Markets

Traditional methods for the stochastic alpha beta rho model tend to focus on expansion approximations that are inaccurate in the long maturity ‘wings’.

In this article, we propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives.

In this article, we present the analytical approximation of zero-coupon bonds and swaption prices for general short rate models.

In this article, we give a general treatment of the Vanna-Volga mark-to-market volatility smile correction in application to pricing of contracts with European exercise on a single underlying.

In this article, we introduce a method for volatility computation from listed prices of American options on an underlying close to log-normal. 

In this article, we present a simple bottom-up dynamic credit model that can be calibrated simultaneously to the market quotes on CDO tranches and individual CDSs constituting the credit portfolio. 

In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility.