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The chosen data and time period is described in section 3. For the chosen cross we have used one set of features given to us from Nordea Quantitative Research as supportive time series. The back testing period for the created models, the comparative index as well as the HMM, has been limited to the period for which adequate time series has been given, for both the chosen currency cross and the given features.

Finally the trading strategy will be implemented to an extent containing step one and two in figure 1. It will not deal with the final trading decision or the execution of the trades Academic Contribution This thesis is written from a financial engineering point of view, combining areas such as computer science, mathematical science and finance. The main academic contributions of the thesis are the following: The master s thesis is one of few applications using hidden Markov models on time dependent sequences of data, such as financial time series.

It is the first publicly available application of hidden Markov models on foreign exchange data Disposal The rest of this master s thesis will be organized as follows. In chapter 2, the theoretical framework will be reviewed in detail to give the reader a clear view of the theories used when evaluating HMM as a tool for AT. In chapter 3 the developed model is described in detail to clear out how the theories has been used in practice to create algorithms based on the framework of HMMs.

The created market index will also be reviewed, described shortly to give a comparable measure of market return. Chapter 4 contains the results of the tests made for the developed models. Trajectories will be presented and commented using different features and settings to see how the parameters affect the overall performance of the model.

The models performance will be tested and commented using statistical tests and well known measurements. The analysis of the results are carried out in chapter 5, on the base of different findings made throughout the tests presented in chapter 4. The purpose of the analysis is to clear out the underlying background to the results one can see, both positive and negative. Its purpose is to go through the three steps addressed in section to finally answer the purpose of the master s thesis.

This chapter will also point out the most adequate development needed to improve the models further. Different variants, like the one making use of GMMs, and improvements to the HMM, that for example takes time attenuation in consideration, will also be presented. The chapter however starts with some background theories regarding market indices and FX benchmarks, which will constitute the theoretical ground for the comparative index.

As one finds in any asset class, the foreign exchange world contains a broad variety of distinct styles and trading strategies. It is harder to find a comparable index for currencies. When viewed as a set of trading rules, the accepted benchmarks of other asset classes indicate a level of subjectivity that would not otherwise be apparent. In fact, they really reflect a set of transparent trading rules of a given market. By being widely followed, they become benchmarks.

By looking at benchmarks from this perspective there is no reason why there should not exist an applicable benchmark for currencies. Their index contains a mixture of three strategies, namely Carry, Momentum and Valuation. These are commonly accepted indices that also other large banks around the world make use of.

Carry is a strategy in which an investor sells a certain currency with a relatively low interest rate and uses the funds to purchase a different currency yielding a higher interest rate. A trader using this strategy attempts to capture the difference between the rates, which can often be substantial, depending on the amount of leverage the investor chooses to use. Theoretical Framework presented.

Lets also assume that the bond pays 5. The trader stands to make a profit of 3. Many professional traders use this trade because the gains can become very large when leverage is taken into consideration. If the trader in the example uses a common leverage factor of , then he can stand to make a profit of 35 percent.

The big risk in a carry trade is the uncertainty of exchange rates. Using the example above, if the USD were to fall in value relative to the JPY, then the trader would run the risk of losing money. Also, these transactions are generally done with a lot of leverage, so a small movement in exchange rates can result in big losses unless hedged appropriately.

Therefore it is important also to consider the expected movements in the currency as well as the interest rate for the selected currencies. Another commonly used trading strategy is Momentum, which is based on the appearance of trends in the currency markets. Currencies appear to trend over time, which suggests that using past prices may be informative to investing in currencies. This is due to the existence of irrational traders, the possibility that prices provide information about non-fundamental currency determinants or that prices may adjust slowly to new information.

To see if a currency has a positive or negative trend one have to calculate a moving average for a specific historical time frame. If the currency has a higher return during the most recent moving average it said to have a positive trend and vice versa. A purchasing power parity exchange rate equalizes the purchasing power of different currencies in their home countries for a given basket of goods.

This is why it is believed that the currencies in the long run tend to revert towards their fair value based on PPP. But in short- to medium-run they might deviate somewhat from this equilibrium due to trade, information and other costs. These movements allows for profiting by buying undervalued currencies and selling overvalued.

