Related papers: Option pricing and hedging with minimum local expe…
In this paper, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to…
We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the…
In this article, we investigate the behavior of long-term options. In many cases, option prices follow an exponential decay (or growth) rate for further maturity dates. We determine under what conditions option prices are characterized by…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…
This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular,…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing,…
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss…