Vanilla times · 2019. 1. 14. · Indeed, the global financial markets have been swinging and dancing to the tune of the song “Volare” recently. “Volare” in Italian means

Nassim Taleb, the veteran options trader and the celebrated

author of the book Black Swan was once quite annoyed when

someone on his trading floor suddenly started singing “Volare,

Volare”. It seems most of the traders on the floor of New York

stock exchange have been singing, albeit in a rather hoarse

voice, the same 1950s Italian song for the past one week.

Indeed, the global financial markets have been swinging and

dancing to the tune of the song “Volare” recently.

“Volare” in Italian means “to fly”. It comes from the Latin

word “Volatilis”. Financial markets are indeed flying; or, in the

financial lexicon, markets are crashing and volatility is on the

rise. The VIX index, which is an index of the implied volatility

of the S&P500 stock index was up more than 20% and hit 41.9

at one point in New York trading this week and some traders

cried “Armageddon”. One index trader in Hong Kong

bemoaned to me over the phone last Wednesday that “It’s the

tails again!” And as the Dollar-Swiss Franc volatility hit 23

(read 23%) this week a terrified FX trader in Tokyo shouted

out to his colleague across the floor, “Are we going to see 35

vols in USD/CHF this time?”

Volatility is all that matters in the financial markets these days.

Everybody, from the floor traders to the interbank dealers to

the G7 Finance ministers and financial journalists, talks about

volatility. It has come to dominate our lives.

But, what is volatility? It is both a profound and a silly

question. We all know what “volatility” is and yet all of us will

have difficulty in explaining the concept articulately and in a

concise manner. This is because volatility can mean different

things to different people and in different context. Is it a fear gauge? Is it a statistical quantity? Is

it a parameter in option pricing model? Is it an asset? In fact, it is all of these things and perhaps

much more. Volatility is the most profound, and yet perhaps the most elusive concept both in the

real financial markets and in the theory of quantitative finance. As a veteran options trader once

told me, “Beware of volatility, it has tails and it can fly”.

Rahul Bhattacharya

Inside this Issue August 12, 2011

Volume I, Issue 1

Volatility has tails and it can fly

Understanding Historical Volatility

Product idea for the Equity Market

Derivatives Trading Terminology

The Silent Mafioso – I: The man

who once ruled Deutsche Bank

Book Review: Options on Foreign

Exchange, 3rd

Edition by David

deRosa.

Vanilla times

2

Broadly speaking, there are two definitions, or rather concepts, of

volatility in the financial markets and within the theory of

quantitative finance: historical volatility and implied volatility.

Historical volatility is a statistical concept and it simply means

the standard deviation. The accepted norm in the market – and the

way volatility is understood and quoted in most asset markets – is

that historical volatility is the standard deviation of the asset

returns (and not the asset price). For example, say, over the last

ten days an asset has taken the following (historical) price path:

100, 101, 101.5, 102, 102.5, 104, 105.5, 105, 104.8, 106.

Here’s the algorithm to calculate the historical volatility from the

above time series of prices. First, calculate the log returns of the

above prices by using the formula: log returns is equal to today’s

asset price divided by yesterday’s asset price; then, then calculate

the mean of the new time series of log returns; the mean is

generally denoted by the Greek letter “mu” and is simply the

arithmetic average of the series; finally, calculate the historical

volatility using the statistical formula for standard deviation. If

we implement the above algorithm on an Excel™ spreadsheet and

do all calculations by ourselves then the value of historical

volatility comes out to 0.6378%. If we use Excel’s library

function =STDEV(.) then the value comes to 0.677%

This would be known as the daily volatility, because the asset

price movement is depicted over days. Daily history will produce

daily volatility; weekly history will produce weekly volatility and

so on. Normally, historical volatility, or any other measure of

volatility, is always annualized. To annualize the above figure we

need to multiply it by square root of 252. Thus the annualized

volatility of the above asset price would be 10.13%.

Team Latte

Historical Volatility

Historical Volatility is the

standard deviation of the asset

returns, defined as natural log of

this period’s price divided by

previous period’s price.

Historical Volatility is analogous

to the concept of realized

volatility or actual volatility.

Get access to high value added quantitative finance

content via www.risklatte.com. Mathematical finance, quantitative models of

derivatives valuation, portfolio analysis, financial risk management and

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3

Given the significantly high volatility in the equity markets

one of the equity linked products that one can consider for

investment purposes is the “Single Asset Best of Option”.

This is typically an institutional product, but can be very

easily tailored to suit small investors, such as high net worth

individuals.

