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 what follows we outline briefly the Credit Support Annex and how it impacts securities pricing. We then proceed to discuss synthetic forward rate calculation and the FX forward invariance relationship from which we show how to calculate CSA collateral adjusted discount factors using GBP...

Presented is the formulation for determining the exact, expected growth-optimal fraction of equity to risk for all conditions, rather than merely the asymptotic growth-optimal fraction. The formulation presented represents the surface in the leverage space manifold, wherein the loci at the peak...

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...

This paper presents an analytic approximation formula for pricing zero-coupon bonds, when the dynamics of the short-term interest rate are driven by a one-factor mean-reverting process in which changes in the volatility of the interest rate are a function of the level of the interest rate

The initial reason for writing this essay was to provide the background and a derivation of the IR quanto adjustment, as a mean of expressing the Hull-White dynamics of foreign currency interest rates under a domestic risk-neutral measure. However, one thing led to another, and the essay ended...

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...

We revisit well-known stochastic volatility models with constant coefficients for single asset driven by one factor stochastic volatility as homogeneous diffusion and demonstrate an alternative to the classifications provided in Albanese and Lawi, and Henry-Labord`ere, to deduce asset price...

We investigate how buyer-supplier firm-specific relationships affect security prices. We propose a structural model of firm dependence in a vertically connected network of firms based on cash flow transfers between buyers and suppliers. We prove that financial market completeness in a closed...