Title page for ETD etd-042711-001313

Document Type masters report

Author Name Zhao, Min

URN etd-042711-001313

Title Risk Measures Extracted from Option Market Data Using Massively Parallel Computing

Degree MS

Department Mathematical Sciences

Advisors
Domokos Vermes, Advisor

Keywords
Financial risk management
Massively parallel GPU comtuing
Stochastic volatility model
Black-Scholes Formula

Date of Presentation/Defense 2011-04-27

Availability unrestricted

Abstract
The famous Black-Scholes formula provided the first mathematically sound mechanism to price financial options. It is based on the assumption, that daily random stock returns are identically normally distributed and hence stock prices follow a stochastic process with a constant volatility. Observed prices, at which options trade on the markets, don¡¯t fully support this hypothesis. Options corresponding to different strike prices trade as if they were driven by different volatilities.
To capture this so-called volatility smile, we need a more sophisticated option-pricing model assuming that the volatility itself is a random process. The price we have to pay for this stochastic volatility model is that such models are computationally extremely intensive to simulate and hence difficult to fit to observed market prices. This difficulty has severely limited the use of stochastic volatility models in the practice.
In this project we propose to overcome the obstacle of computational complexity by executing the simulations in a massively parallel fashion on the graphics processing unit (GPU) of the computer, utilizing its hundreds of parallel processors.
We succeed in generating the trillions of random numbers needed to fit a monthly options contract in 3 hours on a desktop computer with a Tesla GPU. This enables us to accurately price any derivative security based on the same underlying stock. In addition, our method also allows extracting quantitative measures of the riskiness of the underlying stock that are implied by the views of the forward-looking traders on the option markets.

Files
mzhao.pdf

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Document Type	masters report
Author Name	Zhao, Min
URN	etd-042711-001313
Title	Risk Measures Extracted from Option Market Data Using Massively Parallel Computing
Degree	MS
Department	Mathematical Sciences
Advisors	Domokos Vermes, Advisor
Keywords	Financial risk management Massively parallel GPU comtuing Stochastic volatility model Black-Scholes Formula
Date of Presentation/Defense	2011-04-27
Availability	unrestricted
Abstract The famous Black-Scholes formula provided the first mathematically sound mechanism to price financial options. It is based on the assumption, that daily random stock returns are identically normally distributed and hence stock prices follow a stochastic process with a constant volatility. Observed prices, at which options trade on the markets, don¡¯t fully support this hypothesis. Options corresponding to different strike prices trade as if they were driven by different volatilities. To capture this so-called volatility smile, we need a more sophisticated option-pricing model assuming that the volatility itself is a random process. The price we have to pay for this stochastic volatility model is that such models are computationally extremely intensive to simulate and hence difficult to fit to observed market prices. This difficulty has severely limited the use of stochastic volatility models in the practice. In this project we propose to overcome the obstacle of computational complexity by executing the simulations in a massively parallel fashion on the graphics processing unit (GPU) of the computer, utilizing its hundreds of parallel processors. We succeed in generating the trillions of random numbers needed to fit a monthly options contract in 3 hours on a desktop computer with a Tesla GPU. This enables us to accurately price any derivative security based on the same underlying stock. In addition, our method also allows extracting quantitative measures of the riskiness of the underlying stock that are implied by the views of the forward-looking traders on the option markets.
Files	mzhao.pdf