臺灣博碩士論文加值系統

在完備 (complete) 的市場機制裡，每一個或有索取權 (contingent claim) 的價值都可以被一個自我融資交易 (self-financing) 的策略完全複製。然而，當我們的交易時間限制為離散的情況下，就只有 Cox Ross Rubinstein (CRR) 二項樹模型是一個完備的市場，其他的模型都不符合完備市場的機制。因此，在交易時間點為離散時間且不完備的市場機制下，我們希望可以找出最佳二次避險的策略 (optimal variance hedging)。本文探討在 Black-Scholes (歐式) 選擇權定價模型 (以 European call option 為例)，當限制資產配置不為連續時，如何利用遞迴公式解求出最佳化的避險策略表示式，並且與 Black-Scholes 架構下的 delta 避險策略做比較。

In the complete market, each contingent claim can be replicated by some self-financing strategy perfectly. However, as time horizon is discrete, the only complete market is the Cox Ross Rubinstein (CRR) model which is drawn by the binomial tree framework. For the line of this research, we concern on the hedging in the discrete time horizon. We solve the explicit formula of the optimal-variance hedging strategy in the Black-Scholes market but the asset allocation is no more continuous. Also, we give the simulation analysis to compare the optimal-variance hedging strategy and the delta hedging.

中文摘要i
英文摘要ii
誌謝iii
1 Introduction 1
2 Model Setup and Local Quadratic Risk 3
3 Optimal Variance Hedging 7
4 Examples 13
4.1 Black-Scholes Model under Martingale Measure . . . . . . . . . . . . 13
4.2 Black-Scholes Model Under Physical Measure . . . . . . . . . . . . . 16
5 Simulation 22
6 Conclusion 31
References 31

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