Life settlement pricing with fuzzy parameters

Existing literature asserts that the growth of life settlement (LS) markets, where they exist, is hampered by limited policyholder participation and suggests that to foster this growth appropriate pricing of LS transactions is crucial. The pricing of LSs relies on quantifying two key variables: the insured's mortality multiplier and the internal rate of return (IRR). However, the available information on these parameters is often scarce and vague. To address this issue, this article proposes a novel framework that models these variables using triangular fuzzy numbers (TFNs). This modelling approach aligns with how mortality multiplier and IRR data are typically provided in insurance markets and has the advantage of offering a natural interpretation for practitioners. When both the mortality multiplier and the IRR are represented as TFNs, the resulting LS price becomes a FN that no longer retains the triangular shape. Therefore, the paper introduces three alternative triangular approximations to simplify computations and enhance interpretation of the price. Additionally, six criteria are proposed to evaluate the effectiveness of each approximation method. These criteria go beyond the typical approach of assessing the approximation quality to the FN itself. They also consider the usability and comprehensibility for financial analysts with no prior knowledge of FNs. In summary, the framework presented in this paper represents a significant advancement in LS pricing. By incorporating TFNs, offering several triangular approximations and proposing goodness criteria of them, it addresses the challenges posed by limited and vague data, while also considering the practical needs of industry practitioners

Bulanık mantık yaklaşımıyla teknik analiz yönteminin uygulanması : İMKB 30 örneği

