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We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomia ...
I present a tractable framework, first developed in Trolle and Schwartz (2009), for pricing energy derivatives in the presence of unspanned stochastic volatility. Among the model features are i) a perfect fit to the initial futures term structure, ii) a fa ...
We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly faci ...
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 ...
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...
This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for w ...
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and ...
We build a model of investment and financing decisions to study the choice between bonds and bank loans in a firm's marginal financing decision and its effects on corporate investment. We show that firms with more growth options, with higher bargaining pow ...
A growing number of technologies are being developed in order to produce different high added value products, such as phytochemicals, ethanol and other chemicals from biomass, representing an important trend that needs to be evaluated. The use of pressuriz ...
In the first chapter,which is a joint work with Mathieu Cambou and Philippe H.A. Charmoy, we study the distribution of the hedging errors of a European call option for the delta and variance-minimizing strategies. Considering the setting proposed by Heston ...