We construct a new approximate method for pricing barrier options and CDSs. In many cases, prices of barrier options and CDSs of maturities one year and more, at the log-distance 0.1 from the barrier and farther, for 8 spots, can be calculated adding up 4-16 fairly simple terms, with relative...

We develop a general simple methodology for very fast and accurate evaluation of special functions of several classes. We use a family of fractional-parabolic deformations of the contours of integration to appropriate Riemann surfaces, make the corresponding conformal changes of variables and...

Exponential growth of credit default swaps market and the resulting pile of CDS contracts of notional value of $62 trillion by the end of 2007 as well as the OTC nature of the contracts are widely believed to be one of the main causes of the current crisis and its depth, because large volumes of...

We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Levy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results...

The fast Fourier transform (FFT) technique is now a standard tool for the numerical calculation of prices of derivative securities. Unfortunately, in many important situations, such as the pricing of contingent claims of European type near expiry, and the pricing of barrier options close to the...

The standard operator approach to the identification problem of diffusions and more general Markov processes relies on the variational principles for self-adjoint operators. If the process is not time reversible, equivalently, the infinitesimal operator of the process is not self-adjoint, these...

We consider the Heston model with the stochastic interest rate of the CIR type and more general models with stochastic volatility and interest rates depending on two CIR - factors. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...

A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...

A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...

A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...