This talk addresses the main theoretical issues of derivatives pricing. The first part of the talk

introduces two valuation doctrines–pure arbitrage approach vs. equilibrium approach. First,

we consider the concept of spanning, particularly dynamic spanning, which serves as the basis for

the pure arbitrage valuation approach. The Black-Scholes model will be derived by two approaches

(partial differential equation and martingale representation) to illustrate the use of dynamic spanning.

Second, we discuss the Arrow-Debreau equilibrium and move on to the incomplete market equilibrium

in discrete time. The Black-Scholes formula is then established in the discrete time setting using

a combination of preferences and distribution assumptions. We end the first part of the talk with

a question: Is dynamic spanning a fiction or reality?”

The tradition of derivatives pricing theories has an analytical orientation. In short, it is preoccupied

by the desire to obtain closed-form pricing formulas. Empirical regularities are seldom respected

in the search for elegant formulas. The second half of the talk will introduce the second-generation

option pricing models. The second-generation models specifically refer to those models for which

the well-established time series models (intended for statistical analyses) are used as the premises for

deriving option pricing models. The two examples – GARCH and co-integration option pricing

models – will be discussed.

This talk discusses option valuation problems from a numerical implementation perspective. A two way classification of numerical problems – path independent/dependent underlying stochastic processes

and path independent/dependent contingent payoffs – are introduced for a better understanding of

the nature of these numerical problems. We discuss pros and cons of the standard numerical option

valuation methods. The methods covered are (quasi- and pseudo-) Monte Carlo, lattices, finite difference/element, analytical approximation, and neural network.

We then introduce a new numerical method known as Markov chain approximation. We will describe

the method in detail and demonstrate its use for European, American and barrier options under the

Black-Scholes and GARCH option pricing frameworks, respectively.

14:00-15:00　14:00-15:00何淮中 （中研院統計科學研究所）

講題：Modeling financial time series

15:30-16:30　15:30-16:30廖四郎（政大金融學系）

講題：Theory of Dynamic Capital Structure and The Valuation of　re and The Valuation oCorporate Bonds

13:30-14:30　13:30-14:30林建甫（台大經濟學系）

講題：Modeling financial time series

效率市場假說 (efficient market hypothesis； EMH)的存在使得財務市場的資產定價不容易有

套利空間，但是因為財務資料具有獨特的價格波動聚集( volatility clustering) 效果，使得波動性

型式的條件變異數不齊一性 (autoregressive conditional heteroscedasticity; ARCH) 模型出發，談論

其後續發展，如 GARCH, GARCH in mean, nonlinear GARCH, threshold GARCH, exponential GARCH, Markov-switching GARCH, fractional integrated GARCH﹐及其他相關的 random coefficients model, stochastic volatility model 等等。我們並簡要說明估計及檢定應注意的地方。最後我們提出目前

可以發展的新方向﹐Markov-switching fractional integrated GARCH 及 Markov-switching EGB GARCH 模型。我們並以台灣股票市場加權指數及 S&P 500 的資料做一實證的討論。

14:30-15:30　14:30-15:30呂育道（台大資訊工程學系）

講題：Computational techniques in derivatives pricing