By Cheng-Few Lee

Advances in Quantitative research of Finance and Accounting is an annual e-book designed to disseminate contemporary advancements within the quantitative research of finance and accounting. The e-book is a discussion board for statistical and quantitative analyses of matters in finance and accounting in addition to functions of quantitative tips on how to difficulties in monetary administration, monetary accounting, and enterprise administration. Its goal is to advertise interplay among educational learn in finance and accounting with utilized examine within the monetary neighborhood and the accounting career. The chapters during this quantity conceal quite a lot of urgent themes together with safeguard research and mutual fund administration, alternative pricing idea and alertness, rate of interest unfold, and electrical energy pricing.

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**Example text**

Note that this least cost superreplicating portfolio is path-dependent. Now we show that the example just given is a special case of a situation in which there is a unique least cost superreplicating portfolio and it is pathdependent. Theorem 8. Consider a two-period binomial model with parameters S, u, d, R, µ, and λ satisfying d(1 + λ) < u(1 − µ), R(1 − µ) < d(1 + λ) < R. For every contingent claim with terminal holdings {( uu , Buu ), ( Bud ), ( dd , Bdd )} satisfying uu = ud < dd , Buu = Bud , and Bdd − Buu − Sd 2 (1 + λ)( uu − dd ) > 0, ud , (4) there exists a unique least cost superreplicating portfolio.

5) where ρ is a scalar function that depends on L and the unknown parameter θ that will adopt different forms as below, and u t is I (0). The function ρ is speciﬁed in such a way that all its roots should be on the unit circle in the complex plane, and, therefore, it includes polynomials of the form (1−L k )d+θ , where k is an integer and d may be a real value. Thus, in what follows, we assume that ρ(L; θ) = (1 − L k )d+θ . 5 28 Guglielmo Maria Caporale et al. in a model given by Equations (4)–(6).

3) where k is the number of time periods within the year and L k the seasonal lag operator (L k x t = x t−k ). Note that the polynomial on the left-hand side of Equation (3) can be expressed in terms of its binomial expansion, such that, for all real d, ∞ (1 − L ) = k d j =0 d j (−1) j L k j = 1 − d L k + d(d − 1) 2k L − ··· . 2 Clearly, if d = 0 in Equation (3), x t = u t , and a weakly autocorrelated x t is allowed for. If d > 0, the process is said to be a long memory one, so named because of the strong association between observations far apart in time, and the higher the value of d, the stronger will be the association.