This option pays the best of (or the maximum of) the equity

return and a certain fixed percentage. For example, the

product can be structured to pay at maturity, say, one year,

50% of the return of S&P500 index and 4%. In other words,

the product pays either 4% fixed return on the notional capital

or 50% of the return of S&P500 after one year, whichever is

greater. Say, S&P500 index generates a return of 10% after

one year. Then 50% of 10% return is 5%, which is greater

than 4%. Thus, the investor would get 5% on his invested

capital. However, say, if S&P500 after one year generates a

returnof -3% (negative 3%), then 50% of that return would be

-1.5% (negative 1.5%) which is less than 4% and hence the

investor will get 4% return on his invested capital.

This option can be decomposed into a long coupon paying

bond with a coupon of 4% and a leveraged call option. The

strike price of the call option would be 1.08 times the current

(today’s) value of the S&P500 index.

Team Latte

Tails: “Tails” represent the implied volatility of the out of

money (OTM) options with respect to the at the money

(ATM) options in a Black-Scholes world. Looked at another

way, the “tails” represent the fourth moment of a Normal

distribution.

Fat Tails: “Fat Tails” means extremely large Kurtosis, or the

fourth moment, of a Gaussian (Normal) probability

distribution. One would need a wider graph to represent a fat

tailed Normal distribution because the standard deviation, the

second moment of the distribution, blows up and makes tail of

the distribution on both sides of the mean move upwards from

Product Idea Single Asset, Best of Option

The payoff of the option is given by:

Algebraically decomposing the above

product gives:

The above can be further decomposed

as:

This clearly shows that the payoff can

decomposed into a coupon paying

bond (with a coupon of 4%) and a

call option with a strike price of 1.08

times the current price of the asset.

4

the X axis, where returns are plotted. Many statisticians and

mathematicians talk of infinite variance to denote fat tails.

However, experienced option traders consider “fat tails” as

simply the result of rapidly changing volatility captured by

volatility of volatility (vvol). Even if the volatility of an asset is

low, a high volatility of this low volatility can cause fat tails.

VVol: “VVol” stands for volatility of volatility and option

traders believe that the reason the out of the money (OTM)

options have higher implied volatility than the at the money

(ATM) options is because of the existence of volatility of

volatility. In a Black-Scholes world, where options are priced

using a Black-Scholes model, volatility of an asset is assumed to

be constant. However, in the real world, the volatility of assets

such as stocks, FX, bonds, interest rates, etc. display variability.

One way to capture this variability statistically is by estimating

the dispersion or the standard deviation of the volatility, which

in other words, is thought of as volatility of volatility.

Quoted Volatility: In the FX options market, traders quote

option prices in terms of volatility (percentage volatility or

volatility points) rather than in dollars and cents. A 25 delta,

USD call / JPY put option quote could be 15.50 / 16.50, which

would denote a bid volatility of 15.50% and an ask volatility of

16.50%.

Team Latte

Trading Terminology

Tails: Implied volatility of Out of

the money (OTM) options

Fat Tails: Large Kurtosis, or the

fourth moment of a Gaussian

distribution

VVol: Volatility of Volatility, which

is one way to capture variability

of volatility.

Quoted Volatility: Method of

quoting option prices in the FX

options market.

A comprehensive

reference book of formulas, math equations,

algorithms and short explanation for CFE

students and quantitative finance professionals.

5

It feels strange to talk about a

once famous banker ten years

after his death, for ten years is

too short a period for putting

things in “historical perspective”

and too long for any meaningful

analysis in the global financial

markets.

He is the founder and architect of

modern day Deutsche Bank who

died at a very young age in a

tragic accident in December

2000. He was perhaps one of the

most colourful and handsome investment bankers in the City of

London. He was an expert on financial derivatives and a pioneer

in the field of derivatives banking He had a mistress and jet

setting lifestyle. But above all, he was a ruthless manager whose

strategies sometimes were perhaps more in line with that of a

mafia don than a Dartmouth MBA.

His name is Edson Mitchell and he was the head of global

markets at Deutsche Bank and a member of the Bank’s Board

until his tragic death in a plane crash on December 22, 2000;

and his colleagues at Merrill Lynch, the bank where he worked

before joining Deutsche Bank, used to call him The Silent

Mafioso.

