Related papers: Pricing spread option with liquidity adjustments
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a…
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…
In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…
Valuation adjustments are nowadays a common practice to include credit and liquidity effects in option pricing. Funding costs arising from collateral procedures, hedging strategies and taxes are added to option prices to take into account…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…
The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
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…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is…
In this research, we proposed a Mean Convection Finite Difference Method (MCFDM) for European options pricing. The Black-Scholes model, which describes the dynamics of a financial asset, was first transformed into a convection-diffusion…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of…
This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial…
The general and special repo rates are related with the prices of the European call- and American put-options. The evaluation takes into account specific business models of the parties in the repo agreement and the law restrictions. Using…