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PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD
Author(s) -
Zhang Jin E.,
Li Tiecheng
Publication year - 2010
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00389.x
Subject(s) - stock exchange , economics , econometrics , dividend yield , stock price , valuation of options , dividend , volatility (finance) , financial economics , mathematical economics , mathematics , series (stratigraphy) , finance , dividend policy , geology , paleontology
This paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical‐stock‐price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index.