Pstat 170 Spring 2016 Asn 1 Solutions.
Problem 3.10. The initial cost for purchasing a 1050-strike S&R Call and selling a 950-strike
S&R Call is - 71.802 + 120.405 = 48.603.
The initial cost for purchasing a 1050-strike S&R Put and selling a 950-strike S&

Pstat 170 Quiz 4 Winter 2016
Instructions: Clearly explain everything you do. The quiz is scored out of 10 points.
Name:
(10) 1. Consider a stock with = 0.32 and todays stock price of S0 = 33. Assume r = 0.06 and that
you sell 100 Calls with strike K = 35

Pstat 170 Sample Midterm Solutions Winter 2016
Instructions: Clearly explain everything you do. State the general
formulas you use before plugging in any numbers. Provide all numeric
answers to 3 decimal points. The midterm is scored out of 40 points.
(10

PSTAT 170 QUIZ 1 — WINTER 2016
Instructions: Clearly explain everything you do. In plots label/quantify all the important
points such as axis labels, zero—intercepts, slopes, “corner” locations, et cetera. The quiz is
scored out of 10 points.
Name

Pstat 170 Winter 2017 Homework 3
Problem 1
Consider the following table of Put prices for an asset with S0 = 89 and no dividends:
Strike P remium
100
15
90
8
85
5
a) Using the above information ONLY, find the best no-arbitrage bounds on the Put
premium wi

Pstat 170 Quiz 2 Winter 2016
Instructions: Clearly explain everything you do. In plots label/quantify all the important
points such as axis labels, zero-intercepts, slopes, corner locations, et cetera. The quiz is
scored out of 10 points.
Name:
(10) 1. Su

Pstat 170 Spring 2016 Asn 4 Solutions
Problem 1
A European binary (or Digital ) option pays $5 if the stock ends above $56 after 3 months
and nothing otherwise. The following 3-period binomial tree represents the monthly stock
price movements:
71.46
67.42

Pstat 170 Winter 2016 Sample Final.
Instructions:
You have 2 hours 45 min to complete this exam.
The exam consists of seven questions for a total of 100 points.
Youre allowed to use a graphing/financial calculator
Read each question statement carefull

Pstat 170 Spring 2016 Asn 2 Solutions
Problem 4.4. see the description of XYZs business on the bottom of previous page 118.
Solution. The figure below shows the payoffs for the different strategies. We note that the basic
revenue is ST 0.9 and the Call op

PSTAT 170 Winter 2017 Assignment 3 Solutions
Problem 1. Consider the following table of Put prices for an asset with S0 = 89 and no
dividends:
Strike P remium
100
15
90
8
85
5
a) Using the above information ONLY, find the best no-arbitrage bounds on the P

Pstat 170 Midterm Winter 2017
Instructions: The midterm is scored out of 40 points. Clearly explain everything
you do. State the general formulas you use before plugging in any numbers.
Provide all numeric answers to 3 decimal points. Correct and complete

PSTAT 170 Winter 2017 Homework 2 [Solutions]
Problem 1. ln real-life borrowing rates are higher than lending rates. Suppose that you can borrow at
um= 4% but can only invest at r2 = 2%. Both rates are annualized, continuously compounded.
Given that So = 7

PSTAT I70 Winter 2017 Homework 2 [Solutions]
Problem 1. In real-life borrowing rates are higher than lending rates. Suppose that you can borrow at
r1: 4% but can only invest at r2 = 2%. Both rates are annualized, continuously compounded.
Given that So = 7

PSTAT 170 Winter 2017- Homework 1 Solutions
Problem 1. The continuously compounded interest rate is r = 2%. Today is 1/ 11/2017 and
the current price of one Apple shame (AAPL) is 120$.
I How much do you have to put in a bank account today to have 110$ on

Ch 3: Option Strategies
Recap of Chapter 2:
We have several building blocks:
Long/Short Stock
Forwards (Long/Short)
Calls (Long/Short)
Puts (Long/Short)
Distinguish between Payoff, Premium and Profit
Profit is based on Future Value of premium at maturity

Pstat 170 Sample Midterm Winter 2016
Instructions: Clearly explain everything you do. State the general
formulas you use before plugging in any numbers. Provide all numeric
answers to 3 decimal points. The midterm is scored out of 40 points.
(10) 1. Using

