In the existing literature on barrier options, much effort has been exerted to ensure convergence through placing the barrier in close proximity to, or directly onto, the nodes of the tree lattice. In this paper we show that this may not be necessary to achieve accurate option price...

We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the...

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider...

The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for...

We use a reflection result to give simple proofs of (well-known) valuation formulas and static hedge portfolio constructions for zero-rebate single-barrier options in the Black-Scholes model. We then illustrate how to extend the ideas to other model types giving (at least) easy-to-program...

This paper proposes a framework for bank equity valuation based on a path-dependent, barrier option model. A direct implication of this framework is that bank equity will be priced as a down-and-out call option. Using this approach, we examine how bank interest margin, i.e., the spread between...

Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x) using a two-dimensional Gaussian quantum field A(t,x). The strong correlations of...

In this paper, we present closed-forms for the valuation of the barrier option whose underlying is exchange rate under the multi-dimensional Levy process, including stochastic interest rates and stochastic assets. Instantaneous forward interest rates are assumed under the Heath et al. [1992....

Many structural models specify the default barrier, but few have explored its empirical significance and determinants. The effect of liquidity shortage is not well measured, nor is the effect of strategic default well identified. We use the maximum likelihood (ML) approach to estimate the...

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black–Scholes...