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)...

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...

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

The main goal of this paper is to better understand the behavior of credit spreads in the past and the potential risk of unexpected future credit spread changes. One important consideration to note regarding credit spreads is the fact that bond spreads contain a liquidity premium, which...

The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for...

The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

In this work, we propose an efficient and robust valuation of discretely monitored arithmetic Asian options based on Shannon wavelets. We employ the so-called SWIFT method, a Fourier inversion numerical technique with several important advantages with respect to the existing related methods....

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...