مدلی برای قیمت گذاری سواپ زلزله و تحلیل حساسیت آن در ایران
محورهای موضوعی :
مهندسی مالی
نصرالله محمودپور
1
,
عبدالساده نیسی
2
,
مسلم پیمانی
3
1 - گروه مالی و بانکداری، دانشکده مدیریت و حسابداری، دانشگاه علامه طباطبایی، تهران، ایران
2 - گروه ریاضی، دانشکده علوم ریاضی و رایانه، دانشگاه علامه طباطبائی، تهران، ایران
3 - گروه مالی و بانکداری، دانشکده مدیریت و حسابداری، دانشگاه علامه طباطبایی، تهران، ایران
تاریخ دریافت : 1398/05/06
تاریخ پذیرش : 1398/07/09
تاریخ انتشار : 1398/10/01
کلید واژه:
تحلیل حساسیت,
قیمت گذاری سواپ فاجعه,
خسارت زلزله در ایران,
روش تفاضل محدود,
چکیده مقاله :
افزایش خسارت‌های اقتصادی ناشی از وقایع طبیعی طی سال‌های اخیر، یکی از بزرگتر‌ین چالش‌های پیش روی صنعت بیمه و پژوهشگران برای یافتن ابزارهای نوین مالی جهت انتقال ریسک فجایع و کاهش زیان‌های اقتصادی می‌باشد. در این مقاله مدلی برای قیمت‌گذاری سواپ فاجعه با نوسان خسارت ثابت جهت کاهش ریسک شرکت‌های بیمه و بیمه اتکایی در ایران ارائه می شود، طرح تحقیق گذشته‌نگر و تحقیق کاربردی است، روش گردآوری داد‌ها کتابخانه‌ای و ابزار استفاده از اسناد و مدارک مورد بهره‌برداری قرار می‌گیرد، برای استخراج کل داده‌ها از روش همبستگی استفاده می شود و تمام شماری خسارت کل زلزله‌های دارای تلفات، مخرب و تاثیر‌گذار در بازه زمانی 1288 الی 1397 در ایران مورد بررسی قرار گرفته است. احتمال وقوع و شدت خسارت ثابت و به صورت یک حرکت براونی پرش انتشار در نظر گرفته می شود، مدل دیفرانسیلی، انتگرالی استخراج شده با گسسته سازی به مدل دیفرانسیل معمولی تبدیل شده و با روش تفاضل محدود و نرم ابزار متلب جواب‌ها تخمین زده می‌شود، تغییرات مدل ارائه شده با تحلیل حساسیت لاندا مورد بررسی قرار می گیرد و سرانجام با داده‌های واقعی خسارت های زلزله در ایران، که از پایگاه داده ئی ام دات دیتا بیس و نتایج رگرسیون استخراج شده است، مدل اجرا می‌شود. بر اساس نتایج تحقیق قیمت اوراق سواپ فاجعه به ازای خسارت کمتر از آستانه ، روند افزایشی منظمی دارد، اما به محض رسیدن و رد شدن خسارت از آستانه، قیمت ها به شدت کاهش خواهند یافت
چکیده انگلیسی:
In recent years, increasing economic losses as a result of natural disasters are one of the main challenges fronting the insurance industry and researchers to discover original financial instruments so as to transmit disaster risks and minimize economic losses. In the present article, a model is suggested for catastrophe swap pricing with deterministic loss fluctuations in order to decrease the risk of insurance and reinsurance companies in Iran. The research is retrospective and applied; the data collection method is the library, and for the data collection use the documents. For the full data extraction, the correlation method is applied, For the purpose of extracting the complete data, the correlation method is used, all damages of earthquakes that have been fatal, destructive and affecting in the period 1927 to 2018 in Iran, have been investigated. The probability of the deterministic loss occurrence and severity are regarded to be Brownian motion of jump-diffusion. The extracted integral-differential model is converted into the standard differential one, and the answers are estimated via finite difference method and Matlab software. The changes to the suggested model are explored through the Lambda sensitivity analysis. As a final point, the model is implemented with real data of earthquake losses in Iran, which is extracted from the EM-DAT database and the regression results. Based on the results of the study, the price of catastrophe swap securities for less loss than the threshold has regular upward trend; however, once loss reached and passed the threshold, prices will drop dramatically.
