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Sample E4718 Midterm Examination Questions
2015
Formula sheet is at end.
_
Write your name clearly:
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Please sign the honor pledge:
I pledge that I have neither given nor received unauthorized aid during this examination.
Students Name:_
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Page 1 of 8
Sample E4718 Midterm Examination Questions
2015
Formula sheet is at end.
_
Write your name clearly:
_
Please sign the honor pledge:
I pledge that I have neither given nor received unauthorized aid during this examination.
Students Name:_
Signa

Option data and modeling BSM implied
volatility
Matthias R. Fengler
University of St. Gallen
matthias.fengler@unisg.ch
Forthcoming: Handbook of Computational Finance, Springer-Verlag
Forthcoming: Handbook of Computational Finance, Springer-Verlag
1 Introd

14
Laughter In The
Dark
I rst heard about the smile in December 1990 from Dave Rogers, our
head options trader in Tokyo.
I had begun traveling to Japan regularly to bring our traders the latest
releases of our risk management tools and to learn what new m

LECTURE 17
Stochastic Volatility Models:
A Variety of Approaches
Page 1 of 30
Looking Ahead
_
Stochastic Volatility Models
_
Jump Diffusion Models
_
Guest Speakers
Michael Kamal - April 15
Jackie Rosner - April 20
If you have questions come to my office h

LECTURE 16
Wrap-Up on Local Volatility Models
Relation between Skew Statics and Dynamics.
Stochastic Volatility Models
Page 1 of 48
Looking Ahead
Values and Hedge Ratios of Exotics
Wrap up on Local Volatility Models
_
Hedging Rules and their Efficacy/ Sta

E4718: Derman: Homework 8: March 30, 2015
Page 1 of 2
Homework 8: March 30, 2015
Problem 1.
[20]
Assume we look only at options of one-year expiration with any strike K. Suppose that their observed implied
volatility at some instant t is written as (S,K)

LECTURE 15
LOCAL VOLATILITY MODELS:
DUPIRE EQUATION & RULES OF THUMB
HEDGE RATIOS
EXOTIC OPTIONS
Page 1 of 37
Looking Ahead
Dupire Equation and Justification of Rules of Thumb
Hedge Ratios of Vanillas
Values of Exotics
_
Hedging Rules
_
Stochastic Volatil

LECTURE 10
SMILE MODELS
EFFECTS OF THE SMILE
STATIC HEDGING AND IMPLIED DISTRIBUTIONS
Page 1 of 38
Some Behavioral Reasons for an Implied Volatility Skew
Think of options trading as the trading of volatility as an asset, and also the buying of protection.

E4718: Derman: Homework 4: February 23, 2015
Page 1 of 3
Homework 4: February 23, 2015
Due Mar 2, 2015
Problem 1. Hedging Simulation When Implied Not Equal To Realized
[30]
Consider a call with stock price 100, strike 100, time to expiration = 1/12 of a y

LECTURE 9
BACK TO THE SMILE
Page 1 of 39
Page 2 of 39
Implied Volatility as a Function of Strike/Spot for Different Expirations. (Crash-o-phobia: A
Domestic Fear Or A Worldwide Concern? Foresi & Wu JOD Winter 05
The quoting convention is the Black-Scholes

LECTURE 8
P&L OF TRADING STRATEGIES
HEDGING DISCRETELY
TRANSACTIONS COSTS
_
BACK TO THE SMILE
Page 1 of 45
Hedging Errors from Discrete Hedging
We cannot hedge continuously:
A Simulation Approach
You cannot hedge continuously, and therefore it is importan

LECTURE 7
P&L OF TRADING STRATEGIES
THE EFFECTS OF:
HEDGING CONTINUOUSLY
HEDGING DISCRETELY
TRANSACTIONS COSTS
Page 1 of 37
The P&L of Hedged Trading Strategies
Consider an initial position at time t0 in an option C that is -hedged with borrowed money whi

E4718: Derman: Homework 3: February 11, 2015 Due Wed February 18th.
Page 1 of 3
Homework 3: February 11, 2015
Due Wed February 18th.
Total:
[100]
Problem 1: Expected P&L when Hedging at Implied Volatility
[20 points]
We showed that the P&L when hedging at

LECTURE 6
1. VARIANCE SWAPS REPLICATION CONT.
2. P&L OF TRADING STRATEGIES
.
Page 1 of 25
Valuing Volatility Swaps
Volatility is the square root of variance, a derivative. You can replicate it with the continuous
dynamic trading of portfolios of variance

