تحلیل مقایسه‌ای کارایی مدل‌های بلک-شولز و انتشار پرش در مدل سازی قیمت مسکن: مراکز استان‌های ایران

هدف پژوهش، مدل‌سازی قیمت مسکن در مراکز استان‌های ایران در دوره زمانی فروردین 1388 تا اسفند 1401 است. در این مطالعه از مدل‌های بلک-شولز و انتشار پرش در مدل‌سازی قیمت مسکن استفاده ‌شده که مدل بلک-شولز با به‌کارگیری روش حداکثر درستنمایی و مدل انتشار پرش با الگوریتم (gem) برآورد شد. برای شبیه‌سازی قیمت آتی مسکن و انتخاب بهترین مدل از روش مونت-کارلو با عملکرد 6 ماهه، 12 ماهه و 24 ماهه استفاده‌شده است. بر اساس نتایج مشخص است که در اکثر مراکز استان‌های ایران عملکرد 6 ماهه بهتر بوده و در بعضی از مراکز استان‌ها هم عملکرد 12 ماهه و 24 ماهه بهتر بوده است. با توجه به نتایج مشخص شد که الگوی انتشار پرش در توضیح‌دهندگی رفتار قیمت مسکن عملکرد بهتری نسبت به الگوی بلک-شولز داشته است. نتایج الگوی انتشار پرش نشان می‌دهد که قیمت مسکن در مراکز استان‌های ایران دارای پرش بوده و با توجه به شرایط و ساختار بازار مسکن هر استان، پرش قیمت متفاوت است که در بعضی استان‌ها ازجمله شهرهای بزرگ و کلان‌شهرها پرش قیمتی بالا و در شهرهای کوچک کمتر بوده است. با توجه به نتایج الگوی انتشار پرش، بیشترین و کمترین پرش قیمت مسکن مربوط به مراکز استان‌های خراسان رضوی و کهگیلویه و بویراحمد بوده که مقدار آن به ترتیب برابر 0.58 و 0.09 درصد است.

comparative analysis of efficiency of black-scholes models and jump diffusion in housing price modeling: the provincial centers of iran

purpose: during the last two decades, housing price fluctuations in some countries including iran have been a main challenge of the housing market and the country’s economy. in one period, there was a significant increase in housing prices and, in another period, it decreased or stabilized. relatively high and widespread, it governs the price of housing, as a result of which significant developments have occurred in the housing sector and in the entire economy. in new theories, housing prices can fluctuate over time, and housing price fluctuations can be divided into two important categories. first, minor fluctuations result from market structure based on fundamentals. the housing market is based on the housing supply and demand conditions and the endogenous factors of the housing sector. hence, the gradual and slow changes in the housing price over time are caused by the basic and underlying factors of the housing market and through changes in the total cost. housing production changes housing prices. second, housing cyclical shocks or impulses, are the exogenous factors that create cyclical shocks in the housing sector, and the monetary policy’s effect on asset prices, including real estate and housing, is determined. the capital market, household asset portfolio composition and macroeconomic variables are among them.methodology: we assume thatis the probability space,  is a filter created by brownian  and poisson process  with  is intensity. we also assume that brownian process, poisson process  and price jump  are independent of one another.  housing prices are based on time . in the black-scholes model (bsm), housing prices at time t are modeled by the following geometric brownian process:where  is the average and  standard deviation of housing prices. in the jump diffusion model (jdm), housing prices are calculated by the following equation:where  is the expected growth rate,  is the turbulence of the brownian process, and  is the housing price at time t and before the jump.results and discussion: in this research, using gem algorithm, the five parameters of jump diffusion model were estimated and then two parameters of black-scholes model were estimated using the maximum likelihood method. next, the simulation of the future housing price was done based on the monte-carlo method. the simulation was done in 100,000 repetitions, and then the best model was selected. the housing price was simulated based on the real price, so that the price at time t could be calculated with its next monthly price, i.e. t+1. this method was repeated until the last data. in this research, many models were simulated with random numbers generated for housing prices to get the best model with the least error. in three cases of 6 months, 12 months and 24 months, housing prices were simulated and predicted. one way to calculate the accuracy of the model was based on the confidence interval with the assumption of normal approximation. one way to check the stability of the obtained coefficients of the models was to repeat the simulation with different random numbers and calculate the average performance of each model. in this research, in order to avoid bringing a large number of estimated models, 25 models with the best performance and the least error, and among these 25 models, the best models were identified.