equal to zero, the expected return in the
second sub-period must be equal to the half of the expected return in the first sub-period. The second model is derived when the offered investment opportunities are not regular. In that case it is up to the buyer to invest in the second sub-period and wait for only the first subperiod or to continue lending and by the way continue postponing his investment waiting for the opportune moment to invest. The third model is set when investment opportunities are regular with an option to reinvest the payoff of the preceding ZICO contract (ZICO rollingover). The aim of this paper it to extend the discrete ZICO model to continuous time with stochastic returns. The ZICO two sub-periods are decomposed in infinitesimal periods. Returns generated by the first and second ZICO sub-periods respectively are assumed following a Geometrical Brownian motion described by a stochastically differential equation:
The payoff of the ZICO buyer is non linear. It evolutes proportionally to time squared and the difference between twice the instantaneous mean second sub-period return and the instantaneous mean of the first sub-period return. As the difference increases as the payoff of
the ZICO seller decreases and it becomes difficult for him to honour his commitment by reimbursing the buyer at the end of the ZICO first sub-period and lending him the same amount of funds that he borrowed from the ZICO buyer at the beginning of the first subperiod.
In ZICO economy, selection between efficient and inefficient investment decisions is accelerated compared to the standard economy. Acceleration may be measured by the difference of the two instantaneous means’ return . The payoff of the ZICO buyer is generated according to simultaneous effect of half time squared and the difference between twice the
instantaneous mean return that occur in the second sub-period and the instantaneous mean return or opportunity cost in the first sub-period. As selection in the ZICO investmentfinancing strategy is function of time squared this may lead to risk default.
To manage the default risk, velocity variation of the payoff must be reduced. There is a probability that investors will be unable to satisfy some or all of the indenture requirement
so the risk default must be introduce in the initial model to add guarantee and prudence to the fulfilment of the ZICO contract. The idea is to slow down the time quadratic evolution of the
investor’s payoff. To dissipate the velocity of payoff changes we introduce a guarantee term proportional to the return generated in the first ZICO sub-period.
The default risk is defined in the first ZICO sub-period. This risk is materialized by the fact
that the payoff of the seller is a quadratic function of time and if it is negative the seller go bankrupt. The guarantee mechanism allow to assess instantaneously the welfare of the seller as a measure of his ability to satisfy his agreement. With guarantee, return is no longer a linearly increasing function of time but it can be stated as a function that does not change for long term. Return is governed by a function that admit an asymptote determined by the instantaneous mean return over the grantee coefficient.
ZICO is defined as a contract by which an investor lends funds to another investor for a certain predetermined period and acquires the right to borrow from the second investor the
same amount of funds and for the same length of time. To value the payoffs of the ZICO buyer, Abid (2001) considered three states of nature determined by the regularity of
investment opportunities. The first model explains how the one-ZICO period can be stated as two sub-periods of time referenced by three points of time. Each sub-period is governed by a set of investment opportunities entirely described by different rates of return. The ZICO buyer
lends funds to the ZICO seller for the first time sub-period and postpone his investment decision for the second ZICO sub-period. At the end of the first sub-period the ZICO seller
reimburses the borrowed funds and lends the same amount to the ZICO buyer for the same length of time. At the end of the second sub-period, which corresponds to the expiration date
of the ZICO contract, the ZICO buyer reimburses the funds he has borrowed. At this stage the
positions of the buyer and the seller are symmetric and ZICO may be seen as a zero sum game. For the payoffs of the buyer and the seller to be equal to zero, the expected return in the
second sub-period must be equal to the half of the expected return in the first sub-period. The second model is derived when the offered investment opportunities are not regular. In that case it is up to the buyer to invest in the second sub-period and wait for only the first subperiod or to continue lending and by the way continue postponing his investment waiting for the opportune moment to invest. The third model is set when investment opportunities are regular with an option to reinvest the payoff of the preceding ZICO contract (ZICO rollingover). The aim of this paper it to extend the discrete ZICO model to continuous time with stochastic returns. The ZICO two sub-periods are decomposed in infinitesimal periods. Returns generated by the first and second ZICO sub-periods respectively are assumed following a Geometrical Brownian motion described by a stochastically differential equation:
The payoff of the ZICO buyer is non linear. It evolutes proportionally to time squared and the difference between twice the instantaneous mean second sub-period return and the instantaneous mean of the first sub-period return. As the difference increases as the payoff of
the ZICO seller decreases and it becomes difficult for him to honour his commitment by reimbursing the buyer at the end of the ZICO first sub-period and lending him the same amount of funds that he borrowed from the ZICO buyer at the beginning of the first subperiod.
In ZICO economy, selection between efficient and inefficient investment decisions is accelerated compared to the standard economy. Acceleration may be measured by the difference of the two instantaneous means’ return . The payoff of the ZICO buyer is generated according to simultaneous effect of half time squared and the difference between twice the
instantaneous mean return that occur in the second sub-period and the instantaneous mean return or opportunity cost in the first sub-period. As selection in the ZICO investmentfinancing strategy is function of time squared this may lead to risk default.
To manage the default risk, velocity variation of the payoff must be reduced. There is a probability that investors will be unable to satisfy some or all of the indenture requirement
so the risk default must be introduce in the initial model to add guarantee and prudence to the fulfilment of the ZICO contract. The idea is to slow down the time quadratic evolution of the
investor’s payoff. To dissipate the velocity of payoff changes we introduce a guarantee term proportional to the return generated in the first ZICO sub-period.
The default risk is defined in the first ZICO sub-period. This risk is materialized by the fact
that the payoff of the seller is a quadratic function of time and if it is negative the seller go bankrupt. The guarantee mechanism allow to assess instantaneously the welfare of the seller as a measure of his ability to satisfy his agreement. With guarantee, return is no longer a linearly increasing function of time but it can be stated as a function that does not change for long term. Return is governed by a function that admit an asymptote determined by the instantaneous mean return over the grantee coefficient.