匯率連動遠期生效亞洲選擇權

Quanto Forward-Start Asian Options

10.29628/AEP.200403.0006

陳松男(Son-Nan Chen)；姜一銘(I-Ming Jiang)

新奇選擇權 ； 匯率連動 ； 亞洲選擇權 ； Exotic option ； Quanto option ； Asian option

經濟論文

32卷1期（2004 / 03 / 01）

149 - 199

繁體中文

本文考慮針對投資人規避匯率風險與防止股票市場的可能受到人為操縱下，提出幾種匯率連動之遠期生效亞洲選擇權（Quanto Forward-Start Asian Options），同時雖然一般亞洲選擇權無封閉解，本文嘗試提出一階及二階泰勒近似封閉解，並計算避險參數。最後，計算出評價理論公式的最大估計誤差上限，並簡單舉例，發現在波動度較小時，一階及二階泰勒近似封閉解相差不大，可以考慮使用公式簡單的一階泰勒近似封閉解；反之，在波動度較大時，考慮二階泰勒近似封閉解的可靠度相當高。

In this paper, we propose several Quanto Forward-Start Asian options for investors who wish to hedge both currency risk and the risk of being possibly manipulated by some market participants. Although Asian options have no closed-form solutions, we try to find the “approximate” closed-from solution and compute hedge parameters for them. In addition, we also determine the upper bound of maximum estimation error of our pricing model. The numerical results show that the difference between the first-order and the second-order Taylor's expansion of approximate closed-form solution is not significant when the volatility is small. Under this circumstance, we can simply use first-order Taylor's expansion of approximate closed-form solution. However, second-order Taylor's expansion of approximate closed-form solution is employed when the volatility is large.

1. Bouaziz, L.,E. Briys,M. Crouhy(1994).The Pricing of Forward-Starting Asian options.Journal of Banking and Finance,18,823-839.
2. Conze, A.,Viswanathan(1991).European Path Dependent Options: The Case of Geometric Averages.Finance,12,7-22.
3. Duffie, D.(1998).Security Markets: Stochastic Models
4. Harrision, M.,D. Krep(1979).Martingales and Arbitrage in Multiperiod Securities Markets.Journal of Economic Theory,20,381-408.
5. Harrision, M.,S. Pliska(1981).Martingales and Stochastic Integrals in the Theory of Continuous Trading.Stochastic Processes and Their Applications,11,215-271.
6. Karatzas, I.,S. Shreve(1991).Brownian Motion and Stochastic Calculus
7. Kemna, A.,T. Vorst(1990).A Pricing Method for Options Based on Average Asset Values.Journal of Banking and Finance,14,113-129.
8. Klebaner, F. C.(1998).Introduction to Stochastic Calculus with Applications
9. Levy, E.(1992).Pricing European Average Rate Currency Options.Journal of International Money and Finance,11(5),474-491.
10. Milesky, M. A.,S. E. Posner(1998).Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution.Journal of Financial and Quantitative Analysis,33(3),409-422.
11. Musiela, M.,M. Rutkowski(1997).Martingale Methods in Financial Modelling,160-164.
12. Reiner, E.(1992).Quanto Mechanics.Risk,5(10),59-63.
13. Tsao, C. Y.,C. C. Chang,C. G. Lin(2003).Analytic Approximation Formulate for Pricing Forward-Starting Asian Options.Journal of Futures Markets,2006/4/23
14. Turnbull, S. M.,L. MacDonald Wakeman(1991).A Quick Algorithm for Pricing European Average Options.Journal of Financial and Quantitative Analysis,26(3),377-389.

1. 葉仕國、張森林、林丙輝(2016)。台灣衍生性金融商品定價、避險與套利文獻回顧與展望。臺大管理論叢，27(1)，255-304。