This paper proposes a general approximation method for the solutions to second order parabolic partial differential equations (PDEs) by an extension of Leandre's approach and the Bismut identity in Malliavin calculus. We show two types of its applications, new approximations of derivatives...

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise...

In this paper, we propose an efficient Monte Carlo implementation of a non-linear FBSDE as a system of interacting particles inspired by the idea of the branching diffusion method of McKean. It will be particularly useful to investigate large and complex systems, and hence it is a good...

This paper explores Bitcoin intraday technical trading based on artificial neural networks for the return prediction. In particular, our deep learning method successfully discovers trading signals through a seven layered neural network structure for given input data of technical indicators,...

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 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 develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump diffusion stochastic volatility models of spot exchange rates. In particular, we derive...

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for...

This paper studies the approximation accuracy of a singular perturbation method for option pricing up to the second order under a stochastic volatility model. First, numerical experiments confirm that the first order approximation provides sufficiently accurate option prices in a fast...