2016 OPEN ACCESS, PEER REVIEWED PUBLISHED PhD RESEARCH FINDINGS ON FAT TAILED BLACK S
INTRODUCTION
The Economic and Financial Crisis of the late 2007 – 2008 has brought serious debates among the leading Practitioners and Academics about the incompleteness of the Derivatives Pricing Models. One of the most criticized aspects was the fundamental NORMALITY assumption in almost all of the Derivatives Pricing Models. This assumption of course makes the models to either underestimate or overestimate the derivatives prices especially at the times of Economic Recoveries or Recessions.
There were so many attempts by both the markets Practitioners and Academics to improve on the existing derivatives models more especially at the stress periods, unfortunately, up to this date of writing this paper, the models still assumed Normality. Though, Basel II and III extensively recommended the idea of Stress Testing which also extremely important concept to address Global Economic and Financial Crises via Derivatives Pricing. The major problem of Stress Testing Methodologies, mostly it deal with IMPLICIT ASSUMPTION in stressing the fundamental macroeconomic indicators, Scenarios, Financial Ratios, PDs, EADs, LGDs and so on.
Recall that Stress testing has been adopted as a generic term describing various techniques used by financial firms to gauge their potential vulnerability to exceptional but plausible events. The most common of these techniques involve the determination of the impact on the portfolio of a firm or business unit of a move in a particular market risk factor (a simple sensitivity test) or of a simultaneous move in a number of risk factors, reflecting an event which the firm’s risk managers believe may occur in the foreseeable future (scenario analysis). The scenarios are developed either by drawing on a significant market event experienced in the past (historical scenarios) or by thinking through the consequences of a plausible market event which has not yet happened (hypothetical scenarios). Other techniques used by some firms to capture their exposure to extreme market events include a maximum loss approach, in which risk managers estimate the combination of market moves that would be most damaging to a portfolio, and extreme value theory, which is the statistical theory concerned with the behavior of the “tails” of a distribution of market returns. Thanks to the Idea of Stress Testing and by extension Extreme Value Theory. Nassim N Taleb (2011), emphases in most of his papers, the effects of Low – Probability, High – impact Events and incompleteness of prediction models to accurately capture Financial and Economic crises or chaotic situations in the other field of knowledge.
Also, he is the one of the leading actors in the financial markets to propagate the inclusion of “fat – tail effects” in the modeling of credit derivatives models. This is of course gave birth to his popular “Black Swan Idea or Theory”. He seriously criticizes the assumption of Normality in the most of the currently useful Financial and Economic models and in the same vein, the Black Box assumptions of probability distributions in the modeling process of financial models.
However, the main aim of this research paper is to consider the Existing Derivatives Pricing Models and apply JAMEEL’S Contractional and Expansional Stress Methodology such that they can capture Low – probability, High impacts events popularly known as BLACK SWAN events so as to predict future Global Economic and Financial Crises given accurate, valid and reasonable models’ independent variables.
MATERIAL AND METHODS
The methodology adopted in this research work is to consider the traditional Black – Scholes – Merton (1973) and its Greeks, Garman - Kohlhagen (1983) Foreign Exchange Options, Black (1976) for Caps, Floors and Swaptions Pricing Models, and to develop new advanced stressed Derivatives Pricing models that can capture LOW - PROBABILITY, HIGH – IMPACT events popularly known as BLACK SWAN events by incorporating crises components into them.
The IDEA was basically on how to CONTRACTIONALLY and EXPANSIONALLY stress BLACK – SCHOLES – MERTON Options Pricing Model using the respectively Geometric Volatility and Geometric Return of the Arithmetic Means of the Underlying Asset Return and Returns of the explained (Independent) variables as well as the Best Fitted Fat – Tailed Effects Probability Distribution of the Underlying Asset Return.
We shall going to discuss “ONE DIMENSIONAL FAT – TAILED MODIFIED BLACK – SCHOLES FORMULAS FOR STRESS PERIODS” in the FORUM SUBMISSION (2) shortly.
Please, do not hesitate to contact me regarding the Post.
You can also contact me via:
+2348038679094
[email protected]
a), 1.45130(2016/03/18) to 1.44578(2016/03/30) connect highs with trend line, (b), 1.40517(2016/03/16) - 1.40561(2016/03/24) and unfolding low 1.41697 connect lows with trend line. Shioyanama]hi,commitement or ?.
