A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model

A tree approach to options pricing under regime-switching jump diffusion models

“…In addition, the condition 2ηθ > σ 2 v is imposed to ensure v t > 0 (see [20]). Next, to remove the correlation between W 1 t and W t 2 in (36), we use the following change of variable (see [6]):…”

Pricing and calibration of the futures options market: A unified approximation

“…Also, some numerical techniques are developed for pricing the American options under different models, which can be typically divided into three categories: the tree‐based method, the finite difference method, and the simulation‐based method. For the tree‐based method, Maller et al (2006) provided a multinomial approximation method for pricing American options under the general exponential Lévy process, and Beliaeva and Nawalkha (2010) generated path‐independent trees under the Heston (1993) stochastic volatility model. For the finite difference method, Toivanen (2010) priced American options under jump‐diffusion models through implicit finite difference discretization.…”

An efficient pricing algorithm for American options with double stochastic volatilities and double jumps

“…Single-factor stochastic volatility models, including Stein and Stein, 1 Heston, 2 and Schöbel and Zhu, 3 can explain the volatility smile observed in the real market. Many literatures consider American options pricing under these models by developing some numerical methods, including the finite difference methods of Ikonen and Toivanen, 4,5 Ito and Toivanen, 6 Zhu and Chen, 7 and some extensions, such as Kunoth et al., 8 Rambeerich et al., 9 Ballestra and Pacelli, 10 and Burkovska et al., 11 the Monte Carlo simulation method of Abbas-Turki and Lapeyre 12 and the tree methods of Beliaeva and Nawalkha 13 and Ruckdeschel et al. 14…”

“…Single-factor stochastic volatility models, including Stein and Stein, 1 Heston, 2 and Sch€ obel and Zhu, 3 can explain the volatility smile observed in the real market. Many literatures consider American options pricing under these models by developing some numerical methods, including the finite difference methods of Ikonen and Toivanen, 4,5 Ito and Toivanen, 6 Zhu and Chen, 7 and some extensions, such as Kunoth et al, 8 Rambeerich et al, 9 Ballestra and Pacelli, 10 and Burkovska et al, 11 the Monte Carlo simulation method of Abbas-Turki and Lapeyre 12 and the tree methods of Beliaeva and Nawalkha 13 and Ruckdeschel et al 14 However, single-factor stochastic volatility models are not able to fit the implied volatility smile very well. Evidence from Cont and Tankov, 15 Fonseca et al, 16 Christoffersen et al, 17 and Fouque and Lorig 18 indicate that single-factor models can do a poor job in capturing the term structures of implicit volatilities over time.…”