In the Black-Scholes model, consider the problem of selecting a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options. Employing Large Deviations techniques, the asymptotically optimal change of drift is identified as the solution to a one-dimensional variational problem, which may be reduced to the associated Euler-Lagrange differential equ...

Using some results from risk theory on stop-loss order and comonotone risks, we show in this paper that the price of an arithmetic Asian option can be bounded from above by the price of a portfolio of European call options.

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a rec...

Asian options paying the excess over strike, of either the arithmetic or geometric average of the asset price over either discrete or continuous time, are valued using analytical and simulation methodologies. Expressions are developed for the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. Analytical option prices for the continuous arithmetic...

Path-dependent options are options whose payoff depends nontrivially on the price history of an asset. They play an important role in financial markets. Unfortunately, pricing path-dependent options could be difficult in terms of speed and/or accuracy. The Asian option is one of the most prominent examples. The Asian option is an option whose payoff depends on the arithmetic average price of th...

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hypergeometrical, and bounded variables. We have derived explicit formulas and computational methods for designing sampling schemes to ensure prescribed levels of precision and confidence for point estimators. Moreover, we have d...

Operating in energy and commodity markets require a management of risk using derivative products such as forward futures, well options on these. Many the popular stochastic models for spot dynamics weather variables developed from empirical studies belong to class polynomial jump diffusion processes. We derive tailor-made framework efficient approximation main derivatives encountered markets, e...