臺灣博碩士論文加值系統

近幾十年來，由於市場需求增加以致於衍生性商品發展迅速，選擇權即為重要的商品之一。但由於國際事件或者突發事件發生投資者即會過度反應，以致於讓價格劇烈波動。所以政府即設立價格限制的機制來穩定價格。在本文中，我們將使用二項式模型計算出股票價格和風險中性的機率分佈。當市場實施價格限制時，如果股價超出價格限制其機率即為零，並且重新調整其機率分佈，利用隱含二項式模型由Mark Rubinstein (1994) 提出算出市場有價格限制時之股價機率分佈進而利用此機率分佈計算一般歐式選擇權以及障礙型選擇權，並且觀察價格限制對各種選擇權的價格影響。

During the last dozens of years, the market demands have been triggering the rapid booming of Derivatives. The options value, for example, is one of the prominent merchandises. However, the sensitive overreaction of the investors resulting from the international and sudden incidents will often lead the price to fluctuate outrageously. Therefore, in order to stabilize the price and allow the governmental authorities to have the sufficient time in dealing with emergencies, the mechanism of price limit is necessary to be put into effect. The binomial tree model is one of the most significant tools for pricing options. With price limit, we need to modify the binomial tree model so that the stock prices are within the price limitation. The implied probability distribution can then be obtained by the method first proposed by Mark Rubinstein (1994). Therefore this thesis uses the implied binomial tree model in the price limit market for options pricing. We value plain vanilla options and barrier options prices and observe the changes of options price.

Chapter 1 INTRODUCTION……….……………………….………….…1
Chapter 2 OPTIONS PRICING BASICS…….………….……….………2
2.1 Options pricing models………………………………….……2
2.1.1 Options basics……………...…………………….………2
2.1.2 Cox-Ross-Rubinstein model…………………...……….…4
2.1.3 Black-Scholes model…………………………………………7
2.1.4 Historical volatility and implied volatility….……8
2.2 Options categories……………………………………………12
Chapter 3 OPTIONS PRICE ON IMPLIED MODEL……....…….………14
3.1 The implied binomial tree…………………………………..14
3.1.1 Binomial path independent………………...……….…15
3.1.2 Backward induction for building implied trees……16
3.2 Skewing a probability distribution……………..…………17
Chapter 4 OPTIONS VALUING ON PRICE LIMIT MARKET…..………..21
Chapter 5 EXPERIMENTAL RESULT AND CONCLUSION……………….…26
5.1 The effect of probability distribution under the price limit market……………..26
5.2 Options price under the price limit market………………31
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