We model the dynamics of asset prices and associated derivatives by considerationof the dynamics of the conditional probability density process for the value of an assetat some specied time in the future. In the case where the asset is driven by Brownianmotion, an associated \master equation"...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: i) ensures nonnegative interest rates, ii) easily...

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by...

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form...

We study American swaptions in the linear-rational (LR) term structure model introduced. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus. We...

This paper considers the pricing and hedging of collateralized debt obligations (CDOs). CDOs are complex derivatives on a pool of credits which we choose to analyse in the top down model proposed in Filipovic et al. (2009). We reflect on the implied forward rates and bring them in connection...

In this paper we value a callable snowball floater, a complex interest rate instrument with variable coupon payments, which depend on the prevailing interest rates in arrears and recursively on previous coupon payments. The embedded option requires solving an optimal stopping problem using the...

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to...

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump-diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and...