This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin...

The recent financial crisis has spiked the credit and liquidity premia among financial products, and significant widening of basis spreads among Libors with different tenors and currencies has been observed in interest rate markets. Our previous work, "A Note on Construction of Multiple Swap...

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction...

This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these...

This paper proposes a new approximation method of pricing barrier and average options under stochastic volatility environment by applying an asymptotic expansion approach. In particular, a high-order expansion scheme for general multi-dimensional diffusion processes is effectively applied....

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional...

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. Moreover, it confirms that the prices of crude oil and copper futures prices estimated by our model replicate the...

Recently, not only academic researchers but also many practitioners have used the methodology so-called ``an asymptotic expansion method" in their proposed techniques for a variety of financial issues. e.g. pricing or hedging complex derivatives under high-dimensional stochastic environments....

This chapter provides a comprehensive explanation of hedge fund replication. This chapter first reviews the characteristics of hedge fund returns. Then, the emergence of hedge fund replication products is discussed. Hedge fund replication methods are classified into three categories: Rule-based,...

This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou [1997, 2002] and Carr and Wu [2002]. Second, we present a concrete procedure...