Omar Ghattas

Omar GhattasOmar Ghattas

Australian National University


My name is Omar and I am currently finishing up my double degree at the ANU in Actuarial Studies and Finance. Undertaking such a diverse degree gave me the opportunity to really assess which path I wanted to eventually pursue – my passion for maths and statistics trumped every time! Subsequently, I will be completing my honours in statistics next year and my goal for this summer scholarship is to get valuable exposure to a research environment, as well as meet and collaborate with other early researchers that are facing similar challenges.

My proposed research project will attempt to combine my knowledge of economics and statistics to address a real life issue, namely, the emergence of crypto-currencies such as Bitcoin and Litecoin as an alternative to fiat currencies. These new currencies look to address the shortcomings of current currencies such as high transaction costs and their vulnerability to changes in the political climate. My project will seek to address the issue of pricing derivatives contracts, such as options,  on these currencies. Options are a risk management tool that allow a participant to either buy or sell an asset in the future for a predetermined price. The participant then gets the option to exercise the contract, depending on the movement in price. Traditional approaches to pricing options, such as the famous Black-Scholes-Merton equation fail in this case given that the underlying asset has a finite supply. My approach will look at fitting a system of stochastic differential equations to fitting the various parameters that are associated with the currencies liquidity and volatility.

Ultimately, my belief is that as risk management tools are developed, more and more people will no longer be deterred by the high volatility of these currencies, which will ultimately lead to more and more people enjoying the benefits of this – what I think to be a – great idea!

Pricing Contingent Claims on Crypotucurrencies

Cryptocurrencies, such as Bitcoin, have recently emerged as alternatives to fiat money for those seeking low transaction costs, anonymity and protection from the loose monetary policy of central banks. The growth of these new currencies can potentially be hindered by their high price volatility, negating the store of value characteristic that is desirable in any established currency. This will undoubtedly lead to the arrival of derivative securities (aka. contingent claims), in which these currencies are the underlying assets, in an attempt to manage that risk.The traditional Black-Scholes option pricing approach, which revolutionised the role of mathematics in finance, has an obvious shortcoming when employed to pricing options on assets such as Bitcoins. The failure of the model is arguably a direct product of the related assumptions that there is an endless supply of the asset and the market is perfectly liquid (i.e., buying and selling does not change the market price). These assumptions are violated in the case of cryptocurrencies. First, coins are issued into circulation through the process of “mining”. They are rewarded to “miners” as an incentive for solving increasingly difficult and computationally intensive proof-of-work mathematical problems. The difficulty of these problems is directly related to the speed at which they are mined, which in turn affects the supply of coins. Second, as coins are in limited supply, the action of buying and selling (a necessary step in replicating and hedging a contingent claim) can drastically affect the market price of the asset. To fulfil our aim of introducing a new model in the form of a system of stochastic differential equations that accounts for both the liquidity of the market and rate of mining, the project will involve the following stages:

  • Conduct a review of the current literature on stochastic liquidity and modify an existing model(s) to take into account the rate of mining and the liquidity of the Bitcoin market.
  • The calibration of historical data to this modified system by applying a Maximum Likelihood Estimate algorithm to identify the most appropriate model and parameters of that model.
  • Implementation of numerical techniques such as Monte Carlo methods to price contingent claims on Bitcoin.
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