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Pricing Zero-Coupon CAT Bonds Using the Enlargement of Filtration Theory: A General Framework 利用扩大过滤理论为零息CAT债券定价:一个一般框架
Journal of Mathematical Finance Pub Date : 2022-08-04 DOI: 10.4236/jmf.2022.123031
Zied Chaieb, Djibril Gueye
{"title":"Pricing Zero-Coupon CAT Bonds Using the Enlargement of Filtration Theory: A General Framework","authors":"Zied Chaieb, Djibril Gueye","doi":"10.4236/jmf.2022.123031","DOIUrl":"https://doi.org/10.4236/jmf.2022.123031","url":null,"abstract":"The main goal of this paper is to use the enlargement of ltration framework for pricing zerocoupon CAT bonds. For this purpose, we develop two models where the trigger event time is perfectly covered by an increasing sequence of stopping times with respect to a reference ltration. Hence, depending on the nature of these stopping times the trigger event time can be either accessible or totally inaccessible. When some of these stopping times are not predictable, the trigger event time is totally inaccessible, and very nice mathematical computations can be derived. When the stopping times are predictable, the trigger event time is accessible, and this case would be a meaningful choice for Model 1 from a practical point of view since features like seasonality are already captured by some quantities such as the stochastic intensity of the Poisson process. We compute the main tools for pricing the zero-coupon CAT bond and show that our constructions are more general than some existing models in the literature. We obtain some closed-form prices of zero-coupon CAT bonds in Model 2 so we give a numerical illustrative example for this latter.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116750894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exploring the Endogenous Nature of Meme Stocks Using the Log-Periodic Power Law Model and Confidence Indicator 利用对数周期幂律模型和置信度指标探索模因存量的内生性质
Journal of Mathematical Finance Pub Date : 2021-10-12 DOI: 10.4236/jmf.2022.121015
H. Takagi
{"title":"Exploring the Endogenous Nature of Meme Stocks Using the Log-Periodic Power Law Model and Confidence Indicator","authors":"H. Takagi","doi":"10.4236/jmf.2022.121015","DOIUrl":"https://doi.org/10.4236/jmf.2022.121015","url":null,"abstract":"This study examined the endogenous nature of negative bubbles forming in meme stocks with the Log-Periodic Power Law (LPPL) Confidence Indicator (CI). A meme stock is a stock that has gained a significant amount of attention on a large social media platform such as Yahoo! or Reddit. This study examined four meme stocks including Tesla, Inc. (TSLA), GameStop Corp. (GME), Koss Corporation (KOSS), and AMC Entertainment Holdings Inc (AMC). The CI was able to detect numerous bubbles forming in meme stocks, but had difficulty in significantly predicting social media-induced exogenous rallies. This may have been due to price movements affected by external causes such as short squeezes. However, the model did provide proof for the formation of previous bubbles that could have been a catalyst for the meme stocks rallies. This study outlines the real unpredictability of many black-swan events, and further studies could be done examining exogenous bubbles.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132788832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Call and Put Option Pricing with Discrete Linear Investment Strategy 离散线性投资策略下的看涨和看跌期权定价
Journal of Mathematical Finance Pub Date : 2021-10-10 DOI: 10.4236/jmf.2022.121005
N. Ghorbani, A. Korzeniowski
{"title":"Call and Put Option Pricing with Discrete Linear Investment Strategy","authors":"N. Ghorbani, A. Korzeniowski","doi":"10.4236/jmf.2022.121005","DOIUrl":"https://doi.org/10.4236/jmf.2022.121005","url":null,"abstract":"We study the Option pricing with linear investment strategy based on discrete time trading of the underlying security, which unlike the existing continuous trading models provides a feasible real market implementation. Closed form formulas for Call and Put Option price are established for fixed interest rates and their extensions to stochastic Vasicek and Hull-White interest rates.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129504093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Did You Really Beat the Market? A Practical and Parsimonious Approach to Evaluating Risk-Adjusted Performance 你真的赢了市场吗?评估风险调整后绩效的实用而简洁的方法
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113031
David J. Moore
