In the past years, there has been an extensive investigation of class stochastic volatility models for evaluation options and complex derivatives. These have proven to be extremely useful in generalizing classic Black–Scholes economy accounting discrepancies between observation predictions simple log-normal, constant-volatility model. this paper, we study structure market with a that will event...

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...

In this paper, we apply Carr’s randomization approximation and the operator form of theWiener-Hopf method to double barrier options in continuous time. Each step in the resulting backward induction algorithm is solved using a simple iterative procedure that reduces the problem of pricing options with two barriers to pricing a sequence of certain perpetual contingent claims with first-touch sing...

It is only recently that simulation has begun to play an important role in pricing high-dimensional American options. This was due to the fact that since Monte Carlo simulation generally works forward in time while dynamic programming works backwards, it was generally believed that the two were somewhat incompatible. Research in recent years has shown that this is not the case and that Monte Ca...

Derivative securities, when used correctly, can help investors increase their expected returns and minimize their exposure to risk. Options offer leverage and insurance for risk-averse investors. For the more risky investors, they can be ways of speculation. When an option is issued, we face the problem of determining the price of a product which depends on the performance of another security a...

Options with discontinuous payoffs are generally traded above their theoretical Black–Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits superreplication of the...