Quiz 2 Name:
Problem 1 (1 point)
You are given the following information for European options.
Based on the information below, does Put-Call Parity hold? Show your work to get full credit!
S = 40
K = 40
r = 5%
t = 7 months
c = 4.0948
p = 3.7842
Problem 2 (1 point)
You are given the following data on a non-dividend paying European put option for a stock.
Assuming that Put-Call Parity holds, what is the value of the European call?
S = 40
K = 41
r = 4%
t = 10 months
p = 3.2358
Problem 3 (2 points)
You are given the following data on a European call option and put option for a stock. Are there any arbitrage opportunities?
Carefully explain how you would take advantage of arbitrage opportunities. How much, if any, arbitrage profit can you achieve?
S = 81
K = 79
r = 3.50%
t = 0.25 years
c = 5.4503
p = 4.1255
Problem 4 (3 points) Bi-Nomial Option Model
Let S = $39.00 K = $41.00 r = 5% T = 0.5 u = 1.2 d = 0.9
Using a 2-step binomial tree, calculate the premiums of a non-dividend paying European Call at each node.
Each time step is indicated by the value of T (in years) above. Use continously compounded rates and show all your work.
Suu
Cuu
Su
Cu
Stock Sud
Option Cud
Sd
Cd
Sdd
Cdd
FINC 640.01 Summer 2015
39.00
FINC 640.01 Summer 2015 Page: 2
Quiz 2 Name:
Problem 5 (3 points) Black-Scholes-Merton
a) You are given the data below for pricing European Call option. Solve for d1 and d2.
S= $30.00 K = $30.00 r = 5.0% q = 0.0% T = 0.2493 σ = 0.20
b) Now, you are given the following values: N(d1) = 0.5694 N(d2) = 0.5299
Calculate the price of the European Call.
Problem 6 (3 points)
Explain why the true ATM strike price is not equal to the Spot price of an asset.
Hint: Use put-call parity as a proof.
Problem 7 (3 points)
There are a number of assumptions that allowed for the derivation of the Black-Scholes formula for option pricing.
The assumptions can grouped into two categories. Carefully explain what these assumptions are in each of the categories below.
a) Economic and general assumptions:
b) Assumptions about the distribution of stock prices
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