CC BY
18УДК: 004.94
HEDGING: SIMULATION MODELING IMPLEMENTATION
M.A. Nikiforova, student
Financial University under the Government of the Russian Federation, Moscow, Russia E-mail: [email protected]
Abstract. The key purpose of most companies is to make profit and increase it greatly in future. However, profit growth is inextricably linked with the increase in probability of risk realization: FX, commodity and interest rate risks affects all market players which relate to foreign trade activities regardless of the industry, having, for example, exportimport operations, payments in foreign currency, long-term borrowings. Adverse market changes affect financial indicators of the company thus motivating company's management to develop a long-term risk management strategy. One of the most frequently used ways of risk management is hedging. Hedging is a method of protection against undesirable market trends, which consists in buying the opportunity to sell (or to buy) an asset in the future on pre-agreed terms. However, hedging itself does not work properly without the analysis of historical market changes and their accurate predictions. That is why many businesses apply simulation techniques, which consider the majority of potential market movements and assess their impact on financial indicators. This paper focuses on three aspects of simulation technique implementation for hedging purposes: risk estimation, hedging effect measurement and comparison of hedging instrument implementation.
Keywords: hedging, simulation, risk, hedging instruments, evaluation.
ПРИМЕНЕНИЕ ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ ПРИ
ХЕДЖИРОВАНИИ РИСКОВ
Никифорова М.А, магистрант
Финансовый университет при Правительстве Российской Федерации, Москва, Россия
E-mail: [email protected]
Аннотация. Основной целью деятельности большинства компаний является получение прибыли и ее приумножение в дальнешем. Однако, рост прибыли компании неразрывно связан с увлечением вероятности реализации риска: валютным, товарным и процентным рискам независимо от отрасли подвержены все игроки, так или иначе связанные с внешнеэкономической деятельностью, и имеющие, например, экспортно-импортные операции, платежи в иностранной валюте, долгосрочные займы. Неблагоприятные изменения на рынках имеют огромное влияние на различные финансовые показатели компании, что в свою очередь мотивирует менеджмент к созданию долгосрочной стратегии управления рисками, которым подвержена компания. Одним из наиболее часто встречающихся методов управления рисками является хеджирование. Хеджирование представляет собой способ страхования от нежелательных рыночных трендов, заключающийся в покупке возможности продажи (или покупки) актива в будущем на заранее согласованных условиях. Однако, использование хеджирования для минимизации рисков необходимо подкреплять анализом исторической волатильности рыночных показателей и прогнозированием данных показателей на будущие периоды. Имитационное моделирование является одним из методов прогнозирования, который учитывает большинство потенциально возможных изменений на рынке и их влияние на финансовые показатели компании. В данной статье рассматриваются три аспекта реализации имитационного моделирования для целей хеджирования: оценка риска, оценка эффекта от хеджирования и сравнение применения различных инструментов хеджирования.
Ключевые слова: хеджирование, имитационное моделирование, риск, инструменты хеджирование, количественная оценка риска.
Introduction the business, company's management should
In modern world, financial performance of estimate risks caused by the uncertainty of market almost every company is affected by various movements before risks realize and put in place risk volatility factors (exchange rates, the price of goods, mitigation measures if it is necessary. etc.). In order to maintain successful development of
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Simulation modeling is a modern way of risk estimation, which also helps to make hedging decisions. Simulation modeling implies creating a digital prototype of a real-world system that allows to analyze and to predict processes accurately. It is mainly because model can take into account thousands of scenarios that capture uncertainty. Good prediction quality of simulation technique allows the company to hedge when the market goes down and not to in case of the market rise. In other words, accurate prediction gives an opportunity to minimize costs while maximizing benefits [1, pp. 917-923].
The focus of the article is simulation modeling for hedging purposes: risk evaluation, hedging effect estimation and various hedging instruments implementation comparison.
