This paper presents a tractable model of non-linear dynamics of market returns using a Langevin approach.Due to non-linearity of an interaction potential, the model admits regimes of both small and large return fluctuations. Langevin dynamics are mapped onto an equivalent quantum mechanical (QM)...

The ultimate goal of this note is to provide a background for, and describe, the Longstaff-Schwartz LSM (Least-Squares Monte Carlo) algorithm for evaluating derivatives with early (American/Bermudan) exercise.The reason for writing yet another paper on the matter is that this method is often...

This paper discusses the relation between forward price models (FPM) and the so called implied volatility term structure (VTS). We start by considering the case of pure deterministic forward price volatilities and suppose both forward contracts and at-the-money (ATM) options, on a same...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

Spanish Abstract: Se describe la forma como la transformada discreta de Fourier puede ser aplicada a la valoración de opciones financieras en tiempo discreto, en lo que se denomina valoración circular. Esta no es más que una forma gráfica de introducir el uso de la transformada discreta de...

A backward induction procedure for pricing arithmetic Asian options in Levy models is realized in the dual space. Each step of the procedure is the composition of a multiplication operators by an explicitly given function, and the convolution operator ${\cal H}_\Ga$, which belongs to a class of...

This paper introduces an analytically tractable method for the pricing of European and American Parisian options in a flexible jump–diffusion model. Our contribution is threefold. First, using a double Laplace–Carson transform with respect to the option maturity and the Parisian (excursion)...

In this paper we provide an outline of interest rate swaptions and how to price swaptions with different payoff or settlement types. Firstly we review the different settlement styles commonplace in financial markets. Secondly we review the swaption pricing formulae corresponding to each...

In this paper we outline the European interest rate swaption pricing formula from first principles using the Martingale Representation Theorem and the annuity measure. This leads to an expression that allows us to apply the generalized Black-Scholes result. We show that a swaption pricing...

The Black-Scholes (1973) formula is well used for pricing vanilla European options. There are several different variations used by market practitioners dependent on the underlying asset being modelled. In this brief paper we present the generalized Black-Scholes representation, outline it's...