Search

This work is concerned with pricing American fixed lookback put options. The underlying asset is modeled as a switching diffusion process, where the switching is represented by a continuous-time Markov chain. The switching diffusion delineates stochastic volatility effectively. Nevertheless, this formulation together with the lookback style put option makes it virtually impossible to find closed-form solutions. As a viable alternative, a stochastic approximation algorithm is suggested. The convergence and rates of convergence of the algorithm are established. [ABSTRACT FROM AUTHOR]

This article is concerned with a numerical method using stochastic approximation approach for an optimal trading (buy and sell) strategy. The underlying asset price is governed by a mean-reverting stochastic process. The objective is to buy and sell the asset so as to maximize an overall expected return. One of the advantages of our approach is that the underlying asset is model free. Only mean reversion is required. Slippage cost is imposed on each transaction. Convergence of the algorithms is provided. Numerical examples are reported to demonstrate the results. [ABSTRACT FROM AUTHOR]

This work is concerned with option pricing. Stochastic approximation/optimization algorithms are proposed and analyzed. The underlying stock price evolves according to two geometric Brownian motions coupled by a continuous-time finite state Markov chain. Recursive stochastic approximation algorithms are developed to estimate the implied volatility. Convergence of the algorithm is proved. Rate of convergence is also ascertained. Then real market data are used to compare our algorithms with other schemes. [ABSTRACT FROM AUTHOR]