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次級房貸風暴造成全球金融海嘯，投資人對金融衍生性商品一度避之唯恐不及。在各方韃伐之下，卻忽略衍生性商品作為風險管理的工具及促進市場效率及完整性的重要性，未來在金融市場著重風險控管的趨勢下，衍生性商品仍會扮演不可或缺的角色。 本論文針對市場上交易量較大的利率衍生性金融商品及匯率衍生性金融商品，進行個案的評價與分析，提供投資人或發行者一個明確易懂的評價分析方式，能使市場上衍生性商品的交易更具效率性。 本論文以瑞士銀行所發行的「上下限固定期限交換利率利差連動債券」及「數據百慕達式匯率連動債券」為例，分別以LIBOR Market Model和最小平方蒙地卡羅法做為評價方式。依據評價結果分析發行商的避險策略與投資人所面對的投資風險。

Student Number : 0003819T - MSc dissertation - School of Computational and Applied Mathematics - Faculty of Science / The over-the-counter (OTC) interest rate derivative market is large and rapidly developing. In March 2005, the Bank for International Settlements published its “Triennial Central Bank Survey” which examined the derivative market activity in 2004 (http://www.bis.org/publ/rpfx05.htm). The reported total gross market value of OTC derivatives stood at $6.4 trillion at the end of June 2004. The gross market value of interest rate derivatives comprised a massive 71.7% of the total, followed by foreign exchange derivatives (17.5%) and equity derivatives (5%). Further, the daily turnover in interest rate option trading increased from 5.9% (of the total daily turnover in the interest rate derivative market) in April 2001 to 16.7% in April 2004. This growth and success of the interest rate derivative market has resulted in the introduction of exotic interest rate products and the ongoing search for accurate and efficient pricing and hedging techniques for them. Interest rate caps and (European) swaptions form the largest and the most liquid part of the interest rate option market. These vanilla instruments depend only on the level of the yield curve. The market standard for pricing them is the Black (1976) model. Caps and swaptions are typically used by traders of interest rate derivatives to gamma and vega hedge complex products. Thus an important feature of an interest rate model is not only its ability to recover an arbitrary input yield curve, but also an ability to calibrate to the implied at-the-money cap and swaption volatilities. The LIBOR market model developed out of the market’s need to price and hedge exotic interest rate derivatives consistently with the Black (1976) caplet formula. The focus of this dissertation is this popular class of interest rate models. The fundamental traded assets in an interest rate model are zero-coupon bonds. The evolution of their values, assuming that the underlying movements are continuous, is driven by a finite number of Brownian motions. The traditional approach to modelling the term structure of interest rates is to postulate the evolution of the instantaneous short or forward rates. Contrastingly, in the LIBOR market model, the discrete forward rates are modelled directly. The additional assumption imposed is that the volatility function of the discrete forward rates is a deterministic function of time. In Chapter 2 we provide a brief overview of the history of interest rate modelling which led to the LIBOR market model. The general theory of derivative pricing is presented, followed by a exposition and derivation of the stochastic differential equations governing the forward LIBOR rates. The LIBOR market model framework only truly becomes a model once the volatility functions of the discrete forward rates are specified. The information provided by the yield curve, the cap and the swaption markets does not imply a unique form for these functions. In Chapter 3, we examine various specifications of the LIBOR market model. Once the model is specified, it is calibrated to the above mentioned market data. An advantage of the LIBOR market model is the ability to calibrate to a large set of liquid market instruments while generating a realistic evolution of the forward rate volatility structure (Piterbarg 2004). We examine some of the practical problems that arise when calibrating the market model and present an example calibration in the UK market. The necessity, in general, of pricing derivatives in the LIBOR market model using Monte Carlo simulation is explained in Chapter 4. Both the Monte Carlo and quasi-Monte Carlo simulation approaches are presented, together with an examination of the various discretizations of the forward rate stochastic differential equations. The chapter concludes with some numerical results comparing the performance of Monte Carlo estimates with quasi-Monte Carlo estimates and the performance of the discretization approaches. In the final chapter we discuss numerical techniques based on Monte Carlo simulation for pricing American derivatives. We present the primal and dual American option pricing problem formulations, followed by an overview of the two main numerical techniques for pricing American options using Monte Carlo simulation. Callable LIBOR exotics is a name given to a class of interest rate derivatives that have early exercise provisions (Bermudan style) to exercise into various underlying interest rate products. A popular approach for valuing these instruments in the LIBOR market model is to estimate the continuation value of the option using parametric regression and, subsequently, to estimate the option value using backward induction. This approach relies on the choice of relevant, i.e. problem specific predictor variables and also on the functional form of the regression function. It is certainly not a “black-box” type of approach. Instead of choosing the relevant predictor variables, we present the sliced inverse regression technique. Sliced inverse regression is a statistical technique that aims to capture the main features of the data with a few low-dimensional projections. In particular, we use the sliced inverse regression technique to identify the low-dimensional projections of the forward LIBOR rates and then we estimate the continuation value of the option using nonparametric regression techniques. The results for a Bermudan swaption in a two-factor LIBOR market model are compared to those in Andersen (2000).