{"title":"Did You Really Beat the Market? A Practical and Parsimonious Approach to Evaluating Risk-Adjusted Performance","authors":"David J. Moore","doi":"10.4236/jmf.2021.113031","DOIUrl":"https://doi.org/10.4236/jmf.2021.113031","url":null,"abstract":"This study contributes to the literature by modifying and recasting the Modigliani and Modigliani M-Squared risk-adjusted performance measure in a practical setting. Specifically, rather than combine the risk-free asset (Treasury Bill) with the portfolio under consideration to match market risk, this study combines the risk-free asset with a levered (or unlevered) market ETF to match portfolio risk. In so doing, this study addresses the question: Could an investor have earned higher returns with the same risk (standard deviation) using a simple combination of the risk-free asset and a readily available levered (or unlevered) market ETF? The study also addresses the impact of the context where one captures return measurements on outperformance conclusions. Although this study focuses its analysis on in-sample descriptive statistics, the new Risk-Equivalent Excess Performance measure and contextualization provide a basis for future out-of-sample inferential analysis.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124324988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Singular Valued Decomposition and Principal Component Analysis to Compare Market Indexes 市场指标比较的奇异值分解与主成分分析
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113027
F. Vadillo, N. Vadillo
{"title":"Singular Valued Decomposition and Principal Component Analysis to Compare Market Indexes","authors":"F. Vadillo, N. Vadillo","doi":"10.4236/jmf.2021.113027","DOIUrl":"https://doi.org/10.4236/jmf.2021.113027","url":null,"abstract":"In this paper, we used the Singular Value Decomposition (SVD) to find the relationships in the fluctuation of the six market indexes CAC 40, DAX, DOW JONES 30, FTSE 100, IBEX35 and NIKKEI 225 during the year 2018. This technique allows relating several indexes in a very similar way the classical Principal Component Analysis (PCA). In fact, we will just use the statistical software to confirm some results.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132194759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Investors’ Behavior towards the Relationship between Bitcoin, Litcoin, Dash Coins, and Gold: A Portfolio Modeling Approach 投资者对比特币、莱特币、达世币和黄金关系的行为:一种投资组合建模方法
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113028
A. Maghrebi, Fathi Abid
{"title":"The Investors’ Behavior towards the Relationship between Bitcoin, Litcoin, Dash Coins, and Gold: A Portfolio Modeling Approach","authors":"A. Maghrebi, Fathi Abid","doi":"10.4236/jmf.2021.113028","DOIUrl":"https://doi.org/10.4236/jmf.2021.113028","url":null,"abstract":"This study considers a market-based economy that is composed of two asset classes: one is a digital, cryptocurrency, and the other is real, gold. We demonstrated that coins like (BTC, LTC, and DASH) can substitute a traditional safe haven “gold” in an intertemporal investment portfolio to become a new form of safe haven. The cryptocurrency follows a Jump-diffusion process. However, gold prices follow an Ornstein-Uhlenbek process to characterize the stochastic nature of the market. The stochastic optimal control approach, combined with the strategic asset allocation and the intertemporal utility theory, are used through the derivation of a Hamilton-Jacobi-Bellman (HJB) equation to determine an explicit solution of the optimal allocation problem for investors with CRRA utility function. We considered the Gamma Levy process to solve the optimization problem. By using the secant method, we determined numerically the optimal percentage invested in the two asset classes at each time over the holding period. Our results showed that an investor can substitute gold by coins (BTC, LTC, DASH) from an investment portfolio perspective. Although Gold is supposed to be the traditional safe-haven asset, the digital currency seems to emerge as a new form of safe-haven value in a risky environment.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121407145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Exponential GARCH Model with Exogenous Covariate for South Sudanese Pounds—USD Exchange Rate Volatility: On the Effects of Conflict on Volatility 南苏丹镑兑美元汇率波动的外生协变量指数GARCH模型:冲突对波动的影响
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113026
Abui Peter Kur, Oscar Ngesa, R. Sarguta
{"title":"Exponential GARCH Model with Exogenous Covariate for South Sudanese Pounds—USD Exchange Rate Volatility: On the Effects of Conflict on Volatility","authors":"Abui Peter Kur, Oscar Ngesa, R. Sarguta","doi":"10.4236/jmf.2021.113026","DOIUrl":"https://doi.org/10.4236/jmf.2021.113026","url":null,"abstract":"The empirical models that explain the variation in exchange rate on the ground of macroeconomic fundamentals only are usually bias on the account of omitted variable hence, they cannot decently explain variations in exchange rate. However, if socio-political determinants, like civil wars, violence are incorporated in simple time series specification, the variations of exchange rate can be understood better. Apparently in developing countries like South Sudan where socio-political problems like conflict are most prevalent, the subject remains largely under-explored. This paper therefore, applies ARMA (p, q)-EGARCH (p, q) model with exogenous covariate for SSP-USD exchange rate volatility to examine the effect of conflict as an exogenous variable on exchange rate volatility. The proposed