The asymptotic expansion approach to the valuation of interest rate contingent claims

N Kunitomo, A Takahashi - Mathematical Finance, 2001‏ - Wiley Online Library
We propose a new methodology for the valuation problem of financial contingent claims
when the underlying asset prices follow a general class of continuous Itô processes. Our …

An asymptotic expansion approach to pricing financial contingent claims

A Takahashi - Asia-Pacific Financial Markets, 1999‏ - Springer
We propose a new methodology for the valuation problem of financial contingent claims
when the underlying asset prices follow a general class of continuous Itô processes. Our …

On validity of the asymptotic expansion approach in contingent claim analysis

N Kunitomo, A Takahashi - The Annals of Applied Probability, 2003‏ - projecteuclid.org
Kunitomo and Takahashi (1995, 2001) have proposed a new methodology, called small
disturbance asymptotics, for the valuation problem of financial contingent claims when the …

An asymptotic expansion with push-down of Malliavin weights

A Takahashi, T Yamada - SIAM Journal on Financial Mathematics, 2012‏ - SIAM
This paper derives asymptotic expansion formulas for option prices and implied volatilities
as well as the density of the underlying asset price in multidimensional stochastic volatility …

A market model of interest rates with dynamic basis spreads in the presence of collateral and multiple currencies

M Fujii, Y Shimada, A Takahashi - Wilmott, 2011‏ - Wiley Online Library
The recent financial crisis caused dramatic widening and elevated volatilities among basis
spreads in cross‐currency as well as domestic interest rate markets. Furthermore, the …

An asymptotic expansion scheme for optimal investment problems

A Takahashi, N Yoshida - Statistical Inference for Stochastic Processes, 2004‏ - Springer
We shall propose a new computational scheme for the evaluation of the optimal portfolio for
investment. Our method is based on an extension of the asymptotic expansion approach …

Applications of the asymptotic expansion approach based on Malliavin-Watanabe calculus in financial problems

N Kunitomo, A Takahashi - Stochastic processes and applications …, 2004‏ - World Scientific
This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe
Calculus in Mathematical Finance. We give the basic formulation of the asymptotic …

Closed-form expansion, conditional expectation, and option valuation

C Li - Mathematics of Operations Research, 2014‏ - pubsonline.informs.org
Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals
(Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15: 1–39] for analyzing …

[HTML][HTML] Conditional expansions and their applications

N Yoshida - Stochastic processes and their applications, 2003‏ - Elsevier
In the present article, we will consider a conditional limit theorem and conditional asymptotic
expansions. Our discussion will be based on the Malliavin calculus. First, we treat a problem …

Pricing average options on commodities

K Shiraya, A Takahashi - Journal of Futures Markets, 2011‏ - Wiley Online Library
This study proposes a new approximation formula for pricing average options on
commodities under a stochastic volatility environment. In particular, it derives an option …