This paper proposes a general approximation method for the solution to a second-order parabolic partial differential equation(PDE) widely used in finance through an extension of Léeandre's approach(Léandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997))] in Malliavin...

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we...

　　 This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a...

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...

We developed a new scheme for computing "Greeks"of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and vegas of plain vanilla and average call options under general Markovian processes of underlying asset prices. We also...

We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method, but also show its effectiveness through numerical examples such as...

We developed a new scheme for computing "Greeks"of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and Vegas of plain vanilla and av-erage European call options under general Markovian processes of underlying asset prices....

This paper derives an approximation formula for average options under two stochastic volatility models such as Heston and ă(Lambda)-SABR models by using an asymptotic expansion method. Moreover, numerical examples with various parameters some of which are obtained by calibration to WTI...

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using...

　　 This paper develops a new approximation formula for pricing basket options in a local-stochastic volatility model with jumps. In particular, the model admits local volatility functions and jump components in not only the underlying asset price processes, but also the volatility...