Lecture 8: Black-Scholes Option Pricing formula
This lecture presents the famous Black-Scholes option pricing formula. It also shows one way to derive the formula, in a way that is easier and more intuitive than Black and Scholes original derivation. I. A
Graduate School of Business University of Chicago
Professor Robert Novy-Marx
BUS 35100 Winter 2008
Problem Set #0 Background and Preliminaries
The course is highly technical and builds on concepts from the "Investments" class, B35000. This problem set is
Practice Midterm (with answers) Financial Instruments
Robert Novy-Marx Winter 2007
Instructions. Please answer all questions in the space provided. Show all relevant computations. Brief, clear, and accurate responses will get maximum points. Good luck! 1.
Lecture 2: Pricing Forwards and Futures
This lecture studies the pricing of forward and futures contracts. We rst focus on the similarities of the contracts and derive pricing formulas from market equilibrium and the no-arbitrage principle. We then analyz
Practice Midterm (without answers)
Financial Instruments
Robert Novy-Marx
Winter 2007
Instructions. Please answer all questions in the space provided. Show all
relevant computations. Brief, clear, and accurate responses will get maximum
points. Good luck!
Practice Final Exam (with answers)
Financial Instruments
Professor Robert Novy-Marx
Fall 2006
1. (25 points) SHORT QUESTIONS
(a) (5 points) Suppose that Apple and Dell have been producing the
same type of MP3 players over the last year. As a consequence o
Practice Final Exam (w/o answers)
Financial Instruments
Professor Robert Novy-Marx
Fall 2006
1. (25 points) SHORT QUESTIONS
(a) (5 points) Suppose that Apple and Dell have been producing the
same type of MP3 players over the last year. As a consequence of
Lecture 9: Using the Black-Scholes Formula
This lecture extends the Black-Scholes formula to price European style options on dividend paying stocks, on currencies, and on futures. We also derive an approximate pricing formula for American style call optio
Lecture 7: Building the Tree
This lecture shows that the model is a reasonably accurate approximation of more realistic dynamics of the underlying security. We also derive expressions for u, d , and r , and consequently q , for a binomial tree which match
Lecture 4:
Trading Strategies and Slope/Convexity
Restrictions
This lecture studies elementary options trading
strategies. In the process, we derive no-arbitrage
restrictions for options that are identical except for their
strike price. We restrict how qu
Lecture 3:
No-Arbitrage Bounds on Options
Deriving pricing formulas for options is more difﬁcult
than for forwards/futures.
To price an option we
have to make assumptions about the behavior of the
underlying security’s prices (wait for Lecture 6). We can,
Final Review
1. Black-Scholes C (S , K, T , r, ) D SN(d1) where ln d1 D d2 D d1
S K
Ke
rT
N(d2 )
C rC p T p T.
2
2
T
Interpretation: N(d1) D # of shares in the replicating portfolio N(d2) D risk-neutral probability of expiring ITM . Put-call parity impli