Mathematical Finance - Science topic
Mathematical Finance is an imerging subject in which we search the opportunities to find the solution of financial problems with the application of mathematics. After the commencing the two noble prices in economics, its appear a bonanza itself.
Questions related to Mathematical Finance
I am trying to calculate the idiosyncratic volatility for stocks from 2010-2016. The regression window is 30 days, my dependent variable is excess return (return - RF), and my independent variables are F&F's MKTRF (Rm-Rf). SMB, and HML. The R-squared I am receiving is about 10%, but I am expecting 80-90%. Does anybody have any advice, or can share a sample of data so I can verify that my approach is correct?
Mathematics or finance masters or doctoral students can look at decomposing credit rating matrices from market prices as research project.
the project page is given below. Current research questions/ hypotheses are stated on the project page.
I am doing a research on FDI , with six independent variables , my objective is to see long term relationship of IV with DV. FDI is stationary at I(1) , and other five IV are also at I(1) , but one IV is I(0) stationary at level. Can cointegration be applied in such case or some other test is used?
Suppose I have a Yield Curve (assume Semi-Annual Compounding), at term 1M, 3M... 1Y, 2Y... 10Y, 15Y ...30Y (x-axis is maturity / term).
How should I parameterize this yield curve? Any recommendations? Is there any known formula of Yield as a function of Maturity (or any approximations)?
And I have some questions about the property of this yield curve:
First of all, is yield curve (strictly) monotone increase? Does the first order derivative have any meaning?
Secondly, does yield curve has an asymptote, as x -> Inf, y -> constant? Is the y-values bounded by a lower bound when x=0?
Thirdly, what can we say about the second order derivative f''? Does f'' has an upper-bound? Should the f'' be strictly non-negative? Or should we expect f'' change sign? If f'' did change sign, what does it tell us?
Finally, does the Area-Under-Curve has any meaning? (like those ROC curve has a meaningful AUC)
Thank you so much for your help!
All the best,
Kathy Chenying Gao
I'm an unassigned researcher and educator in the mathematics subject. I completed PDF in 2017, under the topic of Mathematical Finance. I seek position currently in the SA institutions of study and learning. I would like to find scholar assigns in the mathematics which to do with the mentioned skills.
During my master's risk-neutral probability measure was the standard in advanced finance theory, with Stanley Pliska's book as the (only) reference.
But nowadays it seems this technique, or, should I say, this paradigm is no longer used, and I wanted an opinion about it.
- is it still though and used in advanced finance courses?
- what could have caused its demise? was it because it was pretty hard to grasp and use?
- what replaces it? if not, is it still relevant and used by a narrow elite?
All relevant inputs, thoughts, advice, opinion is appreciated.
Doing research in the field of finance and investment, I found it difficult to understand various models, such as ARCH; GARCH and many more used in the contemporary research articles.
I am searching such a book(s) which can explain these models and methods in a very simple manner accompanied by example and data set. As I am not an expert in these areas of analysis, I want to learn those model from the very basic and beginners level.
please can anyone help me with possible implications for policy makers, investors and regulators. thank you
Dear all, if one return series is positively skewed or negatively skewed, how one investor can benefit out of this. Whether positively skewed is good or negatively skewed is good for an investor. Kindly justify your answer with an example.
Company ABC trades on two exchanges in India (BSE and NSE). I have total traded volumes and number of trades from each of the Exchanges for company ABC daily.
If i want to calculate overall Volumes per trade, is the below formula the right way to do it?
Volumes per trade = (volumes at BSE + Volumes at NSE) / (Number of trades at BSE + Number of Trades at NSE)
Would be grateful, if researchers can give suggestions on methodology that can be used
I'm currently looking for a scenario tree modeling the return of some stocks or indices. As scenario tree generation is not the focus of my work, but I need some to test my portfolio model, it would be nice, if someone could send me his work. There is no need that the data is up-to-date. Ideally the tree has 3-5 stages and 3-5 stocks/indices.
Thank you very much!
I tests Independent Sample T Test to check the mean difference between pre and post Break period. Each of the period comprises 10 observations, 20 observations and 30 observations. From the descriptive statistics I find mean difference between pre and post break period. But the coefficient of T Test is insignificant. Can you please suggest what to do? average mean differs from period to period but it is not proved from T Test.
I am researching on the impact of a Corporate disclosure on future abnormal returns (in short term).
After reading few whitepapers, i realized one of the accepted way to measure the impact is removing the Normal Return portion from total return, the residual is Abnormal Return.