LECTURE 5
VARIANCE SWAPS CONTINUED
Page 1 of 33
DYNAMIC REPLICATION
Page 2 of 33
Recap: What Should You Pay for Convexity?
Suppose we think we know the future volatility of the stock,
Binomially, this corresponds to S = S t with S
2
2 2
= S t .
2
2 2
1

VolatilityDerivativesinPractice:
ActivityandImpact
ScottMixon
EsenOnur
Jamuary2015
Abstract:
WeuseuniqueregulatorydatatoexamineopenpositionsandactivityinbothlistedandOTC
volatility derivatives. Gross vega notional outstanding for index variance swaps is o

LECTURE 4
REPLICATION:
VARIANCE SWAPS, MOSTLY
Page 1 of 35
Recap: Static Replications of Various Kinds
If you can create a static replicating portfolio for your payoff, you have very little model risk.
European put from a call: Put-Call Parity
call
call S

E4718: Derman: Homework 2
Page 1 of 6
Homework 2
Due Feb 11, 2015.
[100 points]
Problem 1. State securities
[5 points]
stock
SU
1 + r
u
S
SD
risk-free
bond
0
decompose
0
B(1 + r
d
B
1 + r
B(1 + r
Shown above are simple binomial trees for a stock and a ris

LECTURE 3
PRINCIPLES OF VALUATION CONTINUED
Page 1 of 37
The One Commandment of Quantitative Finance
If you want to know the value of a security, use the price of another security thats as similar to it as
possible.
The law of one price, or the principle

E4718: Derman: Homework 1
Page 1 of 5
Homework 1
Due Monday Feb 2, 2015 at beginning of class
Total 100 points
_
Problem 1: The Smile
[20 points]
The graph below shows put prices as a function of strike K for one-year put options on a stock
whose value is

LECTURE 2
PRINCIPLES OF VALUATION
Page 1 of 37
Recap: The Smile
Before 1987
V olatility
20
18
16
14
0.95
0.975
1
1.025
1.05
Strike/Index
After 1987.
V olatility
20
18
16
14
0.95
0.975
1
1.025
1.05
Strike/Index
The volatility of a stock itself cannot de

E4718: Derman: Homework 1
Page 1 of 5
Homework 1
Due Monday Feb 2, 2015 at beginning of class
Total 100 points
_
Problem 1: The Smile
[20 points]
The graph below shows put prices as a function of strike K for one-year put options on a stock
whose value is

Lecture 1: Principles of Valuation; Introduction to the Smile
The volatility surface according to Black-Scholes
According to classic theory, the Black-Scholes implied volatility of an option should be
independent of its strike and expiration. Plotted as a

E4718: Derman: Homework 1
Page 1 of 2
Homework 1
Due Monday Feb 2, 2015 at beginning of class
Total 100 points
_
Problem 1: The Smile
[20 points]
The graph below shows put prices as a function of strike K for one-year put options on a stock
whose value is

E4718: Derman: Homework 10 (April 22 2015: Due Wed April 29)
Page 1 of 5
Homework 10 (April 22 2015: Due Wed April 29)
Problem 1.
[10 points]
n
t t
For a pure jump process for which P n t = -e
is the probability of n jumps occurring in
n!
time t, show th

E4718: Derman: Homework 9 (April 6 2015)
Page 1 of 5
Homework 9 (April 6 2015)
Problem 1.
(20 points)
Consider the stochastic volatility process
d = bdW
dS = SdZ
= 0
where is the correlation between the stock price innovations and the volatility innovati

E4718: Derman: Homework 7: Mar 23, 2015 Due Monday Mar 30th
Page 1 of 7
Homework 7: Mar 23, 2015
Due Monday Mar 30th
Problem 1. From implied to local volatility.
[40 points]
We proved in class that you can find the local volatility from calendar and butte

E4718: Derman: Homework 6: Mar 2 2015 Due Mon Mar 23rd after midterm break
Page 1 of 13
Homework 6: Mar 2 2015
Due Mon Mar 23rd after midterm break
Problem 1:
[30 points]
Write a program to calculate the value of call with S = 100, K = 100, 0.05 years to

E4718: Derman: Homework 8: March 30, 2015
Page 1 of 5
Homework 8: March 30, 2015
Problem 1.
[20]
Assume we look only at options of one-year expiration with any strike K. Suppose that their observed implied
volatility at some instant t is written as (S,K)