Some Homework 1 Solutions
Solutions to #1.1, #1.2, #1.3, and book problem 9.4.
#1.1
By put-call parity, we have that
c p = P V (S K).
The LHS of this equation is 0.15 by the second assumption. This gi
Homework 2
Due Wednesday, September 9th at 6:00am
Name
uu
u
90
99
ud
du
d
81
108.9
89.1
dd
72.9
Use the above diagram for problems 2.1-2.5. S is a stock with multiperiod binomial tree
shown above. The
Homework 1
Due Wednesday, September 2nd at 6am
Name
1.1. Consider a European call option and a European put option on a nondividend-paying
stock. You are given:
The current price of the stock is 60.
Some Homework 5 Solutions
#5.1
We want to model this currency exchange. After some translation, we have that the
current price of 1 is $0.007. The strike in this case is $7/700 or $0.01. Using the for
Some Homework 6 Solutions
Solutions to #6.1, #6.2, #6.3, #6.5, and #6.6.
#6.1
Under the risk free measure, we know that
dS(t) = (r )S(t)dt + S(t)dZ(t)
This stock pays dividends at 4%, so that means th
Some Homework 2 Solutions
#2.1
To solve this problem, we must use the three equations:
Sue0.03 + Be0.0375 = 10
Sde0.03 + Be0.0375 = 0
S + B = C0
(2.1)
(2.2)
(2.3)
The rst two give us that
(Su Sd)e0.03
Some Homework 2 Solutions
Solutions to #2.1, #2.2, #2.3, #2.4, #2.5, #2.6, and book problem 10.18a.
#2.1
To solve this problem, we must use the three equations:
Sue0.03 + Be0.0375 = 10
Sde0.03 + Be0.0
Homework 2
Due Thursday, January 29th
Name
uu
u
90
99
ud
du
d
81
108.9
89.1
dd
72.9
Use the above diagram for problems 2.1-2.5. S is a stock with multiperiod binomial tree
shown above. The following h
Homework 1
Due Thursday, January 22nd
Name
1.1. Consider a European call option and a European put option on a nondividend-paying
stock. You are given:
The current price of the stock is 60.
The call
Homework 7
Due Thursday, March 12th
Name
7.1. Suppose that S is a stock with S(0) = 36. Let V (t, S) be an option on S satisfying the
following:
0.09 2
Vt + 0.03SVs +
S Vss = 0.05V.
2
(a) Determine th
Problem Set 3
1.
Name
Mark bought a call option ten days ago on a stock, the call expires at the end of the
year and has a strike price of 50. John bought a call option on the same stock yesterday,
th
Homework 4
1.
Name
The following call option prices are observed (all options are on the same stock and with
the same expiration time). Is there any arbitrage opportunity? If so, what would you
do to
Some Homework 3 Solutions
Solutions to #3.1, #3.2, #3.3, 10.19, 18.6, and 18.11.
#3.1
We use the standard normal table for part a. The two values we need to use are
and 1.64. We plug these values into
Homework 3
Due Friday, September 18th
Name
3.1. Let S be a stock whose price is modeled using a lognormal distribution such that
ln S(t) N (ln 70 + .02t, 0.09t).
(a) Determine the 90% lognormal predic
Homework 3
Due Thursday, February 5th
Name
3.1. You wish to construct a 2-period binomial tree to model the price of a futures contract.
The following hold:
The continuously compounded risk-free inte
Math 5632: Financial Economics for Actuaries
Autumn Semester 2015 The Ohio State University
Tuesday/Thursday 3:55-5:15pm (section 21526)
Tuesday/Thursday 5:30-6:50pm (section 23495)
Lecturer:
Dr. Brad
Homework 4
Due Friday, September 25th
Name
4.1. Assume the Black-Scholes framework. Let S be a stock such that S(0) = 10, and the
dividend rate is 4% compounded continuously. Let C be a derivative tha
Homework 6
Due Thursday, March 5th
Name
6.1. Assume the Black-Scholes framework. Let S be a stock such that S(0) = 10, and the
dividend rate is 4% compounded continuously. Let C be a derivative that p
Math 5632: Financial Economics for Actuaries
Spring Semester 2015 The Ohio State University
Tuesday/Thursday 3:55-5:15pm
Lecturer:
Dr. Bradley Waller
Ofce:
Mathematics Tower 529
Email:
[email protected]
Worksheet 2: Futures
You suspect that the price of oil will rise in the next three days, so you would like to
determine which if your better choice: a forward contract or a futures contract. You plan
Homework 6 SP Solutions
Math 5632
6.1: To solve this problem, we must use the three equations:
Sue0.03 + Be0.0375 = 10
Sde0.03 + Be0.0375 = 0
S + B = C0
The first two give us that
(Su Sd)e0.03 = 10
Th
Homework 9
Math 5632
Problems Due (PD): 9.2 and 9.3.
Suggested Problems (SP): 9.1 and 9.4.
9.1. Assume the Black-Scholes framework. Let S be a stock such that S(0) = 10, and the
dividend rate is 4% co
Week 4 Formula Sheet
With the exam coming soon, I thought it would be useful for you to have a formula sheet
for most of what weve talked about:
Name
Formula
Forward price of stock
F0,T (S) = S(0)e(r)
Homework 3 SP Solutions
Math 5632
3.1: This should be straight forward; just take a difference of the call and the put.
6.38 1.44 = 4.94
3.4: We must take a difference of the asset-or-nothing call and
Worksheet 4: Put Call Duality
1. Suppose we are given that the price of a one year European call option to buy e1000
currently costs $105.13. In addition, the current price of e1 is $1.07, and the str
Homework 2 PD Solutions
Math 5632
2.2: We can use our work from 2.1 to assist us. Since the futures price and the forward price
are the same, there will be no gain from buying and immediately selling
Worksheet 1: Cash-and-Carry
A cash-and-carry is a hedging strategy where you agree to a forward contract (or with
futures) in which you are the seller, and you purchase the underlying asset at the sam
Homework 6 PD Solutions
Math 5632
6.2: Using the result from 6.1, we know that C0 should cost 5.18. Thus, the market price
of the call is low. That means we buy the call and sell the replicating portf
Homework 4
Name
Problems Due (PD): 4.3 and 4.4(b).
Suggested Problems (SP): 4.1, 4.2, 4.4(a), 4.4(c), and 4.4(d).
4.1. The current cost of a European call on some asset is 7.23. The call expires in 2
Homework 3
Name
Problems Due (PD): 3.2 and 3.3.
Suggested Problems (SP): 3.1, 3.4, and 3.5.
The first 2 problems rely on the table below. The options have the same underlying asset,
expire in 8 months
Homework 6
Name
Problems Due (PD): 6.2 and 6.3.
Suggested Problems (SP): 6.1 and 6.4.
Use the diagram below for problems 6.1-6.4. S is a stock with multiperiod binomial tree
shown above. The following
Homework 4 PD Solutions
Math 5632
4.3: We need to find two distinct arbitrage opportunities. We must have that
p(32)
2
1
p(30) + p(36);
3
3
however, this is not the case because 4.91 > 2 + 2.67 = 4.