考慮交易成本與流動性風險成本下選擇權複製策略之比較

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邱世凱(shi-kai qiu) 查詢紙本館藏

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財務金融學系

論文名稱

考慮交易成本與流動性風險成本下選擇權複製策略之比較
(Comparison of option replication with transaction cost and liquidity risk cost)

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摘要(中)

在現實生活中，無套利定價模型布雷克-休斯模型(Black-Scholes Model)下的假設如無交易成本、可連續時間交易等等的不符合現實的設定使得以此模型所定價出的選擇權價格實際上存在著套利空間。而Leland(1985)、Henrotte(1993)與Martellini(2000)等人分別發展出在time-based策略、move-based策略與diversified time-based策略以修正隱含波動率得到避險波動率的方法使得選擇權價格能夠涵蓋住複製選擇權所需的交易成本。
而在本文中與以往研究的不同是在於吾人加入了流動性風險成本一併做探討，來比較此三種策略在各種情境下的優劣，並以＂蒙地卡羅模擬修正法＂與Leland(1985)等人的方法做比較，吾人發現以蒙地卡羅模擬修正法所得到的避險效果與以Leland等人幾乎一樣，接者吾人便以此方法來修正考慮流動性風險成本與交易成本下的選擇權價格，並且也探討在未知真實股價報酬分配為隨機波動率模型(Stochastic volatility model )下誤以為股價報酬分配為布雷克-休斯模型假設，而使用Leland(1985)等人之修正法與蒙地卡羅模擬的修正方法之效果比較，以蒙地卡羅模擬結果發現即使在未知真實股價報酬分配下，所得的到避險效果也相當不錯。
根據吾人所比較之結果發現diversified time-based策略表現最佳，而move-based策略僅只有在低總成本且高波動率下表現較佳，一但總成本稍高時，表現便會非常不好。此結果不論在布雷克-休斯模型或是隨機波動率模型下都是一致的。

摘要(英)

The assumptions of no-arbitrage Black-Scholes model, such as no transaction cost, time-continuously tradable, do not exist in real world and that make arbitrage possible. However, to make option price cover the transaction cost of replicating options, Leland(1985), Henrotte(1993) and Martellini(2000) have developed time-based strategy, move-based strategy and diversified time-based strategy, respectatively, by deriving hedge volatility revised from implied volatility to cover transaction cost.
In relation to previous works, the major difference in this paper is that we encompass the cost of liquidity risk and we not only compare the various situations of these three strategies but also compare these outcomes that derived from “Monte Carlo simulation revised approach” with outcomes that derived from approaches of Leland (1985) etc. And we find the performance of “Monte Carlo simulation revised approach” is alike to performances of Leland(1985) etc.
Then we use the approach to compute option price when considering liquidity risk cost and transaction cost,compare results of approach of Leland (1985) etc. and Monte Carlo revised approach under Stochastic volatility model is the true stock return process, and we find that the hedge effect by Monte Carlo simulation is good even if stock return true process is unknown.According to our comparison, diversified time-based strategies perform best whereas move-based strategies perform better only under low total cost and high volatility and move-based strategies perform extremely bad when total cost is just a little high.

關鍵字(中)

★ 選擇權
★ 流動性風險成本
★ 交易成本
★ 複製策略

關鍵字(英)

★ replication
★ liquity risk cost
★ transaction cost
★ option

論文目次

第一章前言........................................................1
第二章蒙地卡羅模擬修正法說明......................................3
第一節流動性成本假設模型.......................................3
第二節蒙地卡羅模擬修正法說明...................................4
第三節蒙地卡羅模擬修正法與Leland修正式之比較..................7
第四節蒙地卡羅模擬修正法與Henrotte修正式之比較...............13
第五節蒙地卡羅模擬修正法與Martellini修正式之比較.............15
第三章考慮交易成本與流動性成本後各種避險方法之優劣...............17
第一節避險方法與參數設定說明..................................17
第二節考慮交易成本後各種避險方法之優劣........................18
第三節考慮流動性風險成本後各種避險方法之優劣..................29
第四節考慮交易成本與流動性風險成本後各種避險方法之優劣........34
第五節小結....................................................47
第四章在隨機波動率模型假設下考慮交易成本下各種避險方法的優劣.....47
第一節隨機波動率模型設定說明..................................47
第二節避險方法與參數設定說明..................................49
第三節考慮交易成本下後各種避險方法之優劣......................49
第四節未知真實股價報酬為SV模型假設下，以BS模型假設去做避險..57
第五章總結.......................................................64
參考文獻...........................................................65
附錄A.............................................................67
附錄B.............................................................69
附錄C.............................................................86

參考文獻

Bakshi, G., C. Cao, and Z. Chen, 1997, "Empirical Performance of Alternative Option Models," Journal of Finance, 52, 2003-2049.
Black, F., and M. Scholes, 1973, "The pricing of options corporate liabilities," Journal of Political Economy, 81, 637-654
Cox, J. C., J. E. Ingersoll, and S. A. Ross, 1985, "A theory of the term structure of interest rates," Econometrica, 53, 385-408.
Cox, J. C., S. A. Ross, and M. Rubinstein, 1979, "Option Pricing: A Simplified Approach," Journal of Financial Economics, 7, 229-263.
Edirisinghe, C., V. Naik, and R. Uppal, 1993, "Optimal replication of options with transactions costs and trading restrictions," Journal of Financial and Quantitative Analysis, 28, 117-138.
Jayanto, D., C. Ting, and M. Warachka, 2003, "The impact of liquity on option pricing," working paper, Singapore Management University.
Leland, H. E., 1985, "Option pricing and replication with transaction costs," The Journal of Finance, 40, 283-1301.
Henrotte, P., 1993, "Transaction costs and duplication strategies," working paper, Stanford University and Groupe HEC.
Heston, S., 1993, "A closed-form solution for options with stochastic volatility with applications to bond and currency options," Review of Financial Studies, 6, 327-343.
Hull, J., and A. White, 1987, "The pricing of options with stochastic volatilities," The Journal of Finance, 42, 281-300.
Toft, K., 1996, "On the mean-variance tradeoff in option replication with transaction costs," The Journal of Financial and Quantitative Analysis, 31, 233-263.
Martellini, L., 2000a, "Efficient option replication in the presence of transaction costs," Review of Derivatives Research, 4, 107-131.
Martellini, L., 2000b, "Optimal dynamic hedging in the presence of transaction costs: An empirical investigation," working paper, University of Southern California.
Scott, L., 1987, "Option pricing when the variance changes randomly: theory, estimation, and an application," Journal of Financial and Quantitative Analysis, 22, 419-438.
Wiggins, J., 1987, "Option values under stochastic volatilities," Journal of Financial Economics, 19, 351-372.

指導教授

張森林、何耕宇
(San-Lin Chung、Keng-Yu Ho)

審核日期

2005-7-21

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