Testing option pricing with the Edgeworth expansion

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments. (C) 2004 Elsevier B.V. All rights reserved.

Branch and bound algorithm for transmission system expansion planning using a transportation model

A method for optimal transmission network expansion planning is presented. The transmission network is modelled as a transportation network. The problem is solved using hierarchical Benders decomposition in which the problem is decomposed into master and slave subproblems. The master subproblem models the investment decisions and is solved using a branch-and-bound algorithm. The slave subproblem models the network operation and is solved using a specialised linear program. Several alternative implementations of the branch-and-bound algorithm have been rested. Special characteristics of the transmission expansion problem have been taken into consideration in these implementations. The methods have been tested on various test systems available in the literature.

Bone healing in drill hole defects in spontaneously hypertensive male and female rats' femurs. A histological and histometric study

Objective: the aim of this study was to evaluate the bone healing in spontaneously hypertensive rats (SHR) and compare the results with normotensive rats, evaluating male and female animals.Methods: A bone drill defect was created in the left femur of 24 SHR (12 males and 12 females) and 24 normotensive rats (12 males and 12 females). The animals were divided into two groups and sacrificed 7 and 21 days after the surgical procedure. After the routine laboratory processing, histological and histometric analysis were carried out and data were submitted to ANOVA and Tukey's test (5%).Results: Males and females from the same group had similar histological characteristics. After seven days, all animals presented irregular bone trabeculae. The periosteal osteoblasts were flattened in SHR, and presented a cuboid shape in normotensive animals. After 21 days, the bone defects of all specimens showed a linear closure in all the superficial extension. In addition, SHR presented flattened osteoblasts surrounding the bone trabeculae, while normotensive ones showed cuboidal cells. Statistical analysis of the histometric data indicated similar means between the male and female groups, except for normotensive rats on day 7. In addition, a larger amount of new bone formation was observed in hypertensive when compared to normotensive rats on day 27, in males as well as females.Conclusion: We conclude that bone healing in SHR was more significant than in normotensive ones, as shown by the histological and histometric evaluation 21 days after surgery.

Evaluation of the thermal shrinkage of titanium and the setting and thermal expansion of phosphate-boded investments

Statement of problem. There are few studies on titanium casting shrinkage, and phosphate-bonded investments for titanium casting have not produced appropriate marginal fit.Purpose. The purpose of this study was to determine the thermal shrinkage of titanium and the setting and thermal expansion of 3 phosphate-bonded investments.Material and methods. The thermal shrinkage between the melting temperature and room temperature was calculated using a titanium thermal expansion coefficient. The thermal and setting expansion were measured for 3 phosphate bonded investments: Rematitan Plus (RP) specific for titanium, Rema Exakt (RE), and Castorit Super C (CA), using different special liquid concentrations (100%, 75%, and 50%). Setting expansion was measured for cylindrical specimens 50 mm long x 8 mm in diameter with a transducer. The heating and cooling curves were obtained with a dilatometer (DIL 402 PC). The total expansion curve was drawn using software, and temperatures to obtain expansion equivalent to titanium casting shrinkage were determined (n=5). In addition, the total expansion of the control group (RP at 430 degrees C) was measured, as well as the temperatures at which the other groups achieved equivalent total expansion (n=5). Data were analyzed by 1-way ANOVA and the Tukey HSD test (alpha=.05).Results. Titanium casting shrinkage was estimated as 1.55%. RP did not achieve this expansion. RE achieved expansion of 1.55% only with a special liquid concentration of 100% at 594 degrees C. CA with all special liquid concentrations attained this expansion (351 degrees C to 572 degrees C). Total expansion of the control group was 0.86%, and the other groups reached that expansion within the range of 70 degrees C to 360 degrees C.Conclusions. Only RE and CA demonstrated sufficient expansion to compensate for titanium casting shrinkage. All groups reached total expansion equivalent to that of the control group at significantly lower temperatures.

Parallel simulated annealing applied to long term transmission network expansion planning

The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.

Using traditional heuristic algorithms on an initial genetic algorithm population applied to the transmission expansion planning problem

This paper analyses the impact of choosing good initial populations for genetic algorithms regarding convergence speed and final solution quality. Test problems were taken from complex electricity distribution network expansion planning. Constructive heuristic algorithms were used to generate good initial populations, particularly those used in resolving transmission network expansion planning. The results were compared to those found by a genetic algorithm with random initial populations. The results showed that an efficiently generated initial population led to better solutions being found in less time when applied to low complexity electricity distribution networks and better quality solutions for highly complex networks when compared to a genetic algorithm using random initial populations.

