Dupire’s formulas in the Piterbarg option pricing model |
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| Institution: | 1. University of Louisiana at Lafayette, B.I. Moody III College of Business, Department of Economics & Finance, 214 Hebrard Boulevard, Moody Hall 253, P.O. Box 44570, Lafayette, LA 70504-4570, United States;2. Department of Economics, School of Business and Economics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON N2L 3C5, Canada;1. Department of Applied Economics, Fo Guang University, Yilan, Taiwan;2. Department of Economics, Feng Chia University, Taichung, Taiwan;3. Department of Leisure Management, Tungnan University, Taipei, Taiwan;1. Department of International Business, Feng Chia University, 100 Wenhwa Rd., Seatwen, Taichung 40724, Taiwan, ROC;2. Gordon Ford College of Business, Western Kentucky University, Bowling Green, KY 42101, USA;1. Department of Banking and Finance, National Chiayi University, No. 580, Sinmin Road, Chiayi City 60054, Taiwan;2. Department of Finance, National Yunlin University of Science & Technology, No. 123, University Road, Section 3, Douliou City 64002, Taiwan;3. Department of Wealth and Taxation Management, National Kaohsiung University of Applied Sciences, No. 415, Chien-Kung Road, Sanmin District, Kaohsiung City 80778, Taiwan;4. Graduate Institute of Finance, National Pingtung University of Science and Technology, No. 1, Hseuhfu Road, Neipu, Pingtung 91201, Taiwan |
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| Abstract: | In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface. |
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| Keywords: | Dupire Local volatility Option pricing Piterbarg |
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