This paper analyzes the theoretical problem of the real option with barrier. It models an investment decision with a double irreversibility concern: investing is irreversible, but waiting runs the risk of loosing the opportunity to invest. The optimal strategy leads to earlier investment when the barrier increases, or when uncertainty decreases. Uncertainty has ambiguous effects on the expected...

The valuation and applications of one-touch double barrier binary options that include features of knock-out, knock-in, European and American style are described. Using a conventional Black Ð Scholes option-pricing environment, analytical solutions of the options are derived. The relationships among di€ erent types of one-touch double barrier binary options are discussed. An investor having a p...

Svetlozar T. Rachev Chair-Professor, Chair of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and KIT, Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany and Department of Statistics and Applied Probability, University of California, Santa Barbara, and Chief-Scientist, FinAnalytica Inc. E...

We obtain closed–form expressions for the prices and optimal hedging strategies of American put–options in the presence of an “up–and–out” barrier, both with and without constraints on the short–selling of stock. The constrained case leads to a stochastic optimization problem of mixed optimal stopping/singular control type. This is reduced to a variational inequality which is then solved explic...

An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple and easy to implement analytic formulas for the distribution of one-dimensiona...

Estimators for the price of a discrete barrier option based on conditional expectation and importance sampling variance reduction techniques are given. There are erroneous formulas for the conditional expectation estimator published in the literature: we derive the correct expression for the estimator. We use a simulated annealing algorithm to estimate the optimal parameters of exponential twis...

Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an impl...