標題: An efficient and accurate lattice for pricing derivatives under a jump-diffusion process
作者: Dai, Tian-Shyr
Wang, Chuan-Ju
Lyuu, Yuh-Dauh
Liu, Yen-Chun
資訊管理與財務金融系 註:原資管所+財金所
Department of Information Management and Finance
關鍵字: Option pricing;Numerical method;Lattice construction;Jump-diffusion process;Complexity
公開日期: 1-Dec-2010
摘要: Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset's price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives' specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality. (C) 2010 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.amc.2010.08.050
http://hdl.handle.net/11536/31890
ISSN: 0096-3003
DOI: 10.1016/j.amc.2010.08.050
期刊: APPLIED MATHEMATICS AND COMPUTATION
Volume: 217
Issue: 7
起始頁: 3174
結束頁: 3189
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