PSTAT 170: Introduction to
Mathematical Finance
[email protected]
Office Hours: Tu/We 9am-10am
All course materials are on Gauchospace
Textbook
South Hall 5520
will cover about half of it
Grading
Quizzes during sections
Homework Assignments (hand

Ch 7: Recap
Cashflows at different dates in the future have different
discount factors
$1 at T is worth P(0,T) at t=0
P(0,T) is the bond price with face value 1
Corresponding effective interest rate is r(0,T)
Borrowing/investing in the future carries

Lecture 6: More Forwards
Cash-and-carry: a position in forward against an offsetting
position in the underlying stock
Has zero upfront costs at t=0 and zero risk at maturity t=T
No-arbitrage implies that the profit must also be zero.
Long cash-and-carry:

Ch 3: Option Strategies
Recap of Chapter 2:
We have several building blocks:
Long/Short Stock
Forwards (Long/Short)
Calls (Long/Short)
Puts (Long/Short)
Distinguish between Payo, Premium and Prot
Prot is based on Future Value of premium at maturit

Pstat 170 Winter 2017 HW 1. Due in Week 3 Section.
Problem 1. The continuously compounded interest rate is r = 2%. Today is 1/11/2017 and
the current price of one Apple share (AAPL) is 120$.
How much do you have to put in a bank account today to have 110

Pstat 170 Midterm Spring 2016 Solutions
(10) 1. Stock PSTT pays continuous dividends at = 10% annual. Its price today is $70 and
you observe a forward price of F = 74.330 for T = 2. Assuming interest rate of r = 3%
annual, describe an arbitrage strategy t

Ch 5: Forwards and No-Arbitrage
Goal: what is the correct forward price?
Idea: no pain=no gain, no risk=no profit.
Cash-and-carry: a position in forward
against an offsetting position in the
underlying stock
Has zero upfront costs at t=0
Has zero ris

Lecture 6: More Forwards/Futures
Cash-and-carry: a position in forward against an ose=ing
position in the underlying stock
Long cash-and-carry:
Short forward w/forward price F
Borrow money (S_0)
Buy a share of underlying (long asset)
At maturi

Pstat 170 Winter 2017 Homework 2
Problem 1. In real-life borrowing rates are higher than lending rates. Suppose that you can
borrow at r1 = 4% but can only invest at r2 = 2%. Both rates are annualized, continuously
compounded.
Given that S0 = 70 and the a

Recap: Deriva,ves
Deriva've = a bet
Its value/payo is derived from, or con,ngent
upon, another object
This object is called the underlying
A deriva,ve is a contract a legal agreement
between a buyer and a seller
Has an expira,on date, aka the

Ch 6: Commodity Forwards
For physical commodities there are LOTS of different
forwards/futures, indexed by maturity date T
(typically each months for several years out)
Called the Forward Curve
Storing Oil
Consider a forward contract on crude oil
To i

PSTAT 170: Introduction to
Mathematical Finance
[email protected] South Hall 5505
Oce Hours: Tue 1pm-2pm
All course materials are on Gauchospace
Textbook
will cover about half of it (1-13, 18-20)
3 Quizzes during sections
Homework Assign

Pstat 170 Sample Midterm Spring 2017 - Solutions
(10) 1. Stock PSTT pays continuous dividends at = 10% annual. Its price today is $70 and
you observe a forward price of F = 74.330 for T = 2. Assuming interest rate of r = 3%
annual, describe an arbitrage s

Pstat 170 Spring 2017 Homework 3 Solutions
Problem 1
Consider the following table of Put prices for an asset with S0 = 89 and no dividends:
Strike Premium
100
15
95
11
85
5
a) Using the above information ONLY, find the best no-arbitrage bounds on the put

Pstat 170 Spring 2017 - Solutions to Midterm Test
Instructions: Clearly explain everything you do. State the general
formulas you use before plugging in any numbers. Provide all numeric
answers to 3 decimal points. The midterm is scored out of 40 points.

Recap: Binomial Tree Model
Specify model for evolution of underlying
asset price
Use no-arbitrage to obtain the fair price of
a derivative, such as Call/Put.
Have formulas for the replicating portfolio
Binomial tree model makes price
dynamics analogou

Growing Trees
Recall that Snh = S0 d n (u/d)X where X has a Binomial
distribution
X Bin(n, q) under risk-neutral, that is,
Prob(X = k ) = q k (1 q)(nk )
n!
.
(n k )!k !
Plug-in q which depends on h, :
log(Snh /S0 ) = n log d + X log[u/d]
= (r )nh + h(2X n