The purpose of the study is to analyze the problem of offer pricing and share issuing in the issuer with a dynamic model. The result shows: First, the correlation between discount and the prosperity of the market is not a linear function. Thus, ¡¥the IPO¡¦s timing¡¦ should be the key issue of issuing firm, which can reasonably explain the fluctuations in underpricing over time. Second, we also discover that the relationship between the ownership structure and the prosperity of the market is not a liner function as what Bolton and Thadden (1998) have claimed. Third, the firm with low quality prefers to release issuing shares in IPO when the market is booming. Fourth, the less the IPO discount in traditional industry, the more the share releasing. Finally, the more the phenomena of subscription, the more the investors subscribe blindly and generate an effect of the cascade. One of the contributions in this model comprises the views between the prosperity of the market and IPO discount in the literature to integrate a profound viewpoint by dividing the IPO discount into the offer pricing error and the market pricing error. Another finding is that the offer pricing error will decrease subject to the prosperity of the market. This is consistent with the viewpoint of Chemmanur (1993) that when the market is booming, the issuers can decrease the cost of adverse choice. As for the non-linear relation between the market pricing error and the prosperity of the market is coordinate with what Ma(1999) has claimed that IPO discount is influenced by the offer pricing and the market pricing. Besides, the non-linear relationship between ownership structure and the prosperity of market can reasonably account for the real situation. Besides, the benefit of controlling authority is better than the value of the cash flow of the released shares owing to the depression of the market, even the market is turning booming. Therefore, the issuers will minimize releasing share. However, the issuers will increasing released shares up to the market is keeping booming and the value of the cash flow of the released shares is better than the benefit of controlling authority. An auction model is established to analyze the choice of firms between fixed-price offerings and auctions. Chemmanur and Liu(2003) stated that obtaining the auction information is more advanced; however, the cost is high so that it can not catch enough investors to produce information which does not favor the discovery of the secondary market price. On the contrary, we proclaim that the information transmitting effect produced by auction will be helpful to the discovery of the secondary market price. Thus, a profitable company but suffers from high levels of information asymmetry prior to the IPO might expect the secondly market price to reflect its real value by auction. Moreover, the choice of underwriting mechanisms lies in the prosperity of the market, the reputation of the company and the degree of the releasing shares. The result of the empirical study is consistant with the expectation of our model.

The master thesis is focused on how a local volatility surfaces can be extracted by optimization with respectto smoothness and price error. The pricing is based on utility based pricing, and developed to be set in arisk neutral pricing setting. The pricing is done in a discrete multinomial recombining tree, where the timeand price increments optionally can be equidistant. An interpolation algorithm is used if the option that shallbe priced is not matched in the tree discretization. Power utility functions are utilized, where the log-utilitypreference is especially studied, which coincides with the (Kelly) portfolio that systematically outperforms anyother portfolio. A fine resolution of the discretization is generally a property that is sought after, thus a seriesof derivations for the implementation are done to restrict the computational encumbrance and thus allow finer discretization. The thesis is mainly focused on the derivation of the method rather than finding optimal parameters thatgenerate the local volatility surfaces. The method has shown that smooth surfaces can be extracted, whichconsider market prices. However, due to lacking available interest and dividend data, the pricing error increasessymmetrically for longer option maturities. However, the method shows exponential convergence and robustnessto different initial (flat) volatilities for the optimization initiation. Given an optimal smooth local volatility surface, an arbitrary payoff function can then be used to price thecorresponding option, which could be path-dependent, such as barrier options. However, only vanilla optionswill be considered in this thesis. Finally, we find that the developed

本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知，高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知，跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小，在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。 / In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error.