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...

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...

A growing literature analyzes the cross-section of single stock option returns, virtually always under the (implicit or explicit) assumption of a monotonically decreasing pricing kernel. Using option returns, we non-parametrically provide significant and robust evidence that the pricing kernel...

Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity...

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...

Empirical evidence shows that, in equity options markets, the slope of the skew is largely independent of the volatility level. Single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew. On the other hand, multifactor stochastic...

To bridge the gap between the output of theoretical option pricing models and observed option prices on exchanges, it is necessary to price the volatility risk inherent in financial markets. Non zero market risk premia have been found in previous financial literature through an exploration of...

With the success of variable annuities, insurance companies are piling up large risks in terms of both equity and fixed income assets. These risks should be properly modeled as the resulting dynamic hedging strategy is very sensitive to the modeling assumptions. The current literature has been...