Theory sounds good to me, but my question is, how can i calculate the Abnormal return for a Stock? ( I am not well versed with understanding mathematical notation in whitepapers)
I have Closing Price, volume, Corporate news and its disclosure date.
Any guidance on that please?
I want to calculate the marginal abatement cost by using directional distance function and then distribute that cost among the player by shapely value
I need help with the syntax.
Also, some of my variables are stationary as I(0) and some as I(1).
Please can you also guide me with how I should couple variables for this test?
Examples of my variables are:
I am interested in seeing if anyone has applied the Mahalanobis Distance measurement to public pension funds and public-private partnerships. Please contact me and thank you in advance for your time and thoughtfulness. I am interested in collaborative research for academic publication. Cheers, Daniel G Bauer, Florida Atlantic University
Assume that stock price of a given stock has its own distribution F(X). The industry (sector) of the stock is distributed G(X). The stock market where the stock is traded is distributed H(X). All three arrays are correlated.
What is the effective method of forecasting stock price X?
I would like someone to discuss the following hypothesis:
The Black-Scholes formula is not a valid optionpricing model.
When backtesting S&P stock options using B&S and the real volatility (= standard deviation) ex post the costs exceed the payoffs by 4 percent, using the VIX (=Volatility of the S&P500) by 26 percent.
The method is: buy fictitious call options day by day over 15 years at the money and at the price of fair value - compare the sum with the cumulated payoffs. The rationale:
The payoffs should somehow match the amounted procurement costs at least.
(For puts it's even worse - 18 / 46 percent overpricing.)
Any comment appreciated.
I want guidance or literature from anybody that can guide me to measurement items (questionnanires items) on measurement of pension/hedge/mutual fund or firm performance. The model I developed requires primary data and not secondary data for firm's of fund's performance. Thanks
I'm working with a database of longitudinal data with an unbalanced panel, data with monthly frequency. I'm using the "plm" package of R to analyze and run the models fixed and random.
NOTE: Data presented serial autocorrelation and heteroscedasticity, and I am correcting with the covariance of Arellano (1987) coming in plm package (R software).
1nd - It is redundant to run FE / RE and GMM as robust proof?
2nd - What is the impact of using the GMM if the results come out different?
3nd - What other suggestions would be to perform a robust test?
The analysis is very important.
This text follows up our recent article „Consentaneous Agent-Based and Stochastic Model of the Financial Markets“ published in open access interdisciplinary journal PLoS ONE . This article is a result of the ongoing research at the Institute of Theoretical Physics and Astronomy of Vilnius University implementing the ideas of econophysics. Though our research is mostly related to the modelling of return statistics in financial markets implementing ideas from statistical physics, the concepts behind this work and conclusions are related to the much more extensive interdisciplinary understanding of the social and physical sciences. The desire to extend conventional boundaries and achieve more understanding between researchers of physical and social sciences is a strong motivation for us to deal with econophysics.
The price is a key concept in economics as it enables general quantitative description in economy and theoretical economics. Market price plays a central role as it is assumed to precisely reflect the real exchange values. Therefore a belief that market price is the most objective one lies in the background of mainstream economics, based on the rational expectation and efficient market concepts. These concepts lie in the background of huge financial industry (stock exchange, other securities, derivatives, currency exchange, etc.), making a vast impact on the overall health of the global economy. However, periodically emerging local and global economic crises give rise to the alternative views opposing mainstream concepts of economics.
Econophysics much more often than econometrics criticizes mainstream theory of economics. The observed fluctuations of the market price are larger than it should be accordingto the equilibrium view of the efficient market theory. Alternative views arise even in circles of the economists as behavioral finance and economics receive much more attention. Nobel Prize winner of 2013 professor of Yale University Robert Shiller is an outstanding representative of the behavioral alternative. The decision to award a Nobel price of economics to the most outstanding advocate of efficient market theory prof. E.F. Fama and representative of the alternative view serves as a proof that economics with its concepts is in the crossroad. From our point of view behavioral finance criticism towards econometrics and mathematical finance serves as an obstacle to positively evaluate contribution of econophysics. Nevertheless, the understanding that unstable financial and economic processes have to be considered on the bases of statistical physics is taking place .
