Monte Carlo simulation has been used to value options since Boyle's seminal paper. Monte Carlo simulation, however, has not been used to its fullest extent for option valuation because of the belief that the method is not feasible for American-style options. This paper demonstrates how to incorporate optimal early exercise in the Monte Carlo method of valuing options by linking forward-moving simulation and the backward-moving recursion of dynamic programming through an iterative search process. To demonstrate the potential of this method, we use it to value American-style options on the average price (or Asian options). The computational experience reveals a flexible valuation technique with potential for application to a range of securities and financial decision problems.option valuation, contingent claims valuation, Monte Carlo simulation, Asian options, average-price options, American options, path-dependent options, derivative securities

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Digital currencies, virtual currencies, in-game currencies, etc., have gathered a lot of attention, despite the difficulties of definition, from all corners of society for many years. Cryptocurrency has gained unprecedented attention since the birth of Bitcoin in 2009. Bitcoin is an online system of making and receiving payments in bitcoins. The system distinguishes itself by providing an opensource, cryptographically secure, confidentiality-preserving platform for transactions and/or making payments. The number of transactions as well as the number of accounts (held by individuals and businesses) is steadily increasing. A whole industry of service-providers has sprung up alongside. We consider the development of Bitcoin and its sister currencies as an important disruptive financial innovation which is here to stay unless throttled by ill-considered legislative or regulatory actions. Potential problems are analyzed and solutions offered. The overall assessment is that cryptocurrencies and variants of virtual currencies are a welcome development, they will offer competition to the existing modalities of money and governmental regulation, they will provide alternative means to economic agents for their transactions, and their innovative existence should be encouraged so that their beneficial features outperform any deleterious ones.