We show that the distribution of the arithmetic, continuous average of log-normal variables is log-normal. We also introduce a simple, explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula

We introduce a simple, explicit formula for pricing the Bermudan options. Furthermore, the formula does not require any additional parameter (relative to the European option formula). Moreover, we provide an upper bound for the price

In this paper, we show that the influential Merton jump diffusion model and formula are needlessly cumbersome. In doing so, we provide a simple, explicit formula that doesn't require a computational method. Furthermore, we introduce a new, simple method for solving partial...

This is the first paper to provide a simple, explicit formula (that doesn’t requirenumerical/computational methods) under stochastic volatility. The formulais as simple as the classical Black-Scholes pricing formula. Furthermore,this paper modifies the Black-Scholes model to make it consistent...

We construct realistic equity option market simulators based on generative adversarial networks (GANs). We consider recurrent and temporal convolutional architectures, and assess the impact of state compression. Option market simulators are highly relevant because they allow us to extend the...

Computing Standardized Initial Margin Model Margin Valuation Adjustment (SIMM-MVA) requires the simulation of future sensitivities, but these are expensive to compute for callable products. This paper introduces a method which avoids nested calls to the pricing function, similar to the use of...

We generalize the algorithmic differentiation method proposed by Antonov (2016) from price Greeks to XVA Greeks. This method, named Backward Differentiation (BD), was developed in the context of computing price or PV Greeks for individual callable exotic trades.We start by treating cases where...