In this article we suggest a new method for solutions of stochastic integrals where the dynamics of the variables in integrand are given by some stochastic differential equation. We also propose numerical simulation of stochastic differential equations which is based on iterated integrals method...

This paper discusses an extension of the traditional lognormal representation for the risk neutral spot freight rate dynamics to a diffusion model overlaid with jumps of random magnitude and arrival. Then, we develop a valuation framework for options on the average spot freight rate, which are...

In this paper we propose a multivariate asset model based on L´evy processes for pricing of products written on more than one underlying asset. Our construction is based on a two factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and...

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this...

Multi-factor interest-rate models are widely used. Contingent claims with early-exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm...

We present a simple method for “inverting” a volatility smile: that is, generating a CDF and inverse CDF given a discrete set of implied volatilities. The method is based on constructing a piece-wise linear CDF that is guaranteed to exactly reprice any non-arbitrageable input volatilities....

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of...

The analytic method of Chen, Cosimano, and Himonas (CCH 2009) is extended to prove that the continuous time version of the long run risk model of Bansal and Yaron (2004) has an analytic solution. The long run risk model is dependent on the recursive utility introduced by Duffie and Epstein...

This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping...

Unlike tranches of synthetic CDOs, that depend only on the defaults of the underlying securities, tranches of cashflow CDOs also depend on the interest cash flows from the coupons of the securities. Whilst fast, accurate, (semi-)analytic methods exist for pricing synthetic CDO tranches (Hull and...