Predicting Indian Foreign Exchange Market Crashes through Log-Periodic Power Law.

AuthorSarda, Varun


In the process of prediction of the exchange rate, its movement and the way it is determined becomes an important factor. Even a small fluctuation in the exchange rate can affect the business houses manifolds. Today, the exchange rate system followed by India is the Liberalized Exchange Rate Management System (LERMS). The Tarapore Committee of 1997 on Capital Account Convertibility had made significant recommendations to strengthen the Foreign Exchange Market of India. In the years 1997-98 and 1998-99 the Reserve Bank of India (RBI) stuck to its objective of reducing the volatility and speculation in the foreign exchange market as a part of its exchange rate policy. The velue of rupee was allowed by the RBI to be determined in the market and it intervened whenever undue volatility was introduced into the market due to any political, social or economic reasons. An evaluation of the effective exchange rates indicates that there is a sharp depreciation in the valuation of the rupee in nominal terms. The nominal effective exchange rate (NEER) has also fallen by an approximate value of 23% between Jan 1993 and Jan 1999. The reasons behind the same are attributed to the transition from artificially suppressed "managed rates" to the market determined exchange rates. The same period saw an appreciation in the real effective exchange rate (REER) by about 2.8% indicating that there must have been marginal gain in overall export competitiveness.

Foreign exchange constitutes the largest financial market not only in the rest of the world but also in India. The growth in Indian foreign exchange market has been manifold in the last several years. The daily average turnover has seen a significant rise, from about US $ 5 billion during 1997-98 to US $ 18 billion during 2005-06. Also, the average monthly turnover in Indian foreign exchange market has continuously improved from 175 billion US dollars (USD) in 2003-04 to 359 billion USD in 2005-06. The foreign exchange markets have seen a tripled growth in the years from 2000-01 to 2005-06, with the annual compound growth rate exceeding 25%. There has been a lock step pattern in the movement of the USD and the rupee. Also, the relationship of the Indian Rupee (INR) has been particularly stable with the USD. During the 1999-2004 the correlation between the two was 0.94.

The Tarapore Committee defined the concept of Capital Account Convertibility as "the freedom to convert local financial assets into foreign financial assets and vice versa at market determined rates of exchange". India has seen a speedy accumulation in foreign exchange reserves in the last few years. During 2003 and 2004 the USD fell against the Euro by 19% and against the rupee by 9%. The annual foreign exchange turnover in India in the year 2007 was US $ 10.73 trillion. It increased to US $ 13.08 trillion in 2008, US $ 9.88 trillion in 2009, US $ 12.72 trillion in 2010 and US $ 13.95 trillion in 2011. Thus, the foreign exchange turnover in India has risen steadily from 2007 to 2011.Various theories have been propounded such as Purchasing Power Parity, Interest Rate Parity, Fisher Effect, Asset Market Model and the like to explain the movements in the Foreign Exchange Markets of the World and India. But all these techniques are not able to predict short term volatilities. As of now the majority of trades in the Indian Foreign Exchange Market are done by the institutional players thus the volatility is also not very high.

Log Periodic Power Law

A Log Periodic Power Law (LPPL) can be fitted to financial market bubbles which precede large market falls or crashes, containing parameters which are confined within certain ranges. The underlying principle on which the LPPL is based is the influence perception and martingale condition. The equation of LPPL captures the particular oscillating movement of the financial markets showing their growth and evolution. A crash can be predicted in a financial time series using LPPL. The parameters of the equation can be estimated using a hybrid Genetic Algorithm. With respect to a financial market, a crash can be defined as a sudden and dramatic decline in the price of an asset or an index over a short period of time. As a result of this there is a large percentage drop which further leads to a devastating condition for the market. In a financial market, the price of an asset fluctuates as a function of the supply and demand, which reflects continuous flow of news as interpreted by the analysts and traders. When a condition of panic is triggered by extreme sell orders by the traders it results into a condition of crash. External events have an impact on the market and leads to a crash. These events could be any bad piece of information capable of impacting the market adversely. A speculative bubble occurs when a crash is identified as endogenous and is triggered due to the bubble. At this time the price of an asset or index undergoes a significant increase and becomes overvalued. This is due to a positive feedback.

In two independent works by Feigenheim and Freund (1996), and Sornette, Johansen and Bouchaud (1996), have described the scenario of endogenous crashes in financial markets. According to them, during the bubble there is an increase in the index as a power law decorated with log periodic oscillation and that the ending crash is the climax of LPPL signature. The oscillation of LPPL captures the behavior of a bubble and follows the critical time of a crash. A drawdown can be used to measure losses in a financial time series. It is a way to measure the continuous downward movement from a local maximum to a local minimum. A largest negative drawdown will single out abnormal movements as crashes in financial time series.

According to Johansen and Sornette (2006), a crash is defined as an outlier departing from a fit to a logarithmic expression of the complimentary cumulative Weibull distribution. Jacobsson (2009) has defined a crash as an empirical quantile of 99.5% as against the one described by Johansen and Sornette (2006).

Why do we need to introduce a new measurement of drawdown? In case of a crash, a financial index falls rapidly with large negative returns, where largest ones are extreme events in the market. The real dynamics of price movements is not captured by independency and financial time units. The origin of LPPL is in the prediction of the damage caused by meteorological disasters. The accuracy of predicting these disasters is very crucial. In the vicinity of a catastrophic event it can be observed that LPPL exhibits oscillations with increasing frequency. Thus, by fitting the LPPL to the observations it is possible to predict the catastrophic events. Successful predictions were made in many application areas ranging in ruptures of fuel tanks to earthquakes to stock market disruptions. The LPPL is not a result of a specific nature of a system but occurs due to general properties of the system.


Most technical analysis tools are able to generate sell signal but are not able to predict the percentage fall. Although some techniques are able to do this to a certain extent using Golden mean and Fibonacci series etc., but they are not able to do it precisely. Log-Periodic Power Law structures are able to predict a stock market crash of more than 25% at a very early stage and the similarity between Log-Periodic Power Law structures and other technical analysis tools is that they both generate a sell signal near about the...

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