M.J. Neeley School of Business
Finance 70520
Risk Management & Financial Engineering
Spring 2002
5:30 - 6:50 pm MW
DRH 234
s.mann@tcu.edu
Associate Professor Steven C. Mann
Office: Tandy Hall 386
Tel: 817 257-7569
Office Hours: MW 3:00-4:00
http://sbufaculty.tcu.edu/mann
I. Course Description
In this course we examine the quantification of risk and the use of derivatives in
managing risk exposures. We also examine advanced topics in the creation, valuation, and
hedging of financial contracts.
II. Course Materials
Required Texts (2):
Derivative Securities, 2nd Edition, by R. Jarrow and S. Turnbull, 2000, SouthWestern.
Paul Wilmott Introduces Quantitative Finance, P. Wilmott, 2001, Wiley.
III. Course Policies
Be prepared for class! Read the assigned material and work the problems prior to the
lecture whenever possible.
Your grade will be determined as follows:
Quizzes (2)
Class participation
Final (Wed., March 6)
30%
10%
60%
300 points
100 points
600 points
Class participation will be used primarily to decide borderline grades, but may have substantial
impact.
Exams will contain both problems to solve and essay questions. The tests may cover the
reading assignments, but material covered in the lectures will be the primary focus. Students who
wish to appeal their score on an exam should submit to me in writing a brief discussion of why
more points are warranted. Any such appeal should be in my hands within one week of the day
when the exam is returned. Furthermore, I reserve the right to regrade all questions.
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Tentative schedule; reading assignments & suggested problems (J&T) :
Finance 70520 - Spring 2002.
March 18
March 20
Chapter
Black-Scholes-Merton
Eight
Topics: Continuous-time representations of price movements; Black-Scholes European;
Model properties; hedging; historic and implied volatility; greeks; strategies.
Problems in Chapter 8 and beyond will often require software. Software by Jarrow and Turnbull
is provided with the text. Mann software will usually be provided via Mann's web site.
Questions:
8.1 Relationships among call "moneyness", maturity, and delta
8.2 Relationships among put "moneyness", maturity, and delta
8.3 delta sensitivity to maturity and volatility.
8.4 collar construction.
8.5 find implied volatilities.
problems 8.6 through 8.12 require analysis of the greeks for the position:
8.6 vertical bear spread
8.7 vertical bull spread
8.8 Butterfly
8.9 Strangle
8.10 time spread
8.11 Condor
8.12 Seagull
Wilmott:
March 25
Chapter 8: (all);
Chapter 9 (optional: math lover’s delight)
Chapter 10: (all)
Chapter
Extensions to the Black-Scholes model
Nine:
Topics: Models for known dividends: Psuedo-American model;
Roll model; constant dividend yield models; options on forwards.
Questions:
9.1
9.3
9.4
9.5
9.6
9.8
9.9
9.10
European options with dividends
implied volatility with and without dividends
Psuedo-American call valuation
options on futures contracts
hedging a futures option with either spot or futures.
hedge futures option with nearby futures
implied volatility of futures option
American vs. European futures options.
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March 27 –
April 3
Chapter
Option hedging and risks
Ten
Topics: Problems with Delta hedging; Delta-gamma hedging;
Delta-gamma-vega hedging.
Questions:
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
hedge outcomes
hedge outcomes and stochastic volatility
multiple sources of price changes (total from partials)
delta hedge short call with puts
delta hedge short call with a different call
create delta-vega neutral hedge
create delta-gamma neutral hedge
create delta-theta neutral hedge
delta-gamma hedge a short call
delta hedge a short straddle
Value at Risk
April 8
Wilmott: Chapter 20 (all)
Chapter 21-23 (optional);
Chapter 24 (all)
April 10
Chapter
Eleven
Foreign Currency (FX)
Topics: FX derivatives: options, forwards, futures; payoff definitions and quotes;
Options on FX futures; building exchange rate lattices; hedging.
Questions:
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
(optional: derive FX call lower bound)
derive FX option put-call parity.
FX collar construction.
construct exchange rate lattice; price option.
FX option relationships: maturity and "moneyness"
find FX option implied volatility.
implied volatility patterns (smiles).
construct synthetic currency put.
build an Index Currency option Note (ICON)
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April 15
Chapter
Index and Commodity Derivatives.
Twelve
Topics: Equity Index derivatives; Index futures; program trading; spreads;
Index options and options on futures; Commodity futures and futures options;
Questions:
Wilmott:
April 17
Chapter
Thirteen
Topics:
Questions:
Wilmott:
April 22
April 24
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
Equity Index time spreads.
