A Hybrid Asymptotic Expansion Scheme: An Application to Long-Term Currency Options

On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model

“…Therefore, the difference between f (S ε t ) and f (Ŝ ε t ) is negligible in the small disturbance asymptotic theory, and hence our expansion can be applied to (40) through (41).…”

“…On the contrary, our method are applicable in a unified manner to the problems. As for the concrete applications, see , [35] (2011, 2012) for the basket and discrete average options with stochastic volatilities; Shiraya-Takahashi-Yamada [37] (2012) for discrete barrier options under stochastic volatilities; Shiraya-Takahashi-Yamazaki [38] (2012), Takahashi-Takehara [41] (2010), Takehara-Toda-Takahashi [44] (2011), for swaption or long-term currency option pricing under LMMs with stochastic volatilities of interest rates or foreign exchange rates.…”

“…We remark that this type of expansion technique has been successfully applied with substantial numerical experiment to the finance models widely used in practice: (for instance, see Kato et al [19] (2012), [20] (2013), Li [25] [26] (2010, 2013), Xu-Zheng [52], [53] (2010, 2012), Shiraya-Takahashi [34], [35] (2011, 2012), Shiraya-Takahashi-Toda [36] (2011), Shiraya-Takahashi-Yamada [37] (2012), Shiraya-Takahashi-Yamazaki [38] (2012), Takahashi-Takehara [41] (2010) for the various derivatives pricing; Matsuoka et al [31] (2006) for the Greeks; Li [26] (2013), Takahashi et al [42], [43] (2009, 2012) for computational schemes of high-order expansions, and the references therein.) We also note that there exist many other types of the expansion/perturbation methods which have turned out to be so useful in financial applications: for example see Alos [1] (2012), Alos et al [2] (2011), Bayer-Laurence [3] (2012), Ben Arous-Laurence [4] (2009), Davydov-Linetsky [9] (2003), Foschi et al [11] (2013), Fouque et al [12] (2002), Fujii [14] (2012), Gatheral et al [15] (2012), Hagan et al [16] (2002), Linetsky [27] (2004), Siopacha-Teichmann [39] (2011), and the references therein.…”

On Error Estimates for Asymptotic Expansions with Malliavin Weights -- Application to Stochastic Volatility Model

“…On the contrary, our method are applicable in a unified manner to the problems. As for the concrete applications, see , [35] (2011, 2012) for the basket and discrete average options with stochastic volatilities; Shiraya-Takahashi-Yamada [37] (2012) for discrete barrier options under stochastic volatilities; Shiraya-Takahashi-Yamazaki [38] (2012), Takahashi-Takehara [41] (2010), Takehara-Toda-Takahashi [44] (2011), for swaption or long-term currency option pricing under LMMs with stochastic volatilities of interest rates or foreign exchange rates.…”

“…We remark that this type of expansion technique has been successfully applied with substantial numerical experiment to the finance models widely used in practice: (for instance, see Kato et al [19] (2012), [20] (2013), Li [25] [26] (2010, 2013), Xu-Zheng [52], [53] (2010, 2012), Shiraya-Takahashi [34], [35] (2011, 2012), Shiraya-Takahashi-Toda [36] (2011), Shiraya-Takahashi-Yamada [37] (2012), Shiraya-Takahashi-Yamazaki [38] (2012), Takahashi-Takehara [41] (2010) for the various derivatives pricing; Matsuoka et al [31] (2006) for the Greeks; Li [26] (2013), Takahashi et al [42], [43] (2009, 2012) for computational schemes of high-order expansions, and the references therein.) We also note that there exist many other types of the expansion/perturbation methods which have turned out to be so useful in financial applications: for example see Alos [1] (2012), Alos et al [2] (2011), Bayer-Laurence [3] (2012), Ben Arous-Laurence [4] (2009), Davydov-Linetsky [9] (2003), Foschi et al [11] (2013), Fouque et al [12] (2002), Fujii [14] (2012), Gatheral et al [15] (2012), Hagan et al [16] (2002), Linetsky [27] (2004), Siopacha-Teichmann [39] (2011), and the references therein.…”