The underlying state variables may be the stock prices, interest rates, exchange rates, stochastic volatility, average of stock prices, extremum values of stock priors, etc. Option contracts whose life and payoff depend on the stochastic movement of the underlying asset prices are termed path dependent options.
In this paper, we examine the pricing methods of several prototype path dependent options.
(3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as barrier and lookback options.
In particular, path-dependent options are successful, and most of them comprise barrier options to reduce the cost of hedging [4, 8, 22].
Though highly cost-effective prevention options are available for men (VMMC and male condoms), there is still a great need to seek coitally-dependent options that women can initiate, such as microbicides, in whichever formulation.
Our next goal is to extend the preceding hedging argument to the case of a path-dependent exotic option.
The expected second-cohort contract serves as an endogenous type-dependent outside option for first-cohort buyers, reducing the seller's ability to extract rents via sequential contracts.
While the buyer gains real options for external (economic) value creation as a result of family departure, family exit after the sale triggers a loss of family dependent real options, which may subsequently reduce economic value for the new owner.
Traditional techniques such as the finite-differences method and lattice become less attractive when dealing with pricing derivatives with multiple stochastic variables, problems with many dimensions, or even path-dependent American options, as it is the case of American Asian (Amerasian) options.
In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes.
