In this paper, an exact and explicit solution of the well-known Black-Scholes equation for the valuation of American put options is presented for the first time. To the best of the author's knowledge, a closed-form analytical formula has never been found for the valuation of American options of...

This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states...

This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable...

In this paper, a new decomposition approach for valuing convertible bonds (CBs) is presented. Through developing an appropriate integral representation for the value of convertible bonds, we show that an extra premium associated with the holder’s early conversion right exists in addition to...

In this paper, two analytic solutions for the valuation of European-style Parisian and Parasian options under the Black–Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a...

In this paper, a comprehensive review of the valuation of American options is presented. Various approaches to pricing American option contracts are discussed, with the pros and cons of each being briefly outlined. The paper aims to provide a literature review for those who are interested in...

The pricing of American options has been widely acknowledged as “a much more intriguing” problem in financial engineering. In this paper, a “convergency-proved” IFE (inverse finite element) approach is introduced to the field of financial engineering to price American options for the...