DOMAIN OF INFLUENCE OF LOCAL VOLATILITY FUNCTION ON THE SOLUTIONS OF THE GENERAL BLACK-SCHOLES EQUATION |
Kim, Hyundong
(Department of Mathematics, Korea University)
Kim, Sangkwon (Department of Mathematics, Korea University) Han, Hyunsoo (Department of Financial Engineering, Korea University) Jang, Hanbyeol (Department of Financial Engineering, Korea University) Lee, Chaeyoung (Department of Mathematics, Korea University) Kim, Junseok (Department of Mathematics, Korea University) |
1 | H. Berestycki, J. Busca & I. Florent: Asymptotics and calibration of local volatility models. Quant. Finance 2 (2002), 61-69. DOI |
2 | F. Black & M. Scholes: The pricing of options and corporate liabilities. J. Polit. Econ. 81 (1973), 637-654. DOI |
3 | J.N. Bodurtha & M. Jermakyan: Nonparametric estimation of an implied volatility surface. J. Comput. Finance 2 (1999), 29-60. DOI |
4 | S. Chen, Z. Zhou & S. Li: An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach. Econ. Model. 58 (2016), 655-664. DOI |
5 | E. Derman & I. Kani: Riding on a smile. Risk Magazine 7 (1994), 32-39. |
6 | B. Dupire: Pricing with a smile. Risk Magazine 7 (1994), 18-20. |
7 | J. Geng, I.M. Navon & X. Chen: Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization. Quant. Finance 14 (2014), 73-85. DOI |
8 | J. Glover & M.M. Ali: Using radial basis functions to construct local volatility surfaces. Appl. Math. Comput. 217 (2011), 4834-4839. DOI |
9 | N. Jackson, E. Suli & S. Howison: Computation of deterministic volatility surfaces. J. Comput. Finance 2 (1999), 5-32. |
10 | J. Liang & Y. Gao: Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives. Econ. Model. 29 (2012), 1278-1285. DOI |
11 | R.C. Merton: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4 (1973), 141-183. DOI |
12 | D. Tavella & C. Randall: Pricing financial instruments: The finite difference method. Wiley, New York, 2000. |
13 | L. Thomas: Elliptic problems in linear differential equations over a network: Watson scientific computing laboratory. Columbia University, New York, 1949. |
14 | G. Turinici: Calibration of local volatility using the local and implied instantaneous variance. J. Comput. Finance 13 (2009), 1-18. |
15 | J. Wang, S. Chen, Q. Tao & T. Zhang: Modelling the implied volatility surface based on Shanghai 50ETF options. Econ. Model. 64 (2017), 295-301. DOI |
16 | H. Windcliff, P.A. Forsyth & K.R. Vetzal: Analysis of the stability of the linear boundary condition for the Black-Scholes equation. J. Comput. Finance 8 (2004), 65-92. |
17 | M. Avellaneda, C. Friedman, R. Holmes & D. Samperi: Calibrating volatility surfaces via relative-entropy minimization. Appl. B Math. Finance 4 (1997), 37-64. DOI |
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