Related papers: Unifying Market Microstructure and Dynamic Asset P…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition…
Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both…
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…
In the present paper we fill an essential gap in the Convertible Bonds pricing world by deriving a Binary Tree based model for valuation subject to credit risk. This model belongs to the framework known as Equity to Credit Risk. We show…
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…
Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with…
Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both…
Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this…
Using the Donsker-Prokhorov invariance principle we extend the Kim-Stoyanov-Rachev-Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the…
We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
We introduce a first theory of price impact in presence of an interest-rates term structure. We explain how one can formulate instantaneous and transient price impact on bonds with different maturities, including a cross price impact that…
While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
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…