Finite Difference Schemes for Black-Scholes with Asian Option

Asian option is quite different from European option which can be exercised on the date of expiration, and not like the American option which exercised anytime during the period of contract. It is an unusual derivative that the option payoff depends on the average of a stock price or underlying asset over a certain period in the future. There are some demands from real world application. The attractive point is that Asian option is cheaper than the other options to hedge the similar risk. In addition, some investors need security which can protect them from the volatility and risk from the market, at the same time, the average option can provide an investor with a greater level of flexibility to make a deal. This paper focus on the point that using Finite-difference method to solve the Black-Scholes partial differential equation for the Asian Option valuation problem

Binomial American Option Pricing on CPU-GPU Hetergenous System

Abstract-We present a novel parallel binomial algorithm to compute prices of American options. The algorithm partitions a binomial tree into blocks of multiple levels of nodes, and assigns each such block to multiple processors. Each processor in parallel with the others computes the option's values at nodes assigned to it. The computation consists of two phases, where the second phase can not start until the valuation in the first phase has been completed. The algorithm is implemented and tested on a heterogeneous system consisting of an Intel multicore processor and a NVIDIA GPU. The whole task is split and divided over the CPU and GPU so that the computations are performed on the two processors simultaneously. In the hybrid processing, the GPU is always assigned the last part of a block, and makes use of a couple of buffers in the on-chip shared memory to reduce the number of accesses to the off-chip device memory. The performance of the hybrid processing is compared with an optimised CPU serial code, a CPU parallel implementation and a GPU standalone program. We learned from the experiments that the lack of explicit mechanism in CUDA for synchronising CPU and GPU executions is a major obstacle for the hybrid processing to achieve high performance

PARALLEL OPTION PRICE VALUATIONS WITH THE EXPLICIT FINITE DIFFERENCE METHOD ∗

Abstract. We show how computations such as those involvedin American or European-style option price valuations with the explicit finite difference method can be performed in parallel. Towards this we introduce a latency tolerant parallel algorithm for performing such computations efficiently that achieves optimal theoretical speedup p, wherep is the number of processor of the parallel system. An implementation of the parallel algorithm has been undertaken, and an evaluation of its performance is carriedout by performing an experimental study on a high-latency PC cluster, andat a smaller scale, on a multi-core processor using in addition the SWARM parallel computing framework for multi-core processors. Our implementation of the parallel algorithm is not only architecture but also communication library independent: the same code works under LAM-MPI and Open MPI and also BSPlib, two sets of library frameworks that facilitate parallel programming. The suitability of our approach to multi-core processors is also established