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...

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)...

In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the...

Market mechanisms are increasingly being used as a tool for allocating somewhat scarce but unpriced rights and resources, and the European Emission Trading Scheme is an example. By means of dynamic optimization in the contest of firms covered by such environmental regulations, this paper...

This paper deals with issues related to the choice of the interest rate model to price interest rate derivatives. After the development of the market models, choosing the interest rate model has become almost a trivial task. However, their use is not always possible, so that the problem of...

We develop a two-state regime-switching rational expectation model with the economic states recession and expansion for the valuation of equity-linked life insurance contracts with surrender guarantees. Our valuation model jointly captures the empirically observed macroeconomical...

We consider the problem of pricing options on a leveraged ETF (LETF) and the underlying ETF in a consistent manner. We show that if the underlying ETF has Heston dynamics then the LETF also has Heston dynamics so that options on both the ETF and the LETF can be priced analytically using standard...

We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying...

The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which has been applied to several classical physics systems, including statistical mechanics of neocortical interactions, options in financial markets, and other nonlinear systems including chaotic...

We present an embarrassingly simple method for supervised learning of SABR model's European option price function based on lookup table or rote machine learning. Performance in time domain is comparable to generally used analytic approximations utilized in financial industry. However, unlike the...