Risk evaluation
The simulation technique is quite common nowadays, especially among companies, which take into account risk evaluation when making hedging decisions. For instance, consider a company that decides to contract a debt in US dollars, but all of its input cash flows are in Russian rubles. In order to pay off the debt, the company has to exchange dollars for rubles first, which may result in an overpayment. If the company must pay the debt in five $10,000 tranches, the USD/RUB exchange rate [2] has to be modeled for all payment dates in order to better understand the company's ability to repay the debt.
The best practice for risks forecasting implies simulating up to 100,000 different scenarios [6, p. 9] that are based on historical volatility of the factor and examining the related financial indicators probability distribution [6, p. 16-18]. Some computer programs are used for these purposes, one of the widely used is @Risk software. It is well known among risk managers for the purpose of scenario simulation and following analysis and in this article it is used for simulation modelling for hedging purposes.
Using above-mentioned example, we can build a distribution of the amount of rubles the company must pay for its debt (Picture 1) by means of this software [5, pp. 370-371].
Picture 1 - Debt payment distribution
Histogram on the picture is created based on modelled scenarios of USDRUB rates, demonstrating possible fluctuations of the rate in future [6, p. 10]. Algorithm for rate modelling:
1) The distribution of daily deviation of the rate for the previous 10 years is found using @Risk software [3, pp. 115-119];
2) Using detected distribution and following parameters, the daily deviations of the rate for five dates in future are found;
3) USDRUB rates for five dates in future are recovered, using the last historical rate and results from second step.
Here we can see that in above-mentioned example, program models future rates using normal distribution with positive expected value.
We can see that 90% of scenarios predict that company will have to pay between 3.018 and 3.566 million rubles. At this point, it is up to company's management weather to enter into debt contract and:
1) accept the risk;
2) use hedging instrument / instrument structure.
Simulation technique allows company's management to estimate the risk they might face and make a decision on whether to enter into hedging contracts.
Effect from hedging
Moreover, a large number of companies use simulation modeling in order to understand to what extent hedging is effective. Take as illustration that the above-mentioned company wants to enter into five option contracts in order to be safe in terms of USD/RUB rates on payment dates. The company has an opportunity to buy call options from a bank with terms stated in Table 1.
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Date of entering into a contract Expiration date Option style Volume, $ Option premium, $ Strike price, RUB
10.06.2019 10.07.2019 European 10,000 1,000 66.21
10.07.2019 12.08.2019 European 10,000 1,000 66.75
12.08.2019 10.09.2019 European 10,000 1,000 67.34
10.09.2019 10.10.2019 European 10,000 1,000 68.44
10.10.2019 10.11.2019 European 10,000 1,000 69.81
First long call option's terms show that on 11.06.2019 the company pays $1,000 premium to a bank, signing a contract, which says that on 10.04.2019 company may buy $10,000 at the rate of 66.21 rubles per 1 dollar [4, pp. 22-24]. On 10.07.2019 company may play in two ways:
1) If market USD/RUB spot rate is higher than 66.21 rubles per 1 dollar, company will pay 6,621,000 rubles and receive $10,000 from a bank;
2) If market USD/RUB spot rate is lower than 66.21 rubles per 1 dollar, company will not use the right to buy dollars for 66.21 rubles per 1 dollar and will buy it for market price [4, p. 26].
Other call options work the same way.
Now, using simulation modelling (100,000 scenarios), we can look at the distribution of ruble amount which company will have to pay for its debt if it enters into long call options and compare it to picture without any hedging instruments (Picture 2) [5, pp. 370-371].
Ruble amount of money payed for five payments, 9
3,015 3.5SO
Picture 2. Distribution of debt payment (with option contracts)
Table 2.
Red histogram shows how much company may pay for the debt (five payments) without the use of any hedging instruments, whereas the blue histogram represents the amount of rubles company will have to pay if it enters into option contracts and use them only when they are profitable (option premium is taken into account). In first case, 90% of scenarios indicate that company will need between 3.018 and 3.566 million rubles to repay the debt, whereas in case of using options, 95% of simulated scenarios are in this gap.
