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タイトル: A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options
著者: Takahashi, Akihiko
Takehara, Kohta
著者(別言語): 高橋, 明彦
竹原, 浩太
キーワード: Currency option
libor market model
stochastic volatility
asymptotic expansion
Monte Carlo simulation
発行日: 2010年4月
出版者: 日本経済国際共同センター
抄録: This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates.// Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained.// An asymptotic expansion approach provides a closed-form approximation formula for their values, which can be calculated in a moment and thus can be used for calibration or for an explicit approximation of Greeks of options. Moreover, this scheme develops Fourier transform method with an asymptotic expansion as well as with closed-form characteristic functions obtainable in parts of a model, extending the method proposed by Takehara and Takahashi[2008] to be applicable to a general class of models. It also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of the closed-form characteristic functions.// Finally, a series of numerical examples shows the effectiveness of our scheme.
内容記述: Forthcoming in International Journal of Theoretical and Applied Finance Vol.13-8, 1179-1221, 2010; revised version of CIRJE-F-536 (2008).
URI: http://hdl.handle.net/2261/35800
その他の識別子: CIRJE-F-734
出現カテゴリ:061 ディスカッションペーパー
Discussion Paper F series (in English)


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