منابع و مأخذ:
1) Iman Mohammad Taghi, Philosophy of Research Method in Humanities. second edition. Qom: Research Center and University; 1393.
2) Askari Firooz Hai Ehsan, Sadehvand Mohammad Javad, Insurance Securities. First edition. Tehran: Tehran Stock Exchange; 1393.
3) Ghafouri Ashtiani Mohsen, Naser Asadi Kiarash, Basic Indicators of Earthquake Insurance Rate of Iranian Buildings. Management Report, Tehran: Insurance Research Institute; 1390.
4) Kevin Quick Yu, Mathematical Models of Financial Derivatives. Translated by Abdolsadeh Nisi and Mahtab Mehrasa. First Edition. Tehran: Bourse; 1397.
5) Nisi Abdolsadeh, Salmani Qaraei Kamran, Financial Engineering and Market Modeling with the soft approach of MATLAB tool. second edition. Tehran: Allameh Tabatabai University; 1397.
6) Hal John. Translated by Sajjad Sayyah and Ali Salehabadi. First Edition. Tehran: Mofid Brokerage Company; 1384.
Aase K.K. An equilibrium model of catastrophe insurance futures and spreads. Geneva Papers on Risk and Insurance Theory 1999, 24 (1), 69–96.
Azizi S.M.E.P.M., Neisy A New Approach in Geometric Brownian Motion Model. In: Cao BY. (eds) Fuzzy Information and Engineering and Decision. Advances in Intelligent Systems and Computing, 2018, vol 646. Springer.
Bakshi G., Madan D. Average rate claims with emphasis on catastrophe loss options. Journal of Financial and Quantitative Analysis 2002, 37 (1), 93–115.
Black F., Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 1973, 81 (3), 637–654.
Baryshnikov Y., Mayo A., Taylor D.R. Pricing of CAT bonds. 2001, Preprint.
Bjork T. Arbitrage theory in continuous time, 3rd edn. Oxford University Press, Oxford; 2009.
Borden S., Sarkar A. Securitizing property catastrophe risk. Current Issues in Economics and Finance 1996, 2 (9), 1–6.
Braun A. Pricing catastrophe swaps: A contingent claims approach. Insurance: Mathematics and Economics, 2011, 49(3), 520-536.
Burnecki K., Kukla G. Pricing of zero-coupon and coupon CAT bonds Applicationes Mathematicae 2003, 30 (3), 315–324.
Canter M.S., Cole J.B., Sandor, R.L. Insurance derivatives: a new asset class for the capital markets and a new hedging tool for the insurance industry. Journal of Applied Corporate Finance 1997, 10 (3), 69–81.
Christensen C.V., Schmidli, H. Pricing catastrophe insurance products based on actually reported claims. Insurance: Mathematics and Economics 2000,27 (1),189–200.
Cox S.H., Fairchild J.R., Pedersen H.W. Valuation of structured risk management products. Insurance: Mathematics and Economics 2004, 34 (2), 259–272.
Cox S.H., Pedersen H.W. Catastrophe risk bonds. North American Actuarial Journal 2000, 4 (4), 56–82.
Cox J.C., Ingersoll Jr. J.E., Ross S.A. A theory of the term structure of interest rates. Econometrica 1985, 53 (2), 385–407.
Cummins J.D. CAT bonds and other risk-linked securities: state of the markeand recent developments. Risk Management and Insurance Review 2008, 11 (1),23–47.
Cummins D., Weiss M. A. Convergence of insurance and financial markets: Hybrid and securitized risk‐transfer solutions. Journal of Risk and Insurance 2009, 76(3), 493-545.
