In this paper, arithmetic average Asian options are studied. It is observed that the Asian option is a special case of the option..., Original Research, Computational finance

The revenue risk is considerable in infrastructure project financing arrangements such as build–operate–transfer (BOT). A potential mitigation strategy for the revenue risk is a governmental revenue guarantee, where the government secures a minimum amount of revenue for a project. Such a guarantee is: (1) only redeemable at distinct points in time; and (2) more economical if the government limits the guarantee’s availability to the early portions of a BOT’s concession period. Hence, a guarantee characterized by this type of structure takes the form of either a Bermudan or a simple multiple-exercise real option, depending upon the number of exercise opportunities afforded. The multi-least-squares Monte Carlo technique is presented and illustrated as a promising approach to determine the fair value of this variety of real option. This method is far more flexible than prevailing approaches, so it represents an important step toward improving risk mitigation and facilitating contractual and financial negotiat...

In this article, we define new ‘Greeks’ for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees, are sensitive to these parameters. In order to illustrate the concept of the new ‘Greeks’, we derive probabilistic representations of sensitivities for two classes of financial contracts: forwards on the maximum drawdown and lookback options. These results allow us to interpret the delta-hedge of the contracts in a novel way.

In this paper we studyy arithmetic Asian options when the underlying stock is driven by special semimartingale processes. We show that the inherently path dependent problem of pricing Asian options can be transformed into a problem without path dependence in the payoff function. We also show that the price is driven by a process with independent increments, Levy processes being a special case. This approach applies for both discretely or continuously options.

We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market crashes and rallies in the geometric Brownian motion model.