The binomial tree method, first proposed by Cox, Ross, and Rubinstein [Journal of Financial Economics, 7 (1979), pp. 229–263], is one of the most popular approaches to pricing options. By introducing an additional path-dependent variable, such methods can be readily extended to the valuation of path-dependent options. In this paper, using numerical analysis and the notion of viscosity solutions...

This paper considers the problem of pricing options with early-exercise features whose payoff depends on several sources of uncertainty. We propose a stochastic grid method for estimating the upper and lower bound values of high-dimensional American options. The method is a hybrid of the least squares method of Longstaff and Schwartz (2001) [22], the stochastic mesh method of Broadie and Glasse...

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply function equilibrium (SFE) and Cournot models to develop firms’ optimal bidding strategies by including fo...

Asian options are strongly path-dependent derivatives. Although efficient numerical methods and approximate closedform formulas are available, most lack convergence guarantees. Asian options can also be priced on the lattice. All efficient lattice algorithms keep only a polynomial number of states and use interpolation to compensate for the less than full representation of the states. Let the t...

Asian options can be priced on the unrecombining binomial tree. Unfortunately, without approximation, the running time is exponential. This paper presents efficient and extremely accurate approximation algorithms for European-style Asian options on the binomial tree. For a European-style Asian option with strike price X on an n-period binomial tree, our algorithm runs in O(kn2) time with a guar...