Sloan School of Management Massachusetts Institute of Technology 15.402 Section A Fall 2009 T TH 10:00 a.m. to 11:30 a.m. E51-151 Craig A. Stephenson, Ph.D. E53-305, 617-253-7125 stephenc@mit.edu 15.402 Finance Theory II Introduction to Corporate Finance

Hedging, Pricing, and Predicting Volatility
Supplementary Material
Slide 12-1
Agenda
The expected profit of a delta-hedged market maker depend on the volatility of the underlying asset. Today: estimating volatility (and more.),
Based on option prices -

The Black-Scholes Formula
Nobel Prize in 1997
&
The Option Greeks
Chapter 12 12.3
Slide 12-1
Black-Scholes Formula
European Call Options:
C(S,K,% ,r,T,$) = Se-$T N(d1) # Ke-rT N(d2)
European Put Options:
P(S,K,% ,r,T,$) = Ke-rT N( # d2) # Se-$T N( # d1)

Review
Slide 13-1
The Black-Scholes model
We introduced the Black-Scholes model:
C(S,K,! ,r,T,") = Se-"T N(d1) # Ke-rT N(d2) We discussed analogies between the Black-Scholes model and the binomial model. Like the binomial option pricing formula, the Blac

Binomial Option Pricing: II
Chapters 10 & 11
Slide 11-1
Review: Risk neutral option pricing
Method:
use risk-neutral discount rate to compute an option price as a discounted expected payoff, where the expectation is based on the following riskneutral pr

Binomial option pricing
Risk-neutral pricing: the basic idea Section 10.1, Appendix 11.A
Slide 10-1
Binomial Option Pricing
Binomial option pricing enables us to determine the price of an option, given the characteristics of some underlying asset. The bi

American vs. European Options
Chapter 3, Section 3.2
Slide 9-1
Review
Put-call parity for European options: C(S, Q, T t) P(S, Q, T t) = FPt,T (S) FPt,T (Q) = PV(Ft,T (S) PV(Ft,T (Q) PC parity as a cookbook:
Synthetic forwards (long call+short put), synt

Put-Call Parity
and Other Option Relationships
Chapter 3, Section 3.2 Chapter 9
Slide 9-1
Review
Basic types of options:
Calls and puts Long and short European, American, Bermudan
Payoff vs. profit diagrams:
long position: profit = payoff - FV(option

Introduction to options
Chapters 2 and 3
Slide 1-1
Major types of publicly-traded options
Stock Options (40%)
Major Exchanges: CBOE, NYSE, AMEX, PHILX, PSE 500+ different underlying stocks Size: Each contract is typically on 100 shares
Stock Index Opti

Options and Futures Markets
(FIN 15.437)
Prof. Alex Stomper Teaching Assistant: Apurv Jain
Slide 1-1
Introduction to Derivatives
Chapters 1 & 2
Slide 1-2
What is a derivative?
Definition:
A derivative is a bilateral contract to exchange assets. The valu

Review: Swaps
Slide 8-1
Swap prices
We saw that swap prices are weighted averages of forward prices. Lets review the idea: a swap into a fixed rate.
1st step: view a swap as a strip of forwards. To see this, think about a swap dealer seeking to hedge a

SWAPS
Chapter 8
Slide 8-1
Introduction to swaps
Section 8.1
Definition: A swap is a contract calling for an exchange of payments, on one or more dates, determined by the difference between two prices. A single-payment swap is a cash-settled forward contr

Interest Rate Forwards and Futures
Chapter 7
Slide 7-1
Todays Agenda
Hedging future borrowing and lending rates:
Forward Rate Agreements Eurodollar Futures
Hedging the value of bonds / bond portfolios:
Measuring the interest rate sensitivity of bonds

Hedging with futures
Review A case study: Metallgesellschaft
Slide 6-1
Review: Futures hedging
Tailing Maturity mismatch Asset mismatch Basis risk
Slide 6-2
Hedging with futures: tailing
Gains and losses on futures contracts are settled daily. Cash flow a

Hedging with forwards and futures
Example
A gold mining firm anticipates to produce 500,000 ounces of gold during the next year, and wants to fully hedge its gold price risk. Three possible hedging alternatives Forward hedge Futures hedge Money market hed

Futures Returns: Predictability and Information Content
Question: is futures trading profitable?
Suppose a trader continuously enters into forward contracts and holds these contracts until they expire. Will he/she make money, loose money, or come out +/-