A general framework for pricing Asian options under stochastic volatility on parallel architectures

Abstract

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general affine stochastic volatility framework.The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy and efficiency of the procedure are reported in the paper.

Including Jumps in the Stochastic Valuation of Freight Derivatives

“…Bellow, we consider several processes already used to model the dynamics of different commodities (see [20,26,27]):…”

“…Freight options are a special kind of Asian-options. A large volume of literature is devoted to Asian/Bermudan options where different approaches are considered to approximate its value, see a detailed literature survey on [29] or more recent approaches such as [27,30] or [31].…”

“…We replace (27) into the PIDE ( 25) and obtain that A 1 , A 2 and A 3 satisfy the following system of ordinary differential equations:…”

VIX derivatives, hedging and vol-of-vol risk

“…To obtain quasi-analytical expressions for the prices of VIX derivatives, we use Fourier transform methods similar to Ballotta, Deelstra, and Rayée (2017) . 13 Following Bates (2006) , VIX futures and options in our models can be obtained as follows: 14 11 There are many alternative (and equally tractable) modeling approaches for jumps, such as extensions to infinite-activity Levy-models such as in Carr, Geman, Madan, and Yor (2002) , Corsaro, Kyriakou, Marazzina, andMarino (2019) , Fusai, Germano, andMarazzina (2016) , and Mercuri and Rroji (2018) or other jump size distributions such as in Kou (2002) . We focus on a simple and intuitive model here and comment on extensions further below.…”

Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading

“…First, it is popular in practice in the financial market because it has a lower cost than its counterpart, the plain vanilla option. Second, averaging underlying asset prices can prevent manipulation from the financial market [7][8][9]. Third, it is commonly used in interest rate and foreign exchange markets, providing an expiry price or strike price that remains more stable than plain vanilla over contract periods.…”