Black and Scholes and Merton在1973年推導出選擇權（option）評價公式以來，選擇權市場在近來已呈現出爆炸性的成長。然而選擇權觀念並非只有影響到財務金融領域，例如Myers在1977年提出了實質選擇權（real option）、Merton在1974年亦利用其來推導出了信用風險評價（credit risk）中之結構式評價法（structure form）等。據此我們試著去找尋這或有求償權分析法（continent claim analysis）是否可以運用其他的領域中，甚至幫助我們更能夠去解釋現實世界中的現象。
一開始我們針對了交易契約中常會出現之違約金進行分析，我們發現到在契約中是可以存在著最適違約金比例（optimal penalty ratio），而此最適違約金比例是可以讓此交易是公平的。此外契約賣方相較於契約買方來說，其擁有較多之優勢地位，因此我們建議對於契約賣方之違約金比例應給予較為嚴格之規定。
接下來我們重新檢視了在行銷策略中常會運用到的價金退款保證（money backed guarantee）。當消費者擁有價金退款保證時，他可以選擇賣回商品給予業者，再從業者處收回原先付出之價金，而這類似於賣權的性質也是Heiamn, McWilliams, Zhao and Zilberman利用賣權來評價價金退款保證的原因。然而我們從現金流量和買賣權平價說的觀點來看，我們應該利用買權來評價消費者持有價金退款保證所應多付出之成本。最後我們發現了在給定商品是正常財（normal good）的情形下，業者利用違約金的方式來提供價金退款保證是比較好的選擇。
綜合言之，我們運用了或有求償權分析法的觀念在違約金和價金退款保證的研究上，而我們也發現到可以利用不複雜的模型來解釋現實世界的現象，因此我們認為或有求償權是另一種可以對社會現象提供解釋的方法。

A European option is a contract in which the seller of the option grants the buyer the right, but not the obligation, to purchase from or sell to the seller the underlying asset at pre-specified price at maturity date. Herewith the buyer should pay out a premium for the value of flexibility that he was granted. Such premium as the compensation to the seller was provides in close form by Black and Scholes (1973) and Merton (1973). Even since then the option pricing methodology, or otherwise known as “contingent claim analysis” has found its application in many prospects. Otherwise known as the real option analysis first induced by Myers (1977) and the structure form model of the credit risk analysis first induced by Merton (1974).
In the thesis, we consider the application of the optional pricing methodology to the rationality and valuation of penalty in a contract and extent the penalty to the money back guarantee. In the former, we provide the general form solution to illustrate the both parties all hold the right to default the contract, and prove the existence of the optimal penalty is a policy to protect the disadvantaged minority such as to make the trade contract to be fair. In the latter, we prove the suitable way to evaluate that the consumer buy a good and long a MBG is the call option but the put by reviewing the final cash flow of the replicated strategy and the put-call parity at firstly, and then we find out the better way to grant the consumer to return the good to the vendor is penalty if the good is normal and the utility function of the consumer is concave.
In sum, we integrate the penalty and in the MBG with the contingent claim analysis in this thesis, we find out we can use the uncomplicated model to explain the real world. Herewith we consider the option pricing model as another methodology to illustrate the social environment.

Table of Content
Chapter 1 Introduction………………………………………… 1
Chapter 2 The Key Role that Penalty Played …..…………..… 5
2.1 The Motivations…………………………………………………………….. 5
2.2 The Model………………………………………………………………....... 7
2.2.1 The Assumptions…………………………………………………….. 7
2.2.2 The Cash Flow of the Both Parties All Hold the Option…………..... 8
2.2.3 The Definition of the Penalty Ratio………………………………..... 9
2.3 The Solutions………………………………………………………………. 10
2.3.1 The General Form Solution……………………………………….... 10
2.3.2 The Special Form Solution - Only the Consumer Holds the Call….. 12
2.3.3 The Special Form Solution - Only the Vendor Holds the Put............ 13
2.3.4 The Special Form Solution – No One Holds Option……………….. 14
2.4 The Analytic Results and Economic Intuition……………………………... 14
2.4.1 The Sensitive Analysis of Option Value……………………………. 15
2.4.2 The Optimal Penalty Ratio…………………………………………. 20
2.5 Conclusion…………………………………………………………………. 24
Chapter 3 Is it Idiot that the Seller Supplies the Money Back Guarantee on Marketing?………………………... 27
3.1 The Motivations………………………………………………………….... 27
3.2 The Model…………………………………………………………………. 29
3.2.1 The Assumptions…………………………………………………… 29
3.2.2 The Cash Flow of the Buyer on Maturity Date…………………...... 30
3.2.3 The Expected DCF of the Consumer with MBG…………………... 32
3.3 The Analysis Results………………………………………………………. 33
3.3.1 The Sensitive Analysis…………………………………………....... 33
3.3.2 The Effects of the Penalty………………………………………….. 36
3.4 Conclusion…………………………………………………………………. 38

Chapter 4 Conclusions and Future Researches .…………....... 39
4.1 Conclusions………………………………………………………………... 39
4.2 Future Researches………………………………………………………… 40
List of Figures
Figure 2.1…………………………………………………………………………..... 9
Figure 3.1………………………………………………………………………….... 31


List of Tables
Table 2.1…………………………………………………………………………….. 16
Table 2.2…………………………………………………………………………….. 22
Table 2.3…………………………………………………………………………….. 26
Table 3.1…………………………………………………………………………….. 36

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