Simulation technique allows company's management to see the effect from hedging instruments application and to estimate how much money company may potentially save on making right hedging decision.
Instrument implementation comparison
Using simulation technique, companies may compare the effects from implementation of different instruments / instrument structures.
In previous example, we showed the structure of five consecutive option contracts. However, it is also possible to use forward contracts instead. In our case, forward contract means company's obligation to buy $10,000 at a given USD/RUB rate on an expiration date [4, p. 3]. Therefore, company knows the amount of money that it will pay to the bank to receive $10,000 when entering into the contract. Table 2 represents terms on which bank is ready to sign the forward contract with the company. contracts terms
Date of entering into a contract Expiration dates Volume, $ Strike price, RUB
10.06.2019 10.07.2019 10,000 66.06
10.07.2019 12.08.2019 10,000 66.45
12.08.2019 10.09.2019 10,000 67.12
10.09.2019 10.10.2019 10,000 67.89
10.10.2019 10.11.2019 10,000 68.00
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For all five contracts company will have to pay 3,352,200 rubles to bank in order to receive $50,000. Using 100,000 scenarios and previous results, we can now build a graph to estimate which contract structure is more effective: option or forward (Picture 3) [5, pp. 370-371].
Picture 3. Debt payment distribution (with option and forward contracts)
Blue histogram shows how much the company may have to pay for the debt without the use of any hedging instruments, while the yellow one represents the amount in case of entering into option contracts. The red line indicates the amount the company will have to pay if it decides to sign forward contracts.
At this point company's management can make a decision to use either forward or option contracts. If the choice is to hedge with forwards, company will have to pay fixed amount of rubles (3,352,200 rubles) to receive fix amount of dollars ($50,000 in total). On the other hand, if the company decides to enter into options it is possible it will have to pay either more or less than 3,352,200 to receive $50,000.
In this case, it might be reasonable to go into option contracts. The reason is that the number of scenarios where company pays more than 3,352,200
for $50,000 is less than 6%. While this figure does not seem large enough, some companies believe that 6% of overpayment probability is substantial.
Overall, simulation technique allows companies to compare the results of using various hedging instruments and / or their structures and make a smart decision which one to use.
Conclusion
In conclusion, it should be noted that in contemporary world the issue of accurate data prediction for risk hedging is very critical. Simulation modeling is one of the most preferable methods of forecasting for hedging purposes, which is widespread among risk managers. It helps companies to estimate risks before they realize, to assess the effectiveness of hedging implementation and to choose an instrument or the structure that minimizes costs while maximizing benefits.
However, human resources are limited and in order to use simulation modelling results, computer power should be used. In this article @Risk is used as an example of software for such work.
References
[1] Albright S. C. and Winston W. L. Business Analytics: Data Analysis and Decision Making. - Mason: Cengage Learning Inc, 2019. - 7th: p. 984;
[2] Bloomberg. USD-RUB Historical Exchange Rates [Online] // Bloomberg Professional. - May 22, 2019. -Bloomberg Subscription Service;
[3] Chung C. A. Simulation modeling handbook: A practical approach. - London: Taylor & Francis Ltd, 2019. - 1st: p. 608;
[4] Gottesman A. Derivatives Essentials: An Introduction to Forwards, Futures, Options, and Swaps. - New York: John Wiley & Sons Inc, 2016. - 1st: p. 352;
[5] Rees M. Business Risk and Simulation Modelling in Practice: Using Excel, VBA and @RISK. - New York: John Wiley & Sons Inc, 2015. - 1st: p. 464;
[6] Ringelberg J. [et al.] Modeling with @Risk: A tutorial guide. - West Lafayette: Purdue University, 2016. - pp. 1-31.
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