The main aim of this work is to price defaultable bonds. In order to achieve this goal we link first hitting densities of Brownian motion with functionals of controlled diffusions. From a practical point of view examples of diffusions with this property are: Brownian motion with linear drift,...

A credit default swap (CDS) is a financial contract in which the holder of the instrument will be compensated in the event of a loan default. When available, CDS's are used to monitor the credit risk of countries and companies. In this work we develop a closed form procedure to value a CDS in...

This paper proposes the new concept of stochastic leverage in stochastic volatility models.Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...

We overcome the limitations of the previous literature in the European options pricing. In doing so, we provide a closed-form formula that doesn't require any numerical/computational methods. The formula is as simple as the classical Black-Scholes pricing formula. In addition, we simultaneously...

When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing...

We overcome a major obstacle in the literature. In doing, we introduce a simple, closed-form formula for pricing the American options. In particular, we significantly simplify Alghalith's closed-form formula for pricing American options. In doing so, we introduce a formula that does not require...

Options are financial derivatives which are used as risk management tools for hedging the portfolios. The options traders can play safely in the volatile markets with the help of knowledge of the Greeks associated with the options. This study is focused at providing the knowledge of the Greeks...

We present a numerically efficient approach for machine-learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility...

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...