Using a general equilibrium model in which both capital productivity and temperature are uncertain, we show that the social discount rate (SDR) will decline from 1% in 2010 to 0.6% in 2300 under the conventional, quadratic specification of the damage function, and to -2.0% under the reactive...

In financial markets, traders deal in assets and options. There exist many types of options and the best-known are the European call and put option. These options give holders the right to buy or sell assets at a specific future time for a predetermined price. This paper examines options of...

When Fourier techniques are employed to specific option pricing cases from computational finance with non-smooth functions, the so-called Gibbs phenomenon may become apparent. This seriously impacts the efficiency and accuracy of the pricing. For example, the Variance Gamma asset price process...

We develop three numerical methods to solve coupled forward-backward stochastic differential equations. We propose three different discretization techniques for the forward stochastic differential equation. A theta-discretization of the time-integrands is used to arrive at schemes with...

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). General theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier-cosine series expansions, relying on the availability...

We develop a Fourier method to solve rather general backward stochastic differential equations (BSDEs) with second-order accuracy. The underlying forward stochastic differential equation (FSDE) is approximated by different Taylor schemes, such as the Euler, Milstein, and Order 2.0 weak Taylor...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...

We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main...

We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. A so-called volatility compensator is defined which guarantees that the Heston hybrid model with a non-zero correlation...