Related papers: Super-hedging American Options with Semi-static Tr…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
We study the behavior of the critical price of an American put option near maturity in the Jump diffusion model when the underlying stock pays dividends at a continuous rate and the limit of the critical price is smaller than the stock…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options…
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual…
We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via…
We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the…
In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this…
We consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…
In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other…
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 paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
This article examines neural network-based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the $\alpha$-quantile hedging price converges to the superhedging price…
We solve the superhedging problem for European options in an illiquid extension of the Black-Scholes model, in which transactions have transient price impact and the costs and the strategies for hedging are affected by physical or cash…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit…