Log in
HomeClass Notes1,200,000CA670,000

FIN 401 Lecture Notes - Lecture 5: Stock Split, Delta Neutral, Implied Volatility

41 views8 pages
School
Ryerson University
Department
Finance
Course
FIN 401
Professor
Thomas Barbiero

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Chapter 5: option pricing models: the black-scholes-merton model. 1. (a nobel formula) the formula has two terms: C = s0n(d1), is the present value of the expected value of the stock price, conditional on the option expiring in-the- money discounted at the risk-free rate. 2 is the present value of the expected payout of the exercise price at the expiration. All of this is based on the condition of risk neutrality, meaning that the probability distribution is based on a risk-free expected return on the stock. (variables in the bsm model) a. The delta is the change in the call price for a given change in the stock price. Strictly speaking the delta applies only when the stock price changes by a very small amount. The delta also gives the hedge ratio, which tells how many shares of stock must be held (or sold short) to hedge a given short (or long) position in calls.

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers
Class+
$8 USD/m
Billed $96 USD annually
Class+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
30 Verified Answers

Related Documents

FIN 401 Lecture Notes - Lecture 9: Cash Flow, Option Style, Valuation Of Options
champagneskunk149
FIN 401
Final Exam
Study Guide
FIN 401 Study Guide - Midterm Guide: Liquidating Distribution, Dividend Policy, Tax Shield
ochreguinea-pig475
FIN 401
Final Exam
Study Guide
FIN 401 Study Guide - Final Guide: List Of Blade Runner Characters, Trillium, Asteroid Family
fuchsiachinchilla276

Related Questions

The following information is given about options on the stock of a certain company.

Current stock price = $114
Exercise price = $115
Continuously compounded risk-free rate = 0.1 percent Time to expiration = 6 months (T = 0.5) in June
The volatility = 0.28

(1) Find the values of N(d1) and N(d2)

(2) What value does the Black-Scholes-Merton model predict for the call?

(3) What is the delta of the call?

(4) If the stock price goes up by $1 to $115, what would be the call price based on the delta?

(5) Suppose that June 115 call has the gamma of .0176. If the stock price goes up by $1 to $115, what would be the delta of the call based on the gamma?

(6) Suppose that the call rho (ρ) is 25.523. If the continuously compounded risk-free rate goes up by 1 percent to 1.1 percent, what would be the expected call price based on the rho?

(7) Suppose that the call vega (ν) is 32.106. If the volatility of the continuously return on the stock increase by 1 percent, what would be the expected call price based on the vega?

(8) Suppose that the theta (θ) is 9.04. If the time to expiration decreases so that the call expires in 3 months (T = .25), what would be the expected call price based on the theta?

A stock price has an expected return of 16% and a volatility of 25%. The current price is $38. What is the prices of European call and put options (Using The Black-Scholes-Merton Model) on the stock with an exercise price of $40 and a maturity date in six-months? Assume that risk free interest rate is 6%.

Question 1

The following information is given about options on the stock of a certain company.

Current stock price = $23

Exercise price = $20

Continuously compounded risk-free rate = 9.0 percent

Time to expiration = 6 months (T = 0.5)

The variance of the continuously compounded return on the stock = 15.0 percent

The volatility = Sqrt(.15)

d1 = [ln(S0/X) + (rc + σ2/2)T]/σSqrt(T) = [ln(23/20) + (.09 + .15/2)(.5)]/(.3873 x sqrt(.5)) = [.1398 + (.165)(.5)]/.2739 = .2223/.2739 = .8116

d2 = d1 - σSqrt(T) = .8116 – (sqrt(.15))(sqrt(.5)) = .8116 – .2739 = .5377

No dividends are expected.

Find the values of N(d1) and N(d2) using the excel function ‘=normsdist( ).

What value does the Black-Scholes-Merton model predict for the call?

What is the delta of the call?

If the stock price goes up by $1 to $24, what would be the call price based on the delta?

Suppose that June 20 call has the gamma of .0456. If the stock price goes up by $1 to $24, what would be the delta of the call based on the gamma?

Suppose that the call rho (ρ) is 6.74. If the continuously compounded risk-free rate goes up by 1 percent to 10 percent, what would be the expected call price based on the rho?

Suppose that the call vega (ν) is 4.67. If the volatility of the continuously return on the stock increase by 1 percent, what would be the expected call price based on the vega?

Suppose that the theta (θ) is 3.02. If the time to expiration decreases so that the call expires in 3 months (T = .25), what would be the expected call price based on the theta?