A slight modification of the standard GARCH equation results in a good modeling of historical volatility. Using this generated GARCH volatility together with the inputs: spot price divided by strike, time to maturity, and interest rate, a generated Neural Network results in significantly better...

In 1973, Fisher Black, Myron Scholes and separately Robert Merton derived the Black-Scholes-Merton (BSM) model, which was rewarded the Nobel Prize in 1997. Despite its limitations, the model has survived until today as the dominant pricing model for standard and exotic European style options....

Traditionally probability is considered as a function that takes values in the interval [0, 1]. However, researchers found that negative, as well as larger than 1 probabilities could be a useful tool in making financial modeling more exact and flexible. Here we show how larger than 1...

This paper has two main contributions. We first build a general framework for valuing credit default swaps (CDS) with counterparty risk. We extend the work of Hull and White, and Hamp, Kettunen and Meissner, and build two quadruple trees. One tree represents the CDS spread payments, and one tree...

Financial markets have developed formulas and models to derive fair values for bonds, futures, swaps, options and other securities. This model derives a fair value of an exchange rate, which might be used as a benchmark for a long-term equilibrium level to stabilize currency markets. The model...