From the point of view of representatives of behavioral economics and finance the behavior of agents acting in the market is much more like the behavior of realistic personalities with inherent intellectual and psychological bugs than like the behavior of extraordinarily capable individuals with ability to evaluate and account for all of the surrounding circumstances and information. For example, they pay much more attention to the tendency of imitation than to the individual capabilities of agents to make independent decisions. In our work we aim to demonstrate that it is possible to build a consentaneous model of financial markets, where choice of agents between three different trading strategies is based only on the transition probabilities between these choices. From the mathematical point of view these transition probabilities between two of the choices are the same as proposed by Alan Kirman to describe the herding interactions of agents . This way we propose an adaption of the herding model to the financial markets, which can be solved by using method from statistical physics to shape macroscopic description of financial markets by the set of two stochastic differential equations. The main objective of this model is to reproduce general statistical properties of price movements observed in the real stock exchanges from Vilnius to New York.
The detailed simulation of market return statistics, reproducing power law probability density functions, power spectral densities and autocorrelations of absolute return as well as reproducing very details of these statistics, shows that herding of market participants is the most general property dominating their very heterogeneous and less meaningful rationality. We think that rationality is so heterogeneous and so ambiguous, that in the final macroscopic view of the whole agent society only the most general statistically meaningful property – herding –is observed. Rationality as very diverse can be neglected in a same way that physicists neglect trajectories of separate particles in thermodynamic consideration.
Our proposed structure of agent groups is based on a conventional choice considering three opportunities : 1) intrinsic (fundamental) value oriented market traders – fundamentalists, which buy stocks, when market price is lower than fundamental value and sell when market price is higher than fundamental value; 2) speculative traders, who forecast price movement and believe that market price will go up – optimists and 3) speculative traders, who believe that market price will go down, pessimists. Permanent dynamical change of traders’ choices impacts the demand and supply ratio and so forms a long term dynamics of market price. In order to make such agent population dynamics comparable with real financial markets we had to combine it with permanent exogenous impact – external information flow or order flow noise. These are all necessary assumptions to reproduce main general properties of market price dynamics, observed for all markets and all stocks. Though the model proposed has few independent parameters, the same choice of parameter values is appropriate for all markets and all stocks is the main it‘s advantage.
Proposed model provides evidence that price dynamics can be reproduced by the memory-less Markov transitions of traders between possible choices of behavior. From our point of view the proposed model suggests new interpretation of market price, which may exhibit very large deviations from fundamental value. In this new interpretation market price highlights herding based drifts of agent-based societies, neglecting intrinsic (fundamental) understanding of value and surrendering to the imitational waves of collective wandering. Such wandering can be supported by the public tales about unexpected economic opportunities, emerging in the context of new financial, technological, social and political tendencies. As the proposed model is based on the agent opinion dynamics, we ask a question – whether the market price is economic or sociological category? Answering the question we would prefer to assume that fundamental value is more likely to be economic concept and market price is more likely to be sociological concept. To make practical distinction between different market price constituents might be a hard task, nevertheless, the new market price interpretation can be helpful looking for the opportunities to diminish observed huge market price movements, responsible for the local or global economic crises.
From our point of view, the herding as a statistically dominating behavioral property of agents can be used for the stabilization of undesirable market price fluctuations. It appears that only a small number of agents trading exceptionally based only on fundamental values is required to make a considerable influence on other market participants leading to the much more stable movement of the market price . Certainly, it is obvious that for the implementation of such mechanism a new and more comprehensive understanding of fundamental price is needed. It should help to define a new reference point in economics instead of the currently used market price.
1. Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi:10.1371/journal.pone.0102201
2. Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Reviews of Modern Physics 81: 591–646. doi: 10.1103/revmodphys.81.591
3. Kirman AP (1993) Ants, rationality and recruitment. Quarterly Journal of Economics 108: 137–156. doi: 10.2307/2118498
4. Lux T, Westerhoff F (2009) Economic crysis. Nature Physics 5: 2–3. doi: 10.1038/nphys1163
5. Kononovicius A, Gontis V (2014) Control of the socio-economic systems using herding interactions. Physica A 405: 80–84. doi: 10.1016/j.physa.2014.03.003
We use the Wiener process for modeling stock prices. What are the differences between this model and time series models when the observations are stock prices? Let time series model be AR model, MA model, or ARIMA model.
I am using a barrier option, in particular a Down-And-Out call option, to simulate default probability of a firm where the asset values follow a geometric brownian motion. For reasonable values of volatility, drift, barrier and strike price, the code returns me default probability larger than one. The formula for PD is that of Black,Cox (1976) but with constant barrier (Reisz, Perlich 2007).