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This paper explores the application and significance of the second-order Esscher pricing model in option pricing and risk management. We split the study into two main parts. First, we focus on the constant jump diffusion (CJD) case,…
In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model.…
This paper deals with the numerical solution of the two-dimensional time-dependent Merton partial integro-differential equation (PIDE) for the values of rainbow options under the two-asset Merton jump-diffusion model. Key features of this…
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the…
We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…
We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation…
In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit form of moment…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…