Black-Scholes summaryBlack-Scholes matches qualitatively and quantitatively the following sensitivities we discussed previously:•Black-Scholes takes these five inputs (?, 𝑋, 𝜎, ?, 𝑟) and tells you what they imply call and put option premia should be▪Also tell you what current replicating portfolio Δ, BisCall PricePut PriceStock price (?)IncreasesDecreasesExercise price (𝑋)DecreasesIncreasesVolatility (𝜎)IncreasesIncreasesMaturity (?)IncreasesUsually IncreasesInterest rate (𝑟)IncreasesDecreases
Finance 367 - Lecture 23
Option Valuation
18
Black-Scholes Option Valuation

10
Finance 367 - Lecture 23
Option Valuation
19
Implied volatility
•
In practice, we observe every ingredient in Black-Scholes
formula except
𝜎
▪
Can estimate
𝜎
using past returns, as in Data Exercise 1
•
Can also reverse the Black-Scholes formula: instead of
using
𝜎
to find
?
and
?
, use
?
and
?
to solve for
𝜎
▪
“Implied Volatility”, typically annualized
▪
?
and
?
high relative to
? ⇒
high implied volatility
▪
?
and
?
low relative to
? ⇒
low implied volatility
▪
Predicts future stock volatility very well
TLSA implied volatility for 6-month ATM options: 72%
GOOGL implied volatility for 6-month ATM options: 31%
S&P implied volatility for 6-month ATM options: 27%
▪
Requires fancy Excel spreadsheet or other software (just Google
“implied volatility calculator”)
▪
Available on Yahoo! Finance
Implied volatility over time
Gulf war
LTCM
9/11
Iraq
Lehman etc.
US Debt
Downgrade
Covid-19

1
Travis Johnson
Finance 367
Lecture 24:
Mutual Funds,
Hedge Funds,
Course Wrap-up
Chapter 4
Announcements
•
Final Exam on Friday, May 15
th
Covers entire course, with a focus on the last Unity
15-20 questions on last unit, 15-20 questions on first three units
Your choice of 9am-noon or 2-5pm
No need to tell use in advance which one you’ll chose
•
Same rules as Midterm 3:
Open notes, textbook, internet etc.
You definitely still need to study!
Must be on Zoom call with us, video enabled if possible
No discussing with anyone else inside or outside class
•
Main Concepts in Unit 4: forward and futures terminology,
hedging & speculating using futures, futures arbitrage pricing,
futures curve, put and call option terminology & payoffs,
payoffs vs net payoffs, hedging & speculating using options,
option strategies, put-call parity (& arbitrage), intrinsic vs time
value, general option valuation properties, binomial options
pricing (& arbitrage), implied volatility, mutual funds, hedge
funds
Finance 367 - Lecture 24
Mutual Funds, Hedge Funds, Wrap-up
2

2
Pre-exam schedule
•
Pre-exam schedule:
TA Review Session:
Thursday, May 14th
TA office hours
Jangwoo Lee Thursday 5/7 5-6pm
Thomas Lee Monday 5/11 5-6pm
Changyong Song 5/13 3-4pm
My office hours (Tuesday 5/12 4-6pm)
Finance 367 - Lecture 24
Mutual Funds, Hedge Funds, Wrap-up
3
Mutual fund idea
•
Investors pool their money, have manager invest it
Cheap way to get diversification
Less effort than managing your own assets
Save on transaction costs
Professional money manager may do a better job than you
would?

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- Spring '08
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