The asymptotic expansion approach to the valuation of interest rate contingent claims
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 …
when the underlying asset prices follow a general class of continuous Itô processes. Our …
An asymptotic expansion approach to pricing financial contingent claims
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 …
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
Kunitomo and Takahashi (1995, 2001) have proposed a new methodology, called small
disturbance asymptotics, for the valuation problem of financial contingent claims when the …
disturbance asymptotics, for the valuation problem of financial contingent claims when the …
An asymptotic expansion with push-down of Malliavin weights
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 …
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
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 …
spreads in cross‐currency as well as domestic interest rate markets. Furthermore, the …
An asymptotic expansion scheme for optimal investment problems
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 …
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
This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe
Calculus in Mathematical Finance. We give the basic formulation of the asymptotic …
Calculus in Mathematical Finance. We give the basic formulation of the asymptotic …
Closed-form expansion, conditional expectation, and option valuation
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 …
(Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15: 1–39] for analyzing …
[HTML][HTML] Conditional expansions and their applications
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 …
expansions. Our discussion will be based on the Malliavin calculus. First, we treat a problem …
Pricing average options on commodities
This study proposes a new approximation formula for pricing average options on
commodities under a stochastic volatility environment. In particular, it derives an option …
commodities under a stochastic volatility environment. In particular, it derives an option …