A takeover announcement does not necessarily mean good news for stockholders of the acquiring firm. In fact, for a majority of takeovers it means losses in share prices. Motives that can explain this trend are agency and hubris. This thesis is an event study of 28 acquir-ing firms in Sweden between the years 1997-2005, and the purpose is set to see whether stock prices are affected or not. This has been done by the help of the market model. The empirical results show that the takeovers are on average value decreasing operations which indicate that agency and hubris are the primary motives even though one can not for cer-tain exclude synergy.

<p>A takeover announcement does not necessarily mean good news for stockholders of the acquiring firm. In fact, for a majority of takeovers it means losses in share prices. Motives that can explain this trend are agency and hubris. This thesis is an event study of 28 acquir-ing firms in Sweden between the years 1997-2005, and the purpose is set to see whether stock prices are affected or not. This has been done by the help of the market model. The empirical results show that the takeovers are on average value decreasing operations which indicate that agency and hubris are the primary motives even though one can not for cer-tain exclude synergy.</p>

經過GATT各回合的多邊談判,傳統的關稅障礙以逐漸消除,各國為了防止國外的不公平貿易措施,紛紛制定了各種進口救濟措施,反傾銷制度即屬其中一種,我國目前已有一些反傾銷的案例 本文目地即在探討我國反傾銷制度對我國廠商的影響,利用市場模型分析法來測度我國廠商提起反傾銷訴訟對廠商價值的影響,其中選擇鋼鐵產業為研究對象,實證結果發現反傾銷制度對廠商價值有顯著的影響且價格具結的效果大於課徵反傾銷稅的效果. / Importing countries frequently use instruments of trade policy for the purpose of retaliating against the practices of foreign exporting companies. The market model is used to study the issue of whether or not Taiwanese steel producers capture the economic rents created by trade restrictions.Estimates of the trade impacts of Taiwanese antidumping law are provided. Empirical findings are that relief is valuable to the petitioning firms.

Previous empirical analyses have concluded that political events can have significant linkages with stock returns. Using Brown & Warner’s (1984) OLS market model, I examine the effect of political disruptions in the 2010-2011 Arab uprisings on major stock indices of Egypt, Tunisia, Jordan, Lebanon, Saudi Arabia, Dubai and London. My analysis finds mostly negative abnormal returns, highly statistically significant relative to the S&P 500, associated with many key events between December 1st, 2010 and December 1st, 2011. My findings suggest that the loss of investor wealth can be attributed to dramatic regime changes and large scale protests during that time period.

Walking tracks with provision for overnight stays exist in many countries. They are a tourism drawcard and some (e.g. the Milford Track in New Zealand) have icon status. In Australia, long-distance tracks exist in most states but had not until recently been developed in north Queensland. The working hypothesis for this thesis is that a new long-distance walking track in the tropical rainforest environment could be a valuable recreation asset for the region, and a major tourism attractor. Since a long-distance walking track in a natural environment would be situated in a rural region away from major cities, there is potential for tourism expenditure by long-distance hikers to contribute positively to the economy of remote towns. It is proposed that a walking track can be created relatively easily in the rainforests if disused former logging roads are used as the basis. The new walking track on a logging road base could be developed at moderate cost, and with minimal ecological and environmental disturbance. A new track created within a protected natural area is usually regarded as a public good and most associated costs may be considered to be appropriately funded through the taxation system. However, it may be argued that the recreational use of a long-distance walking track provides benefits to those who use it, and that hikers should contribute towards the recovery of managerial costs. An appropriate level of user fee may be obtained from a market model. In this thesis, an annual market model is estimated for the recreation service which provides a short-term efficient price. A long-distance walking track is an investment in recreation infrastructure the benefits of which are intergenerational. Thus efficiency in the long-term is also an important consideration. Both a static analysis and cost-benefit dynamic analysis are presented in this thesis. When a track does not exist (as was the case in north Queensland when this thesis commenced) or when it is under construction (as when the thesis was nearing completion), direct evaluation is not possible and so demand (consumer surplus) and supply (marginal cost of recreation service) estimates for a new track must be obtained from other sources. A key original contribution in this thesis is the application of economic transfer to derive a market model for a proposed recreation service infrastructure item, and a further application of economic transfer involves the use of the benefit level from the market model as an input into the cost-benefit analysis. Demand estimates have been obtained from surveys of visitors on two other walking tracks in north Queensland. Zonal travel cost methodology has been applied to the survey data to develop demand curves for these long-distance hiking opportunities and measures of value in terms of consumer surplus. Zonal rather than individual travel cost was necessary since most respondents were walking the particular track for the first time. Since the Centenary of Federation in Australia in 2001, when seed funding was made available, some new long-distance walking tracks have been developed in the Queensland Wet Tropics World Heritage Area. One of these has been selected as the case study developing track for this thesis. Demand and cost estimates for the new trail have been transferred, with appropriate adjustments, from the studies conducted on the two other trails. An interesting feature in this transfer process is that close substitutes exist for the target walking track but not for either of the two source walking tracks. An innovation in this thesis is the development of a market model for the new track. Two market models are derived, one from each of the source tracks, and are used to determine the socially efficient price and visitation levels. These may be used by management as a basis for the setting of user fees. The equilibrium values obtained from the static analysis have also been incorporated into the dynamic analysis together with the consumer surplus estimates from the travel cost demand curve. The equilibrium quantities provide the basis for an estimate of the visitation level expected for the new track on which many of the continuing management costs depend. Two scenarios (with and without hut infrastructure) have been investigated in cost-benefit analyses. Both scenarios were found to be economically worthwhile.

