Economical hardware often uses a FiXed-point Number System (FXNS), whose constant absolute precision is acceptable for many signal-processing algorithms. The almost-constant relative precision of the more expensive Floating-Point (FP) number system simplifies design, for example, by eliminating worries about FXNS overflow because the range of FP is much larger than FXNS for the same wordsize; h...

We consider the problem of finding bounds on the value of fixed-strike and floatingstrike Asian options. A good lower bound for both types was derived in Rogers & Shi (1995). We provide an alternative derivation, which leads to a simpler expression for the bound, and also to the bound given by Curran (1992) for fixed-strike options; we derive an analogous bound for floating-strike options. Comb...

Asian options on a single asset under a jump-diffusion model can be priced by solving a partial integro-differential equation (PIDE). We consider the more challenging case of an option whose payoff depends on a large number (or even a continuum) of assets. Possible applications include options on a stock basket index and electricity contracts with a delivery period. Both of these can be modeled...

Asian options belong to the so-called path-dependent derivatives. They are among the most difficult to price and hedge both analytically and numerically. Basket options are even harder to price and hedge because of the large number of state variables. Several approaches have been proposed in the literature, including Monte Carlo simulations, tree-based methods, partial differential equations, a...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable is the average price of given assets sampled over a period of time. Due to this structure, Asian options display a lower volatility and are therefore cheaper...

This paper studies symmetries between fixed and floating-strike Asian options and exploits this symmetry to derive an upper bound for the price of a floating-strike Asian. This bound only involves fixed-strike Asians and vanillas, and can be computed simply given one of the many efficient methods for pricing fixed-strike Asian options. The bound coincides with the true price until after the ave...