Making sector bets with futures.
implied volatility of index options.
implied volatility and index dividend yields.
hedging index options with index futures.
implied volatility patterns.
hedge option position with futures.
gold options.
commodity linked bond construction.
Chapter 19: (optional)
Interest rate contracts.
Zero-coupon bonds, coupon bonds; yield curves and yield curve construction;
interest rate risk measures and limitations; interest rate futures contracts.
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
Price value of basis point for T-bill.
simple interest vs. continuous compounding.
discount rates and simple interest.
discrete vs. continuous yield-to-maturity.
Yield-to-maturity.
clean and dirty prices.
calculate Treasury Bond conversion factors.
determine cheapest-to-deliver bond.
use term structure to price T-note.
build spot and forward yield curves.
Chapter 14 (all)
Chapter
Swaps
Fourteen
Topics: Interest rate swaps; pricing and valuation; varieties; FX swaps;
Commodity swaps; Equity swaps
Questions:
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
Wilmott:
Use term structure to price fixed-for-floating swap.
value an existing swap.
value an existing amortizing swap.
price swap by choosing spread rather than fixed rate.
build a swap to meet client needs.
price a currency swap.
commodity swap usage.
price a commodity swap.
price a forward commodity swap.
application of equity swap.
Chapter 15 (all)
4
(optional)
Chapter
Using term structure models.
Fifteen
Topics: Interest rate evolution; term structure models; lattice construction;
Options on T-bills; T-Bill futures.
Questions:
(optional)
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
Use Heath-Jarrow-Morton model to evaluate interest rate risk of Bill.
use HJM to create delta neutral hedge of a T-bill.
Hedge T-notes with T-bills.
Gamma hedging
using HJM to hedge notes with bills.
Redington's duration.
use a bond to hedge a bond.
use bill futures to hedge bond.
forward vs. futures prices.
Chapter
Term structure models and interest rate options.
Seventeen
Topics: Options on bills; Caps, Floors, Caplets, Floorlets; The Black model;
Options on Bonds; Swaptions; Options on Bond futures;
Questions:
(optional)
Use Black-Derman-Toy model to price an interest rate cap.
Black-Derman-Toy cap pricing and hedging.
Bill options.
Pricing T-Bill futures with the Black-Derman-Toy model.
Chapter
Term structure models, bonds, bills, and interest rate futures.
Sixteen
Topics: Heath-Jarrow-Morton model; interest rate mean reversion and volatility reduction;
Bond hedging; Delta and gamma hedging; duration and delta; convexity and gamma.
Questions:
(optional)
15.2
15.3
15.4
15.5
17.1
17.2
17.3
17.4
17.5
17.6
Options on T-Bills.
synthetic options on Bills.
Value a floor with the Heath-Jarrow-Morton model.
Use the Black model to value a floor.
Use Bills to hedge bond option.
price a swaption.
Chapter
Credit risk
Eighteen
Topics: Bonds with credit (default) risk; yield spreads; pricing risky debt;
martingale default probabilities; swaps and options with default risk.
Questions:
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
Use lattice and martingale default probabilities to price risky bond.
Price an option on the risky bond of problem 18.1
Price an option on a riskless bond written by a risky counterparty.
Embedding default risk into bond prices.
Use Information in 18.4 to determine martingale default probabilities.
use info from 18.4 and 18.5 to price an option on a risky bond.
Price caps with default risk.
Usage of credit swaps.
Find swap rate for risky counterparty.
Wilmott: Chapters 16-18 (optional)
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April 29 –
May 1
Chapter
Exotic Options: Non-path dependent.
Nineteen
Topics: Digital (binary) options; gap options; Paylater options; Compound options;
Chooser options; Rainbow options.
Questions:
19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8
(optional proof: lower bound of digital option value)
logic of range digital options.
price a chooser option.
using FX digital options to hedge currency payments; hedge outcomes.
hedge a short digital option position.
using FX paylater options to hedge currency payments; hedge outcomes.
chooser options.
hedging strategies with compound options.
Chapter
Exotic Options: Path dependent.
Twenty
Topics: Barrier options; Lookback options; extrema options;
Asian options (average price options).
Questions:
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
using ordinary FX options to hedge barrier options.
hedging with barrier puts.
FX down-and-in calls.
price an up-and-out barrier FX put.
price a lookback put.
hedging with call vs. extrema put.
lookback extrema call.
Asian put.
Wilmott: Chapters 12 & 13
Final exam: Friday, May 3, 1:00-3:00, DRH 234
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