AN EFFICIENT AND ROBUST NUMERICAL METHOD FOR OPTION PRICES IN A TWO-ASSET JUMP-DIFFUSION MODEL
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We present an efficient and robust finite difference method for a two- asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.
Abstract
We present an efficient and robust finite difference method for a two- asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.
참고문헌 (21)
- F. Black, "The pricing of options and corporate liabilities", J. Polit. Econ, 81(3), pp.637~654 (1973)
- L. Bo, "The pricing of basket options: A weak convergence approach", Oper. Res. Lett., 45(2), pp.119~125 (2017)
- J.C. Bogle, "Black Monday and black swans", Financ. Anal. J., 64(2), pp.30~40 (2008)
- 최용호, "Robust and accurate method for the Black--Scholes equations with payoff-consistent extrapolation", 대한수학회논문집, 30(3), pp.297~311 (2015), 대한수학회
- S.S. Clift, "Numerical solution of two asset jump diffusion models for option valuation", Appl. Numer. Math., 58(6), pp.743~782 (2008)
- S.D. Conte, "Elementary Numerical Analysis: An Algorithmic Approach" (1980), McGraw-Hill
- D.J. Duffy, "Finite Difference methods in financial engineering: a Partial Differential Equation approach" (2013), John Wiley & Sons
- M. Fakharany, "Numerical valuation of two-asset options under jump diffusion models using Gauss–Hermite quadrature", J. Comput. Appl. Math., 330, pp.822~834 (2018)
- A. Fereshtian, "RBF approximation by partition of unity for valuation of options under exponential L´evy processes", J. Comput. Sci., 32, pp.44~55 (2019)
- J. Foo, "A Comparison of Global Financial Market Recovery after the 2008 Global Financial Crisis", Folia Oeconomica Stetinensia, 17(1), pp.109~128 (2008)
- S. Gulen, "A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities", Mathematics, 7(8), pp.760~ (2019)
- D. Jeong, "A comparison study of ADI and operator splitting methods on option pricing models", J. Comput. Appl. Math., 247, pp.162~171 (2013)
- DARAE JEONG, "A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL", 순수 및 응용수학, 22(2), pp.159~168 (2015), 한국수학교육학회
- V. Kaushansky, "Numerical analysis of an extended structural default model with mutual liabilities and jump risk", J. Comput. Sci., 24, pp.218~231 (2018)
- S.G. Kou, "A jump-diffusion model for option pricing", Manage. Sci, 48(8), pp.1086~1101 (2002)
- S.S. Lee, "Jumps and information flow in financial markets", Rev. Financ. Stud., 25(2), pp.439~479 (2011)
- R.C. Merton, "Option pricing when underlying stock returns are discontinuous", J. Fi-nanc. Econ., 3(1-2), pp.125~144 (1976)
- R. Rebonato, "Volatility and correlation: In the pricing of equity, FX and interest-rate options" (1999), John Wiley & Sons
- P. Tankov, "Financial modelling with jump processes", pp.2003, Chapman and Hall
- P. Tankov, "Jump-diffusion models: a practitioners guide", Banque et March´es, 99(1), pp.24~ (2009)
- Q. Wei, "Zero-sum games for continuous-time Markov jump processes with risk-sensitive finite-horizon cost criterion", Oper. Res. Lett, 46(1), pp.69~75 (2018)