کاربرد درخت دوجمله‌ای در تعیین قیمت اختیار معامله آسیایی و محاسبه پارامترهای حساسیت ریسک (مطالعه موردی کنجاله سویا و ذرت دانه‌ای)

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه تبریز

چکیده

بورس کالای ایران می‌تواند با استفاده از ابزارهای مشتقه مانند قراردادهای آتی و اختیار معامله نقش زیادی در رفع دغدغه و نگرانی فعالان بازار محصولات استراتژیک کشاورزی ازجمله کنجاله سویا و ذرت داشته باشد. هدف این مطالعه تعیین قیمت اختیارمعامله آسیایی و پارامترهای حساسیت این نوع اختیارمعامله می‌باشد. از بین روش‌های کمی برای محاسبه مشتقات و پارامترهای حساسیت ریسک اختیارمعامله، مدل درخت دوجمله‌ای به‌وفور مورداستفاده قرار می‌گیرد. در مطالعه حاضر قیمت اختیارمعامله آسیایی با میانگین حسابی و هندسی و همچنین دو نوع قیمت انقضاء ثابت و شناور برای دو محصول کنجاله سویا و ذرت دانه‌ای با استفاده از مدل درخت دوجمله‌ای محاسبه گردید. همچنین حساسیت قیمت اختیارمعامله به تغییرات (تغییر در قیمت دارایی پایه، دلتا، نوسان قیمت، زمان باقی‌مانده تا سررسید و نرخ بهره بدون ریسک) با استفاده از پارامترهای حساسیت سنجیده و میزان اثرگذاری آن‌ها محاسبه گردید. داده‌های موردنیاز این مطالعه به‌صورت سری زمانی قیمت هفتگی از فروردین 1392 الی مرداد 1395 جمع‌آوری گردیده است و جهت تجزیه‌وتحلیل از نرم‌افزار DerivaGem و متلب استفاده می‌گردد. نتایج نشان داد که اختیار آسیایی نسبت به اختیار ساده اروپایی ارزان‌تر است. افزایش قیمت دارایی، افزایش میزان نوسان قیمت دارایی و افزایش نرخ بهره بدون ریسک سبب افزایش قیمت اختیارمعامله خرید می‌شود و با کاهش زمان باقی‌مانده تا سررسید، با فرض ثابت ماندن بقیه عوامل، از ارزش اختیارمعامله کاسته می‌شود. به‌طورکلی می‌توان گفت برای اتخاذ یک موقعیت مناسب در اختیارمعامله، لازم است تمام متغیرهای مؤثر بر قیمت را در نظر گرفته و با توجه به میزان حساسیت اختیارمعامله به هر یک از این متغیرها، راهبرد مناسبی را برای پوشش ریسک این قراردادها در نظر گرفت.

کلیدواژه‌ها


عنوان مقاله [English]

Application of Binomial Tree in Determining the Price of an Asian Option and Calculation of Risk-Sensitive Parameters (Case Study: Soybean Meal and Corn)

نویسندگان [English]

  • Esmaeil Pishbahar
  • Mariam Baghestani
  • Ghader Dashti
University of Tabriz
چکیده [English]

Introduction: The use of new financial instruments, and specifically option contracts, as a tool for risk management and create profitability, can help to boom exchanges and reduce the problems of the agricultural sector. Given the increasing population and the growing need for animal protein, the fluctuation in prices of these products can have a significant impact on the food security of individuals. The fluctuation of the prices of production inputs, including soybean meal and corn, can lead to fluctuations in the price of meat. The Iran Mercantile Exchange can play a major role in eliminating concerns and concerns of market participants for strategic agricultural products, including soybean meal and corn, using derivatives such as futures contracts and options. The trend of development of commodity exchanges in the world suggests that the emergence and development of these markets activities in the field of economy, seeks to dispel some of the economic needs and in many cases, eliminate some of the bottlenecks and barriers in the commodity market. The trend of development of commodity exchanges in the world suggests that the emergence and development of these markets activities in the field of economy, seeks to dispel some of the economic needs and in many cases, eliminate some of the bottlenecks and barriers in the commodity market. Option contracts is one of derivatives in commodity exchange that can have effective roll in agricultural market for overcome the problems of traditional market and reduce the risk of investors in this market. According to population, growth and increasing demand for Chicken meat and eggs, soybean meal and maize prices volatility may be fluctuating prices for white meat and egg. According to this, the aim of this study is determine the price of Asian option and Sensitivity parameters.
Materials and Methods: Among quantitative methods to calculate derivatives and risk sensitivity parameters of an option, binomial tree model is frequently used. Arithmetic and Geometric Asian option with fixed and floating expiration prices were calculated using the binomial tree model for soybean meal and maize. Moreover, the sensitivity of an option's price to changes (Change in the price of the underlying asset, Delta, price volatility, time until maturity and risk-free interest rate) measured by using sensitive parameters and the impact has been obtained. Required information includes historical data on the weekly prices of soybean meal and corn in the years 2007-16.
Results and Discussion: The results indicate that an Asian option is cheaper than a European simple option. Increase in asset prices, increase in asset price volatility and increases risk-free interest rate, increase the price of call option. By reducing the remaining time to maturity (T), with other factors constant, the value of an option is reduced. The hedge ratio for soybean meal is equal to 0.69 and 0.81 for corn, which means that in order to reduce the income fluctuations due to changes in the price of soybean and corn, 69 and 81 percent of the products must be sold in future and option markets. Two methods of Monte Carlo simulation and binomial tree model were used to determine the price of Asian option whit fixed strike for soybean meal and corn were 12.5 and 9.2, respectively. The results indicate that the control variate in variance reduction Monte-Carlo simulation method has a very good performance and significantly reduced the variance. Increase in asset prices, increase in asset price volatility and increases risk-free interest rate, increase the price of call option.
Conclusions: In general, it can be said that to adopt a proper position in an option, is necessary to consider all the variables affecting the price. In addition, according to the sensitivity of an option to each of these variables, it should consider a good strategy to hedge these contracts. The option is a good tool for risk management, but it is also associated with risks. In volatile markets where volatility is high, the value of options is changing rapidly. Therefore, risk managers should regularly review the value of an option and thoughtful strategies to update these changes, because perhaps once-profitable option other time is extremely unprofitable.

کلیدواژه‌ها [English]

  • Binomial model
  • Greeks
  • Mercantile exchange
  • Option
  • Premium
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