model is ARMA (1, 2)-EGARCH (1, 1) class of models with exogenous covariate in both mean and volatility equations. An empirical application of the proposed model is demonstrated by incorporating the conflict index as covariate in both mean and volatility equations of the proposed model. Parameter estimation was performed using maximum likelihood estimation method. The estimation results with classical maximum likelihood estimation method suggested that exchange rate volatility was persistent as evidenced by higher values of the coefficient of the parameter that accounts for persistence (β) in conditional volatility. Furthermore, the parameter for leverage effect in our models was found to be significant. The results showed that the effects of conflict on volatility of SSP-USD was found positive and statistically significant in both equations indicating that higher prevalence of conflict makes the exchange rate to be more volatile.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124962643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Estimation of Conditional Weighted Expected Shortfall under Adjusted Extreme Quantile Autoregression 调整极值分位数自回归条件加权期望缺口估计
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113021
Martin M. Kithinji, P. Mwita, Ananda O. Kube
{"title":"Estimation of Conditional Weighted Expected Shortfall under Adjusted Extreme Quantile Autoregression","authors":"Martin M. Kithinji, P. Mwita, Ananda O. Kube","doi":"10.4236/jmf.2021.113021","DOIUrl":"https://doi.org/10.4236/jmf.2021.113021","url":null,"abstract":"In this paper, we present an estimator that improves the well-calibrated coherent risk measure: expected shortfall by restructuring its functional form to incorporate dynamic weights on extreme conditional quantiles used in its definition. Adjusted Extreme Quantile Autoregression will is used in estimating intermediary location measures. Consistency and coherence of the estimator are also proved. The resulting estimator was found to be less conservative compared to the expected shortfall.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132846423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Option Pricing Model with Transaction Costs and Jumps in Illiquid Markets 非流动性市场中具有交易成本和跳跃的期权定价模型
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/JMF.2021.113020
Praewnapa Seelama, D. Thongtha
{"title":"Option Pricing Model with Transaction Costs and Jumps in Illiquid Markets","authors":"Praewnapa Seelama, D. Thongtha","doi":"10.4236/JMF.2021.113020","DOIUrl":"https://doi.org/10.4236/JMF.2021.113020","url":null,"abstract":"Option pricing model is a wildly interested topic in an area of financial Mathematics. The pioneer model was introduced by Fischer Black and Myron Scholes which is known as the Black-Scholes model. This model was derived under various assumptions such as liquidity and no transaction costs for which a underlying asset price in stock market might not be satisfied. With this fact, the underlying asset price models were remodeled, in order to determine an option value. This research aims to extend the Black-Scholes model by relaxing the assumption of no transaction costs in illiquid markets. Also, jumps of asset price are considered in this work. To do this, a differential form of asset price with transaction costs and jumps in illiquid markets is introduced and then used to construct the extended option pricing model. Furthermore, a numerical result of a call option price under a new situation is provided.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133126850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Description of Minimal Entropy Hellinger Sigma Martingale Density of Order One, Order q and Order Zero 一阶、q阶和零阶最小熵Hellinger Sigma鞅密度的描述
Journal of Mathematical Finance Pub Date : 2021-06-09 DOI: 10.4236/jmf.2021.113030
W. Mwigilwa, J. Aduda, Ananda O. Kube
{"title":"Description of Minimal Entropy Hellinger Sigma Martingale Density of Order One, Order q and Order Zero","authors":"W. Mwigilwa, J. Aduda, Ananda O. Kube","doi":"10.4236/jmf.2021.113030","DOIUrl":"https://doi.org/10.4236/jmf.2021.113030","url":null,"abstract":"Generally in this paper, we show how the new version of parameter  in Jacod decomposition will change an expression of entropy-Hellinger process of order one, order q and order zero and consequently an equation of minimal entropy Hellinger sigma martingale density for all orders. This is because even the measurable function  which is an important parameter of an equation of minimal martingale density changes. In order to get a required parameter , we introduce the function  during our calculation for all orders. The result is different to order zero because we failed to get an equation of minimal entropy-Hellinger sigma martingale density of order zero.","PeriodicalId":299894,"journal":{"name":"Journal of Mathematical Finance","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125876661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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