Dassios A., Jang J. Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity. Finance and Stochastics 2003, 7 (1), 73–95.
Embrechts P., Meister S. Pricing insurance derivatives: the case of catfutures In: Proceedings of the 1995 Bowles Symposium on Securitization of Risk, Georgia State University Atlanta, Society of Actuaries, Monograph 1997, M-FI97-1, pp. 15–26.
EM-DAT: The Emergency Events Database - Université catholique de Louvain (UCL) - CRED - www.emdat.be, Brussels, Belgium.
Investopedia (2019). INVESTING, FINANCIAL ANALYSIS, Financial Modeling, Feb 11. (https://www.investopedia.com/terms/f/financialmodeling.asp)
Investopedia (2018). INSURANCE, Catastrophe Loss Index, May 16. (https://www.investopedia.com/terms/c/catastrophe-loss-index.asp)
Investopedia (2018).INVESTING, ALTERNATIVE INVESTMENTS, Catastrophe Swap, Apr 13. (https://www.investopedia.com/terms/c/catastrophe-swap.asp)
Investopedia (2019). INVESTING, FINANCIAL ANALYSIS, Sortino Ratio, Mar 3. ( https://www.investopedia.com/terms/s/sortinoratio.asp)
Jaimungal S., Wang T. Catastrophe options with stochastic interest rates and compound Poisson losses. Insurance: Mathematics and Economics 2006, 38 (3), 469–483.
Lee J.-P., Yu M.-T. Pricing default-risky CAT bonds with moral hazard and basis risk. Journal of Risk and Insurance 2002, 69 (1), 25–44.
Loubergé H., Kellezi E., Gilli M. Using catastrophe-linked securities to diversify insurance risk: a financial analysis of CAT bonds. Journal of Insurance Issues 1999, 22 (2), 125–146.
Macmillan Publishers Limited. Pool knowledge to stem losses from disasters, Nature 2015, vol 522, 18 june.
Muermann A. Actuarially consistent valuation of catastrophe derivatives Working Paper 2003, Wharton Financial Institutions Center.
Munich Re NatCatSERVICE .Natural catastrophes in the first half of 2018.
Neisy A, Salmani K .An inverse finance problem for estimation of the volatility. Computational Mathematics and Mathematical Physics 2013, Volume 53, Issue 1, pp 63–77. Springer.
Schmidli H. Modelling PCS options via individual indices. 2003, Working paper.
Vasicek O. An equilibrium characterization of the term structure. Journal of Financial Economics 1997, 5 (2), 177–188.
Vaugirard V.E. Pricing catastrophe bonds by an arbitrage approach Quarterly Review of Economics and Finance 2003a, 43 (1), 119–13.
Vaugirard V.E. Valuing catastrophe bonds by Monte Carlo simulations Applied Mathematical Finance 2003b, 10 (1), 75–90.
Vaugirard V.E. A canonical first passage time model to pricing nature-linked bonds. Economics Bulletin 2004, 7 (2), 1–7.
Vickery P., Skerlj P., Lin J., Twisdale L., Jr Young M., Lavelle F. HAZUS-MH Hurricane model methodology. II: Damage and loss estimation. Natural Hazards Review 2006, 7, 94–103.
Unger, A.J.A., Pricing index-based catastrophe bonds: Part 1: Formulation and discretization issues using a numerical PDE approach, Computers & Geosciences 2010, 36 (2), 139-149.
Xu Y. “A Study of the Loss Distribution of Natural Disasters in Norway Comparing a Common Model with a Model Broken Down into Catastrophe Types”, University of Oslo Library, 2016.
Zolfaghari M.R., Campbell K.W. A NEW INSURANCE LOSS MODEL TO PROMOTE CATASTROPHE INSURANCE MARKET IN INDIA AND PAKISTAN, The 14th World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China.
_||_
