In the present paper we explore the problem for pricing discrete barrier options utilizing the Black–Scholes model for the random movement of the asset price. We postulate the problemas a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number...

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-tr...

Path-dependent options are options whose payoff depends nontrivially on the price history of an asset. They play an important role in financial markets. Unfortunately, pricing path-dependent options could be difficult in terms of speed and/or accuracy. The Asian option is one of the most prominent examples. The Asian option is an option whose payoff depends on the arithmetic average price of th...

Risk-shifting incentive problem in financial contracting, which typically arises in the context of a lenderborrower relationship, stands for the borrower’s incentive to influence the risk of his project. Thus, the borrower can increase the value of his payoff at the expense of the lender. However, the lender also may have a risk incentive under some circumstances so that he may render it diffic...

During the last decade, financial models have acquired increasing popularity in option pricing. The valuation of different types of option contracts is very important in modern financial theory and practice – vanilla and especially exotic options have become very popular speculation instruments in recent years. The problem of determining the fair price of such an option is standardly formulated...

Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in...

Based on the works of Brockman and Turtle (2003) and Giesecke (2004), we proposed in this study a hybrid barrier option model with corporate capital gains tax which is free of problems within the structural model in explaining observed credit spreads. Our approach does not predict credit spreads that are too low for investment grade corporate bonds; neither does it predict credit spreads that a...