Related papers: Pricing Derivatives in Hermite Markets
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus…
SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with…
In this study we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY driven Ornstein- Uhlenbeck process. To this end, we first calculate the characteristic function of the…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure,…
An attempt to obtain market directional information from non-stationary solution of the dynamic equation: "future price tends to the value maximizing the number of shares traded per unit time" is presented. A remarkable feature of the…
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
In this article, we analyze two modeling approaches for the pricing of derivative contracts on a commodity index. The first one is a microscopic approach, where the components of the index are modeled individually, and the index price is…
The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a…
We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments…
We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients…
We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed…
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the…
Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes,…
This paper delves into the dynamics of asset pricing within Bachelier market model, elucidating the representation of risky asset price dynamics and the definition of riskless assets.