Beside these there is a lot of other strategies, trying to find the alpha in the market. Alpha is a way of describing excess return, captured by a specific fund or individual trader. Hidden Markov Models 13 The above description of alpha is valid for more or less all financial assets. But when it comes to FX, it might sometimes be difficult to assign a particular risk free rate to the portfolio.

One suggestion is simply to use the rates of the country from where the portfolio is being managed, but the most reoccurring method is to leave out the risk free rate. There are mainly two reasons for this; first the models are very rich in mathematical structure and hence can form the theoretical basis for many applications. Second, the models, when applied properly, work very well in practice.

The first include signal filtering, model parameter identification, state estimation, signal smoothing, and signal prediction. The latter refers to selecting actions which effect the signalgenerating system in such a way as to achieve ceratin control objectives. Essentially, the goal is to develop optimal estimation algorithms for HMMs to filter out the random noise in the best possible way.

The use of HMMs is also motivated by empirical studies that favors Markov-switching models when dealing with macroeconomic variables. This provides flexibility to financial models and incorporates stochastic volatility in a simple way. Early works, proposing to have an unobserved regime following a Markov process, where the shifts in regimes could be compared to business cycles, stock prices, foreign exchange, interest rates and option valuation.

The motive for a regime-switching model is that the market may switch from time to time, between for example periods of high and low volatility. The major part of this section is mainly gathered from [17] if nothing else is stated. This article is often used as a main reference by other authors due to its thorough description of HMMs in general Hidden Markov Models used in Finance Previous applications in the field of finance where HMMs have been used range all the way from pricing of options and variance swaps and valuation of life insurances policies to interest rate theory and early warning systems for currency crises.

The drift and the diffusion parameters are here modulated by an underlying hidden Markov process. In this way could the value of the short rate successfully be predicted for the next time period. HMMs has also, with great success, been used on its own or in combination with e. Theoretical Framework The wide range of applications together with the proven functionality, in both finance and other communities such as speak recognition, and the flexible underlying mathematical model is clearly appealing Bayes Theorem A HMM is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters from the observable parameters.

The extracted model parameters can then be used to perform further analysis, for example for pattern recognition applications. A HMM can be considered as the simplest dynamic Bayesian network, which is a probabilistic graphical model that represents a set of variables and their probabilistic independencies, and where the variables appear in a sequence.

Bayesian probability is an interpretation of the probability calculus which holds that the concept of probability can be defined as the degree to which a person or community believes that a proposition is true. Bayesian theory also suggests that Bayes theorem can be used as a rule to infer or update the degree of belief in light of new information. The probability of an event A conditional on event B is generally different from the probability of B conditional on A.

However, there is a definite relationship between the two, and Bayes theorem is the statement of that relationship. To derive the theorem, the definition of conditional probability used. This lemma is sometimes called the product rule for probabilities. It is somewhat harder to derive, since probability densities, strictly speaking, are not probabilities, so Bayes theorem has to be established by a limit process.

The notation have here been somewhat abused, using f for each one of these terms, although each one is really a different function; the functions are distinguished by the names of their arguments. According to the authoritative Triennial Central Bank Survey. Evolution of Forex the Active Trader s Market The practice of trading currencies online has increased threefold from to , and the growth curve is expected to continue.

Forex, an abbreviation for. This notice is provided. Remember that trading in forex is inherently risky, and you can lose money as well as make money. Manage your. Seminar Global Foreign Exchange Markets Chapter 9 9- Learning Objectives To learn the fundamentals of foreign exchange To identify the major characteristics of the foreign-exchange market and how governments.

International Finance Prof. Please be advised that. General Forex Glossary A ADR American Depository Receipt Arbitrage The simultaneous buying and selling of a security at two different prices in two different markets, with the aim of creating profits without. More sophisticated algorithms such as support. CommSec CFDs: Introduction to FX Important Information This brochure has been prepared without taking account of the objectives, financial and taxation situation or needs of any particular individual.

What is Forex Trading? Foreign exchange, commonly known as Forex or FX, is the exchange of one currency for another at an agreed exchange price on the over-the-counter OTC market. Forex is the world. For the sake of simplicity, the examples that follow do not take into consideration commissions and other transaction fees, tax considerations, or.

