قیمت گذاری اوراق اختیار معامله با کمک روش نیکی وورو اوواروف
محورهای موضوعی : مهندسی مالی
مهدی ابوالی
1
(گروه مالی، واحد علوم تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران)
مریم خلیلی عراقی
2
(گروه مالی، واحد علوم تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران)
حسن حسن آبادی
3
(گروه فیزیک، دانشکده فیزیک، دانشگاه صنعتی شاهرود، شاهرود، ایران)
احمد یعقوب نژاد
4
(گروه حسابداری، واحد تهران مرکز، دانشگاه آزاد اسلامی، تهران، ایران)
کلید واژه: اختیار معامله, معادله قیمتگذاری بلک‌شولز, معادله شرودینگرگونه و روش پارامتریِ نیکیوورو – اووراروف,
چکیده مقاله :
اوراق اختیار از ابزارهای مهم بازارهای مالی بوده و قیمتگذاری اوراق با معادله قیمتگذاری بلک شولز بسیار متداول است. این معادله جهت قیمتگذاریِ اختیارهای اروپائى استفاده میشود. با بکارگیریِ علوم ریاضی در مباحث مالی، امکان ارائه مدلهای جدیدترِ قیمتگذاری اختیار معامله فراهم شده است. در این مقاله با روش جدید حل معادله دیفرانسیل تحت عنوان نیکیوورو - اوواروف، امکان ارائه مدل متفاوت قیمتگذاری بلک شولز بررسی گردید. سپس، معادله ای جدید برای قیمتگذاری اوراق اختیار معامله ارائه شد. افزایش دقت قیمتگذاری، رفع نواقص مدل بلک شولز، حل منطقی جدید و قابلیت مقایسه خروجی با حل عددی، اهمیت و نوآوری پژوهش حاضر میباشند. نتایج نشان داد؛ امکان ارائه مدل جدید قیمتگذاری اختیار معامله با روش نیکیوورو – اوواروف امکانپذیر بوده و در سطح اطمینان 95 درصد بین قیمتگذاری روش جدید و مدل بلک شولز تفاوت معنادار وجود ندارد. دقت بیشتر قیمتگذاری برای مبالغ بالا، امکان بکارگیریِ معادله در قیمتگذاری اختیار معامله های اروپایی و آمریکایی و اعمال محدودیتهای کمترِ اثبات معادله، مزیتهای مدل جدید هستند. به منظور مقایسه مدل جدید و مدل بلک‌شولز از اطلاعات 50 اختیار معامله زعفران در فرابورس ایران از سال 1395 لغایت 1398 استفاده و از آزمون مقایسه ای دو گروه مستقل ناپارامتریکِ من ویتنی استفاده گردید.
The Black-Scholes pricing theory is important ways of valuating transaction options. In this paper, a new method was developed to prove and improve the Black-Scholes equation by focusing on the Black-Scholes main Schrödinger equation and solving this equation using the NikkeuroOvaryov method. In the following, while investigating the possibility of improving the Black-Scholes equation with this method, a new equation for the pricing options was presented and tested. Increasing the accuracy of pricing arbitrary deals by using the equation provided, especially for high-value trades, logical solution in a new way, comparing output with numerical solution and innovating. Option based on Lagrange polynomial functions, the goals of doing research are present. The results showed a different positive probability for the Black-Scholes equation by solving the differential equation by the method Nikkirovo-Ovaryov is feasible and at 95% confidence level, there is no significant difference between the price of the two main black-hole groups and the new model. In order to compare the output of the new model with the Black Sholes main model, information from the 50 Saffron Deal options in Iran's Overseas Branch was limited to the 1395 to 1398 period and the Mann-Whitney independent nonparametric group was used to compare.
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Madan, mark. (2008). Combination of Black Schulz formulas with Brownian motion and limited connections. Applied Mathematics, 15(2), 97-115.
Meng, Li., Wang, Mei. (2010). Comparison of the Beckhelsell formula with the frequency Black-Scholes formula in the exchange derivatives market by changing the oscillation. Basic and Applied Sciences, 99–111.
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Sturm, Matthew., Goldstein, Henry. Huntington, Thomas. (2017). Using the pricing model approach to assess strategic decisions in turbulent environments: Black Scholes and airborne changes. Climatic Change, 2, 437–449.
Xu Chen. Jian-ping Wan. (2007). "Pricing options to change the route of the Levy model under the MEM". Mathematical Statistics, vol 23, issue 4, pp 651 -664.