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bulanık mantık yaklaşımı, yapay zeka çalışmalarının bir alt dalı olarak incelenmektedir. Aristoteles'in iki değerli mantık önermesine karşı, çok değerli mantık çalışmalarının bir ürünü olarak ortaya çıkmıştır. İlk olarak buhar makinesi denetleme sisteminde kullanılan bulanık mantık yaklaşımının günümüzde çok geniş sahada uygulama alanı bulduğu görülmektedir. Teknik analiz yöntemi ise geçmiş fiyat hareketlerinin gelecekte de devam edeceği varsayımına dayanarak normalin üzerinde getiri elde etme iddiasında bulunur. Bu yöntemin kullandığı farklı araçlar, fiyatların gelecekteki yönü hususunda yatırımcısına ipuçları verir. Bu ipuçlarını değerlendiren yatırımcı, gelecekteki muhtemel fiyat hareketlerine göre pozisyon alarak normalin üzerinde getiri elde etmeyi amaçlar.Bu çalışmanın amacı, bulanık mantık yaklaşımı ile teknik analiz yönteminin birlikte kullanılacağı bir modelin geliştirilmesidir. Oluşturulan simülasyonda, sistemin hisse senetlerini al - sat yapması suretiyle normalin üzerinde getiri elde edip edemeyeceği test edilmiştir. Bu amaçla İMKB 30 endeksinden belli kısıtlar çerçevesinde hisse senetleri seçilmiştir. Bu kısıtlar; hisselerin İMKB'nin iki seans olarak çalışmaya başladığı 1995 yılından 2012 Şubat ayına kadar kesintisiz ve aynı isimle işlem görmeleridir. Bu kısıtlara uyan 12 adet hisse senedinin günlük fiyatları üzerinden ADX, CCI, ROC, Stokastik ve RSI teknik analiz gösterge değerleri hesaplanmıştır. Bu gösterge değerleri, bulanık mantık yaklaşımı ile değerlemeye tabi tutularak her bir gün için tek bir çıktı elde edilmiştir. Elde edilen bu çıktılar oluşturulan simülasyonda al - sat kararlarının verilmesinde kullanılmıştır. Öne sürülen simülasyon modelinde 1995 yılı ile 2012 yılı arasındaki 17 yıllık periyot ikiye ayrılmış, bunlardan ilki ölçme periyodu, ikincisi tahmin periyodu olarak tasarlanmıştır. Ölçme periyodunda, al - sat kararlarına esas teşkil eden bulanık mantık çıktılarından, periyodun getirisini maksimize eden al sinyal değeri ve sat sinyal değeri optimizasyon yapılarak bulunmuş, bu ikilinin tahmin periyodundaki performansı ölçülmüştür. Tahmin periyodunda, al - sat sinyalleri ile elde edilen getiri ve al - tut stratejisi ile elde edilen getiri karşılaştırılmıştır.Karşılaştırmanın hipotez testi temelinde yapılabilmesi için getiri verilerinin normal dağılıma sahip olup olmadığı test edilmiştir. Gerek al - sat stratejisi gerek al - tut stratejisi getiri verilerinin normal dağılıma sahip olmadığı tespit edilmiştir. Ayrıca bu verilerin farklı türevlerinin de normal dağılıma sahip olmadığı belirlenmiştir. Bu sebeple hipotez testleri parametrik olmayan yöntemlerden Mann Whitney U Testi ile yapılmıştır. Ancak merkezi limit teoremine göre veri sayısı arttıkça değişkenler normal dağılım özelliği gösterdiğinden parametrik yöntemlerden Z testi de uygulamaya dahil edilmiştir. Yapılan analizler sonucunda tahmin periyodunda Mann Whitney U Testine göre 12 hisse senedinden 4 tanesi, Z Testine göre 3 tanesi normalin üzerinde getiri sağlamıştır.Anahtar Kelimeler: Bulanık Mantık, Teknik Analiz, Hisse Senedi Fiyat TahminiFuzzy logic approach is discussed as a sub-branch of artificial intelligence studies. It has developed as a result of multi valued logic studies carried out against the two valuable logic proposals of Aristotle. It is seen that the fuzzy logic approach which was first used in steam engine control system is used in a wide range of application field nowadays. Technical analysis method argues that it will make profit over normal based on the assumption that past price movements will continue in the future. The different tools that this method uses give tips to the investors regarding the future direction of prices. The investor evaluating these tips aims to make profit over normal by doing planning according to the probable future price movements.The aim of this study is to develop a model in which the fuzzy logic approach and the technical analysis method will be used together. In the generated simulation, it was tested whether the system will be able to make profit provided that the system makes the shares buy-sell. For this purpose, the shares were chosen in ISE 30 index within the frame of certain constraints. These constraints are that the shares were processed as straight through processing between 1995 when ISE started to work in two sessions and 2012 February and these shares were processed with the same name. ADX, CCI, ROC, Stochastic and the RSI technical analysis indicator values based on the daily prices of 12 shares which are in accordance with these constraints were calculated. These indicator values were evaluated by the fuzzy logic approach and a single output for each day was obtained. The obtained outputs were used to determine the buy-sell decisions of the generated simulations.In the proposed simulation model, 17-years period between 1995 and 2012 years were divided into two parts, the first one is the measurement period, and the second one is designed to be the period of prediction. In the measurement period, the signal value and sell signal value maximizing the profits of the period were obtained by optimization from the fuzzy logic outputs which constitute the basis for buy-sell decisions and the performance of these two in the measurement period was evaluated. The profit obtained by buy-sell signals and the profit obtained by buy-hold strategy were compared in the prediction period.In order to make this comparison on the basis of test hypotheses, whether the profit data has normal distribution or not was tested. It was determined that both buy-sell strategy and buy-hold strategy profit do not have normal distribution. In addition, it was found that the different derivatives of these data were not normally distributed. For this reason, non-parametric hypothesis tests were carried out by Mann Whitney U test which is one of the non-parametric methods. However, according to the central limit theorem, the variables has the normal distribution feature as the data number increase, therefore Z test method was included in the application. As the result of the conducted analyses, in the prediction period, 4 of 12 shares made profit over normal according to Mann-Whitney U Test, and 3 of 12 shares made profit over normal according to Z Test.Keywords: Fuzzy Logic, Technical Analysis, Stock Price Predictio

Option price sensitivities through fuzzy numbers

The main motivation in using fuzzy numbers in finance stays in the need of modeling uncertainty and vagueness that are implicit in many situations. However the fuzzy approach has not to be considered as a substitute of the probabilistic one but, moreover, a complementary way to describe the model peculiarities. Here we consider, in particular, the Black and Scholes model for option pricing and we show that the fuzzification of some key parameters enables a sensitivity analysis of the option price with respect to the risk-free interest rate, the final value of the underlying stock price, the volatility, and also better forecasts (see Thavaneswaran et al (2009) for details. The Greeks, in addition, play an important role in the definition of the shape of the fuzzy option price

Option price sensitivities through fuzzy numbers

The main motivation in using fuzzy numbers in finance lies in the need for modelling the uncertainty and vagueness that are implicit in many situations. However, the fuzzy approach should not be considered as a substitute for the probabilistic approach but rather as a complementary way to describe the model peculiarities. Here, we consider, in particular, the Black and Scholes model for option pricing, and we show that the fuzzification of some key parameters enables a sensitivity analysis of the option price with respect to the risk-free interest rate, the final value of the underlying stock price, the volatility, and also better forecasts (see Thavaneswaran et al. (2009) [12] for details). The sensitivities with respect to the variables of the model are represented by different letters of the Greek alphabet and they play an important role in the definition of the shape of the fuzzy option pric