Introduction to currency futures The South African Rand is one of the most volatile currencies in the world; it can exhibit moves of greater than 0. Forex Basics brought to you by MatrasPlatform. What is a Forex?

Forex is the market where one currency is traded for another Unlike stocks and futures exchange, foreign exchange is indeed an interbank, over-the-counter OTC market which means there. Most ETF s are cost effective, broad market funds. We have put together a layman s explanation.

FxPro Education Within any economy, consumers and businesses use currency as a medium of exchange. Trading Costs and Taxes! Aswath Damodaran Aswath Damodaran! The Components of Trading Costs! Brokerage Cost: This is the most explicit of the costs that any investor pays but it is usually the smallest. An introduction to direct access trading strategies. Contents Risk Disclaimer The relationship between exchange rates, interest rates In this lecture we will learn how exchange rates accommodate equilibrium in financial markets.

For this purpose we examine the relationship between. The carry trade is a trading strategy in which you simultaneously. Overview 3 2. What is a CFD? Why Trade CFDs? AlphaQuest CTA Research Series 1 The goal of this research series is to demystify specific black box CTA trend following strategies and to analyze their characteristics both as a stand-alone product as.

It takes a lot of the risk and hassle out of trading and. A practical guide to FX Arbitrage FX Arbitrage is a highly debated topic in the FX community with many unknowns, as successful arbitrageurs may not be incentivized to disclose their methodology until after. Your capital is at risk. Spread Betting and CFDs are not suitable for all investors and you should ensure that you understand the risks.

General Informations regarding Foreign Exchange Forex We ve always believed that one of the best ways to protect investors is to provide them with the materials they. Financial Markets and Institutions Abridged 10 th Edition by Jeff Madura 1 12 Market Microstructure and Strategies Chapter Objectives describe the common types of stock transactions explain how stock transactions. Consequently, risk management must be good and transparency high in this market. An EU regulation. How a thoughtful FX strategy can give Fund Managers a competitive edge Executive summary Each alternative investment fund takes a different approach to its investment strategy, but the ultimate goals are.

International Investments Bruno Solnik H. MSc Finance and Economics detailed module information Example timetable Please note that information regarding modules is subject to change. Give a full definition of the market for foreign exchange. Answer: Broadly. Introduction Investment professionals face a tough climate. Foreign exchange transactions are significant components of millions of daily financial transactions, yet most.

Important Information and Disclaimer 1. Chapter 2. However, from time to time those charts may be speaking a language you. Terms and definitions Abnormal market conditions mean Fast market. Account history means a list of completed transactions and non-trading operations on the Client s account. Account type means the terms. Risk Disclosure Statement The risk of loss in trading commodity futures contracts can be substantial.

You should, therefore, carefully consider whether such trading is suitable for you in light of your. The Foreign Exchange Market The foreign exchange market provides the physical and institutional structure through which the money of one country is exchanged for that of another country, the rate of.

Intro to Forex and Futures 1 Forex Trading Forex is a term meaning foreign exchange, and refers to trading the currency of one country against the currency from another country simultaneously. Purer return and reduced volatility: Hedging currency risk in international-equity portfolios Currency-hedged exchange-traded funds ETFs may offer investors a compelling way to more precisely access. Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,.

A new model of a market maker M. Tsvetkov 1, D. Posthuma 2 and S. Borovkova 3 MSc. Trading leveraged products carries a high. Leonberger, FSA Director of Research Abstract As portfolios have expanded to include international investments, investors must be aware of.

Foreign Currency Options So far, we have studied contracts whose payoffs are contingent on the spot rate foreign currency forward and foreign currency futures. Risk categories Foreign exchange. Introduction to CommSec CFDs Important Information This brochure has been prepared without taking account of the objectives, financial and taxation situation or needs of any particular individual.

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Hidden Markov Models (HMMs) is applied to learn the historical trend patterns, and use to predict the next day movement trends. We use the This dissertation proposes a new Hidden Markov Model (HMM) approach to pattern discovery using. MACD and RSI technical indicators to assist in the HMM forecast. Hidden Markov Models (HMMs) is applied to learn the historical trend patterns, and use to predict the next day movement trends. We use the Forex.