Pricing Average Options on Commodities

This paper proposes a new approximation formula for pricing average options on commodities under a stochastic volatility environment. In particular, it derives an option pricing formula under Heston and an extended -SABR stochastic volatility models (which includes an extended SABR model as a special case). Moreover, numerical examples support the accuracy of the proposed average option pricing formula.

Improved Lossy Image Compression with Priming and Spatially Adaptive Bit Rates for Recurrent Networks

We propose a method for lossy image compression based on recurrent, convolutional neural networks that outperforms BPG (4:2:0 ), WebP, JPEG2000, and JPEG as measured by MS-SSIM. We introduce three improvements over previous research that lead to this state-of-the-art result. First, we show that training with a pixel-wise loss weighted by SSIM increases reconstruction quality according to several metrics. Second, we modify the recurrent architecture to improve spatial diffusion, which allows the network to more effectively capture and propagate image information through the network's hidden state. Finally, in addition to lossless entropy coding, we use a spatially adaptive bit allocation algorithm to more efficiently use the limited number of bits to encode visually complex image regions. We evaluate our method on the Kodak and Tecnick image sets and compare against standard codecs as well recently published methods based on deep neural networks