Related papers: Option pricing using a skew random walk pricing tr…
In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of…
We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
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…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with…
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account.…
Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an…
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities…
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…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…