Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these derivatives for (T,k) approaching the origin within the...

We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat...

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based...

Numerous studies find S-shaped pricing kernels, which is conflicting with standard theory. In contrast to that, based on a novel GARCH model with structural breaks, I show that the pricing kernel is consistently U-shaped. The results are robust to variations in the methodology and hold for...

Short sell bans are often imposed during a financial crisis as a desperate measure to stabilize financial markets. Yet, the impact of short sell bans on option pricing and hedging is not well quantitatively studied until very recently when Guo and Zhu (2017) and He and Zhu (2018) formulated a...

This paper describes a method for computing risk-neutral density functions based on the option-implied volatility smile. Its aim is to reduce complexity and provide cookbook-style guidance through the estimation process. The technique is robust and avoids violations of option no-arbitrage...

This paper introduces an option pricing algorithm based on non-orthogonal series expansion methods. More precisely, Gabor frame decomposition is used to split the risk neutral option pricing formula into the sum of two inner products that can be evaluated efficiently by means of Parseval's...

In this paper we present drawbacks of the Black-Scholes option pricing theory. Shorter version of this paper were announced in [8]. Black-Scholes option theory represents unified construction of no arbitrage pricing. It is common to think that in the theory Black-Scholes price represents the...

In some papers we remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular, there are two problems which can be raised by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and the other the pricing definition...