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We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).
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참고문헌 (18)
참고문헌 신청
D. Applebaum / 2009 / Levy Processes and Stochastic Calculus / Cambridge University Press
L. Bachelier / 1900 / Theorie de la sp´eculation / Ann. Sci. Ecole Norm. Sup. (3) 17:21~86
F. Black / 1973 / The pricing of options and corporate liabilities / J. Political Economy 81(3):637~654
T. Chan / 1999 / Pricing contingent claims on stocks driven by Levy processes / Ann. Appl. Probab 9(2):504~528
E. F. Fama / 1965 / The behavior of stock market prices / J. Business 38(1):34~105
L. Bachelier / 1900 / Theorie de la sp´eculation / Ann. Sci. Ecole Norm. Sup. (3) 17:21~86
F. Black / 1973 / The pricing of options and corporate liabilities / J. Political Economy 81(3):637~654
T. Chan / 1999 / Pricing contingent claims on stocks driven by Levy processes / Ann. Appl. Probab 9(2):504~528
E. F. Fama / 1965 / The behavior of stock market prices / J. Business 38(1):34~105
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