This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1

Instantaneous rate models, although theoretically satisfying, are less so in practice. Instantaneous rates are not observable and calibra- tion to market data is complicated. Hence, the need for a market model where one models LIBOR rates seems imperative. In this modeling process, we aim at regaining the Black-76 formula[7] for pricing caps and °oors since these are the ones used in the market. To regain the Black-76 formula we have to model the LIBOR rates as log-normal processes. The whole construction method means calibration by using market data for caps, °oors and swaptions is straightforward. Brace, Gatarek and Musiela[8] and, Miltersen, Sandmann and Sondermann[25] showed that it is possible to con- struct an arbitrage-free interest rate model in which the LIBOR rates follow a log-normal process leading to Black-type pricing for- mulae for caps and °oors. The key to their approach is to start directly with modeling observed market rates, LIBOR rates in this case, instead of instantaneous spot rates or forward rates. There- after, the market models, which are consistent and arbitrage-free[6], [22], [8], can be used to price more exotic instruments. This model is known as the LIBOR Market Model. In a similar fashion, Jamshidian[22] (1998) showed how to con- struct an arbitrage-free interest rate model that yields Black-type pricing formulae for a certain set of swaptions. In this particular case, one starts with modeling forward swap rates as log-normal processes. This model is known as the Swap Market Model. Some of the advantages of market models as compared to other traditional models are that market models imply pricing formulae for caplets, °oorlets or swaptions that correspond to market practice. Consequently, calibration of such models is relatively simple[8]. The plan of this work is as follows. Firstly, we present an em- pirical analysis of the standard risk-neutral valuation approach, the forward risk-adjusted valuation approach, and elaborate the pro- cess of computing the forward risk-adjusted measure. Secondly, we present the formulation of the LIBOR and Swap market models based on a ¯nite number of bond prices[6], [8]. The technique used will enable us to formulate and name a new model for the South African market, the SAFEX-JIBAR model. In [5], a new approach for the estimation of the volatility of the instantaneous short interest rate was proposed. A relationship between observed LIBOR rates and certain unobserved instantaneous forward rates was established. Since data are observed discretely in time, the stochastic dynamics for these rates were determined un- der the corresponding risk-neutral measure and a ¯ltering estimation algorithm for the time-discretised interest rate dynamics was pro- posed. Thirdly, the SAFEX-JIBAR market model is formulated based on the assumption that the forward JIBAR rates follow a log-normal process. Formulae of the Black-type are deduced and applied to the pricing of a Rand Merchant Bank cap/°oor. In addition, the corre- sponding formulae for the Greeks are deduced. The JIBAR is then compared to other well known models by numerical results. Lastly, we perform some computational analysis in the following manner. We generate bond and caplet prices using Hull's [19] stan- dard market model and calibrate the LIBOR model to the cap curve, i.e determine the implied volatilities ¾i's which can then be used to assess the volatility most appropriate for pricing the instrument under consideration. Having done that, we calibrate the Ho-Lee model to the bond curve obtained by our standard market model. We numerically compute caplet prices using the Black-76 formula for caplets and compare these prices to the ones obtained using the standard market model. Finally we compute and compare swaption prices obtained by our standard market model and by the LIBOR model. / Economics / D.Phil. (Operations Research)