VALUING AND HEDGING AMERICAN OPTIONS UNDER TIME-VARYING VOLATILITY

Abstract

Journal of Derivatives AccountingVol. 01, No. 02, pp. 195-204 (2004) ARTICLESNo AccessVALUING AND HEDGING AMERICAN OPTIONS UNDER TIME-VARYING VOLATILITYIN JOON KIM, SUK JOON BYUN, and SONYA SEONGYEON LIMIN JOON KIMGraduate School of Management, Korea Advanced Institute of Science and Technology, Korea Search for more papers by this author , SUK JOON BYUNGraduate School of Management, Korea Advanced Institute of Science and Technology, Korea Search for more papers by this author , and SONYA SEONGYEON LIMDepartment of Finance, DePaul University, Korea Search for more papers by this author https://doi.org/10.1142/S0219868104000191Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThere has been considerable interest in developing stochastic volatility and jump-diffusion option pricing models, e.g. Hull and White (1987, Journal of Finance, 42, 281–300) and Merton (1976, Journal of Financial Economics, 3, 125–144). These models, however, have some undesirable aspects that arise from introducing some non-traded sources of risks to the models. Furthermore, the models require much analytical complications; thus, if they are applied to American options then it is not easy to acquire practical implications for hedging and optimal exercise strategies. This paper examines the American option prices and optimal exercise strategies where the volatility of the underlying asset changes over time in a deterministic way. The paper considers two simple cases: monotonically increasing and decreasing volatilities. The discussion of these two simple cases gives useful implications for the possibility of early-exercise and optimal exercise strategies.Keywords:American optionhedgingearly exercisevolatility References G. S. Bakshi, C. Cao and Z. W. Chen, Journal of Finance 52, 2003 (1997), DOI: 10.2307/2329472. Crossref, Google ScholarD. Bates, Journal of Finance 46, 1009 (1991), DOI: 10.2307/2328552. Crossref, Google ScholarF. Black and L. Scholes, Journal of Political Economy 81, 637 (1973), DOI: 10.1086/260062. Crossref, Google Scholar Derman, E. and I. Kani. Riding on a smile. RISK (February), 32–39 . Google ScholarJ. C. Duan, Mathematical Finance 5, 13 (1995), DOI: 10.1111/j.1467-9965.1995.tb00099.x. Crossref, Google ScholarB. Dupire, RISK 18 (1994). Google ScholarS. L. Heston, Review of Financial Studies 6, 327 (1993), DOI: 10.1093/rfs/6.2.327. Crossref, Google ScholarS. L. Heston and S. Nandi, Review of Financial Studies 13, 585 (2000), DOI: 10.1093/rfs/13.3.585. Crossref, Google ScholarT. Ho, R. Stapleton and M. Subrahmanyam, Journal of Derivatives 2, 52 (1994), DOI: 10.3905/jod.1994.407897. Crossref, Google ScholarJ. Hull and A. White, Journal of Finance 42, 281 (1987), DOI: 10.2307/2328253. Crossref, Google ScholarH. Johnson and D. Shanno, Journal of Financial and Quantitative Analysis 22, 143 (1987), DOI: 10.2307/2330709. Crossref, Google ScholarI. Kim, Review of Financial Studies 3, 547 (1990), DOI: 10.1093/rfs/3.4.547. Crossref, Google ScholarI. Kim and S. Kim, Pacific-Basin Finance Journal (2003). Google ScholarD. B. Madan, P. Carr and E. C. Chang, European Finance Review 2, 79 (1998), DOI: 10.1023/A:1009703431535. Crossref, Google ScholarA. Melino and S. M. Turnbull, Journal of Econometrics 45, 239 (1990), DOI: 10.1016/0304-4076(90)90100-8. Crossref, Google ScholarR. C. Merton, Bell Journal of Economics and Management Science 4, 141 (1973), DOI: 10.2307/3003143. Crossref, Google ScholarR. C. Merton, Journal of Financial Economics 3, 125 (1976), DOI: 10.1016/0304-405X(76)90022-2. Crossref, Google ScholarE. Naik and M. Lee, Review of Financial Studies 3, 493 (1990), DOI: 10.1093/rfs/3.4.493. Crossref, Google ScholarL. O. Scott, Journal of Financial and Quantitative Analysis 22, 419 (1987), DOI: 10.2307/2330793. Crossref, Google ScholarE. M. Stein and J. C. Stein, Review of Financial Studies 4, 727 (1991), DOI: 10.1093/rfs/4.4.727. Crossref, Google ScholarJ. B. Wiggins, Journal of Financial Economics 19, 351 (1987), DOI: 10.1016/0304-405X(87)90009-2. Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 1Valuation and Optimal Strategies for American Options Under a Markovian Regime-Switching ModelLu Jin, Marko Dimitrov and Ying Ni26 January 2023 Recommended Vol. 01, No. 02 Metrics History KeywordsAmerican optionhedgingearly exercisevolatilityPDF download