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Economic and industrial growth in the twentieth century allowed electricity to be generated centrally and transported over long distances. Economies of scale in electricity generation led to an increase in power output and massive power systems. A balance of demand and supply was possible by the average combination of large, instantaneously varying loads. Security of supply increased because the failure of one power plant was compensated by other power plants in an interconnected system. For the purposes of this book, the electric power system grid is composed of the generation system, the transmission system, the distribution system, and the loads. Although the electric power market had experienced steady growth for several decades, changes in fuel economy, congestion, and required investments in transmission, distribution, and generation were required to meet ever-increasing demand. This demand eventually reached a critical level that threatened system integrity, reliability, and ef ciency. Deregulation of the power industry made the transmission network accessible in a nondiscriminatory manner. Distributed generation made remote central power plants a feasible and cost-effective strategy for power generation. This type of clean, full-time on-site power generation is based on technologies such as turbines



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Due to the comprehensiveness of the book, it can be used by professors as either a primary text or a supplementary text in their courses The chapters are grouped into two main sections: The rst focuses on the pricing of equity derivatives and comprises 1 to 9, and the second part focuses on the pricing of interest rate derivatives: 10 to 14 1 focuses on the derivation and foundations of the Black-Scholes model for asset pricing in the risk-neutral world The Black-Scholes partial differential equation describes the evolution of all derivatives whose payoff is a function on a single underlying asset following geometric Brownian motion (GBM) and time 2 discusses Monte Carlo methods for valuation of European as well as path-dependent derivatives Various random number generators for pseudorandom, quasi-random (deterministic), Sobol, and Faure sequences are discussed.





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Only a slight modification of the theory in Section 9.3 is required to accommodate this situation. Let us assume we have waves W1, W2, . . . Wq, with n1, n2, . . . nq respondents. Panel members may have missing values in a subset of the waves. The total number of respondents who participate in at least one of the waves is equal to n. For each wave W a population total t (or a population mean mt =t /N ) is given for a vector of auxiliary variables x , =1, 2, . . . q. These auxiliary variables may be constant over time (like year of birth) or may vary over time (like income). We formulate the problem in terms of population means. Then the question is: can we construct weights in such a way that the correct expected sampling totals at time are reproduced, that is, X wi xki n k : 9:5

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Variance reduction techniques using control variates and antithetics are discussed to overcome the computational inef ciency of the Monte Carlo method in its basic form, which typically requires hundreds of thousands of simulations to achieve good accuracy 3 discusses the binomial tree model for pricing European and American equity options The binomial tree is shown to be a two-state discrete approximation to continuous GBM: The mean and variance of the binomial model match the mean and variance of the lognormal distribution underlying GBM Furthermore, the binomial model can be adapted to incorporate time-varying volatility, to pricing path-dependent options, and to pricing derivatives depending on more than one asset with two-variable binomial trees 4 generalizes binomial trees to the more exible and widely used trinomial trees, which approximate GBM diffusion processes with three states It also discusses implied trees, which are trees constructed to t observable market prices.

Hull (1996), 447.

Thus, this method builds trees implied by the market 5 discusses nite-difference methods, numerical methods (actually, extensions of the trinomial method) for discretizing PDEs that (path-dependent) derivatives with complex payoffs must satisfy and then solving them over a state-time lattice The explicit, implicit, and Crank-Nicolson nite-difference methods are dis-.

3.36 6.95 5.17 0.84 2.01 7.13 0.06 13.01 6.69

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