Cross-hole and seismic CPT tests in a tropical soil site

A large portion of Brazil is covered with tropical soils but literature about dynamic parameters of these soils is very limited. SCPT and cross-hole tests were carried out at an experimental research site inland in the state of São Paulo, Brazil. Shear wave velocities (VS) determined based on both tests are presented and compared. A good agreement was observed between both test results and the differences can be associated with soil variability, which was very sensitive to CPT tests. It was also observed that Go/q c ratio determined based on SCPT appears to be an interesting technique to help identify tropical soils. Copyright ASCE 2006.

Market-driven security-constrained transmission network expansion planning

This paper presents a Bi-level Programming (BP) approach to solve the Transmission Network Expansion Planning (TNEP) problem. The proposed model is envisaged under a market environment and considers security constraints. The upper-level of the BP problem corresponds to the transmission planner which procures the minimization of the total investment and load shedding cost. This upper-level problem is constrained by a single lower-level optimization problem which models a market clearing mechanism that includes security constraints. Results on the Garver's 6-bus and IEEE 24-bus RTS test systems are presented and discussed. Finally, some conclusions are drawn. © 2011 IEEE.

A combinatorial approach for transmission expansion & reactive power planning

A metaheuristic technique for solving the short-term transmission network expansion and reactive power planning problems, at the same time, in regulated power systems using the AC model is presented. The problem is solved using a real genetic algorithm (RGA). For each topology proposed by RGA an indicator is employed to identify the weak buses for new reactive power sources allocation. The fitness function is calculated using the cost of each configuration as well as constraints deviation of an AC optimal power flow (OPF) in which the minimum reactive generation of new reactive sources and the active power losses are objectives. With allocation of reactive power sources at load buses, the circuit capacity increases and the cost of installation could be decreased. The method is tested in a well known test system, presenting good results when compared with other approaches. © 2011 IEEE.

Domain reduction using GRASP construction phase for transmission expansion planning problem

This paper proposes a new strategy to reduce the combinatorial search space of a mixed integer linear programming (MILP) problem. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) is employed to reduce the domain of the integer variables of the transportation model of the transmission expansion planning (TM-TEP) problem. This problem is a MILP and very difficult to solve specially for large scale systems. The branch and bound (BB) algorithm is used to solve the problem in both full and the reduced search space. The proposed method might be useful to reduce the search space of those kinds of MILP problems that a fast heuristic algorithm is available for finding local optimal solutions. The obtained results using some real test systems show the efficiency of the proposed method. © 2012 Springer-Verlag.

Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem

This paper proposes strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem (TEP). The concept of the binary numeral system (BNS) is used to reduce the number of binary and continuous variables related to the candidate transmission lines and network constraints that are connected with them. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) and additional constraints, obtained from power flow equilibrium in an electric power system are employed for more reduction in search space. The multistage TEP problem is modeled like a mixed binary linear programming problem and solved using a commercial solver with a low computational time. The results of one test system and two real systems are presented in order to show the efficiency of the proposed solution technique. © 1969-2012 IEEE.

Risk/investment-driven transmission expansion planning with multiple scenarios

This study presents a new methodology based on risk/investment to solve transmission network expansion planning (TNEP) problem with multiple future scenarios. Three mathematical models related to TNEP problems considering multiple future generation and load scenarios are also presented. These models will provide planners with a meaningful risk assessment that enable them to determine the necessary funding for transmission lines at a permissible risk level. The results using test and real systems show that the proposed method presents better solutions compared with scenario analysis method. ©The Institution of Engineering and Technology 2013.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Multistage Transmission Expansion Planning Considering Fixed Series Compensation Allocation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A mixed-integer quadratically-constrained programming model for the distribution system expansion planning

This paper presents a mixed-integer quadratically-constrained programming (MIQCP) model to solve the distribution system expansion planning (DSEP) problem. The DSEP model considers the construction/reinforcement of substations, the construction/reconductoring of circuits, the allocation of fixed capacitors banks and the radial topology modification. As the DSEP problem is a very complex mixed-integer non-linear programming problem, it is convenient to reformulate it like a MIQCP problem; it is demonstrated that the proposed formulation represents the steady-state operation of a radial distribution system. The proposed MIQCP model is a convex formulation, which allows to find the optimal solution using optimization solvers. Test systems of 23 and 54 nodes and one real distribution system of 136 nodes were used to show the efficiency of the proposed model in comparison with other DSEP models available in the specialized literature. (C) 2014 Elsevier Ltd. All rights reserved.