I discovered him on a recent trip to London. Over a sumptuous

dinner with an old friend at the famous restaurant La Portes des

Indes at Marble Arch, discussion turned towards financial

derivatives, Bankers Trust, Deutsche Morgan Grenfell, Deutsche

Bank etc., etc. One thing led to the other, as it usually happens at

such dinner table discussions, and along the way my friend

casually mentioned the name of Edson Mitchell. He knew this

man many years ago and had apparently once been interviewed

by him. A half an hour interview with Mitchell had left an

indelible mark on my friend. He thought he had met the

fictitious character, Don Coreleone, from the movie Godfather,

only this real life replica was infinitely more handsome, far

more polite and suave, had an Ivy League MBA and could talk

about financial derivatives and golf in the same dispassionate

Edison Mitchell

The Man who once Ruled

Deutsche Bank

Edson Mitchell can be considered

the founder and the architect of

modern day Deutsche Bank.

He was one of the heads of global

markets at Deutsche Bank until his

tragic death in a plane crash in

December 2000. He had a

multimillion dollar pay package

and a ravishing French mistress.

He was a young and handsome

investment banker who epitomized

the dictum that cheque book can

make any feat possible.

6

tone. Our lives are shaped by characters from novels and

movies; his was shaped by Edson Mitchell.

A half an hour job interview and the impression of a lifetime.

My friend never saw him again, though he ran into him a few

times, in Christmas parties, airports, and financial news

articles. Edson Mitchell not only single handedly transformed

Deutsche Bank into a top tier investment bank from a sleepy

German lender of no particular repute, he also changed the

entire investment banking landscape of the City of London. He

inspired loyalty amongst his subordinates and brought with

him a large army of investment bankers when he defected

from Merrill Lynch to Deutsche Bank. Many of them revered

him and some idolized him. His peers, including Josef

Ackerman, the head of investment banking at Deutsche Bank

at that time, were in awe of him. He was a deity at the altar of

money and power, who epitomized the notion that the cheque

book can make any feat possible. At the turn of the

millennium, he was the future of Deutsche Bank

And, he was in love with Estelle, a thirty something, ravishing

French beauty whom he met in London and who became his

mistress. Today, however, he is the tragic hero, whom no one

wants to remember; least of all, his ex-colleagues and the

senior management team of Deutsche Bank.

After dinner, I realized that someone needs to tell this story

not because Edson Mitchell’s story is a story about Deutsche

Bank, one of the most successful investment banks in the

world today. Someone needs to tell this story because this is a

story about human greed, power, love and lust. It is a story

about a man’s desire to become God.

The story continues in the next issue………….

Rahul Bhattacharya

Who was Edson Mitchell?

He was a pioneer in the financial

derivatives business, especially the

dollar interest rate swaps market.

Before joining Deutsche Bank,

Mitchell worked at Merrill Lynch in

the U.S. for 15 years, turning Merrill

into a global derivatives

powerhouse.

The name of Mitchell’s mistress was

Estelle and it is rumored that he was

living with her in London.

In 1995 Deutsche Bank recruited him

on a two year contract with a pay

package of GBP4.0 million per year.

7

Options on Foreign Exchange, 3rd

Edition by David deRosa: ***

This week’s book is Options on Foreign Exchange, 3rd

Edition by

David deRosa. It is an excellent book and we highly recommend it to

all those who want to get good understanding of FX exotic options

and how they are priced and structured. It is also a book, which has

one whole chapter on volatility where the author clearly and

concisely talks about various concepts surrounding volatility,

especially FX volatility, and some of that explanation is very intuitive

and puts things into historical context. In fact, that is the case,

throughout the book, where many of the advanced mathematical and

quantitative concepts are explained intuitively which enhances a

reader’s understanding of these concepts. In short, this book is a must

have for all those in the business of financial derivatives, especially,

those in the FX options and FX structured products markets. This

book also has a great chapter on Barrier and Binary Currency Option and what is really cool are

the ways the formulas for “One Touch”, “Double No Touch”, “Double Barrier” Binary and other

“out” options are presented and explained. For example, Hui (1996) formula for double barrier

binary option is explained in a lucid manner and so is the formula of Reiner, Rubinstein (1991)

and Wystup (2007) for One Touch binary option. The Chapter on American Exercise Currency

Options is also quite illuminating and easy to follow. Overall, we would rate it Triple Star out of

Five Stars.

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Notes: i. Edson Mitchell’s photographs is courtesy Google images

ii. The cover image of the book Options on Foreign Exchange, 3rd Edition is courtesy of

Google images.

Excel™/VBA based, 100% applications course covering

quantitative modeling for derivatives valuation and risk

analysis, financial risk management, portfolio analysis &

asset allocation models, algorithmic & derivatives trading

and financial mathematics. Write to [email protected]

for more information on CFE.