q1
The spot price of an investment asset is $27 and the risk-free rate for all maturities (with continuous compounding) is 7%. The asset provides $2 income at the end of the second year. What is the three-year forward price? (margin of error = +/- $0.10)
question 4
Calculate the present value of $100 in 9 years using 8.80% interest rate with continuous compounding.
Current Value
Years
Interest Rate
100
9
8.80%
PV
45.29
question 8
A 2-year long forward contract on a nondividend-paying stock is entered into
Question 1
Put option
Strike price
Stock Price
option price
Expiration stock PRICE
100
20
16.25
5.64
18.57
Price of put option
gain on per share
564
1.43
143
-421
Option Profit
An interest rate is 11.75% per annum expressed with continuous compounding. Wh
A stock index is currently 1050 and has a
volatility of 20% and a dividend yield of 2%. The
risk-free rate is 5%. What is the value of a
European 6-month call option with a strike price
of 1000 using a 2-step tree?
96.76
What is a lower bound for the pric
1. Consider a European call option
when the stock price is $28, the
exercise price is $25, the time to
maturity is 7 months, the volatility is
30% per annum, and the risk-free
rate is 10% per annum. The stock is
expected to pay $0.20 dividend in 2
months
Q1. Derivagem is useful for pricing options but it has some limitations. Explain why its impossible to solve Q12.5 in page 293 with Derivagem.
does not provide volatility
or cant factor in continous compounding
software does not provide means to account f
Q1
a.Doesput-callparitymeantheputpriceandthecallpricealwaysbethesame?
Put-call parity doesnt mean put price and the call price are the same. For these 2
prices to be the same, the exercise price and the stock price must meet a special condition.
b.Ifnot,u
CHAPTER 4
Interest Rates
Practice Questions
Problem 4.8.
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond
that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that
will pay cou
Black-Scholes formula for European Call
c = S0 * N(d1) - K * exp(-r*T) * N(d2)
d1 = (ln(S0/K) + (r + sigma^2 / 2) * T) / (sigma*sqrt(T)
d2 = d1 - sigma*sqrt(T)
For European put
p = K * exp(-r*T) * N(-d2) - S0 * N(-d1)
5 factors for option pricing
S0: curr
Before the class, please watch a 15-min video tutorial on binomial option pricing
https:/www.youtube.com/watch?v=Sb5n7jq4DQI
3 stages to price options using binomial model
1. Calculate p (using Eq 12.6)
2. Draw the underlying stock price tree
3. Draw the
Q1. The 6-month, 12-month, 18-month, and 24-month interest rates are 1.00%,12.25%, 1.50%, and 2.00% with continuous compounding.
a. Calculate the present value of $100 in 2 years.
$96.08
b. Calculate: what are the equivalent 6-month, 12-month, 18-month, 2
Question 1
The use of Derivagem Software cannot be used to solve question 12.5 as the software
does not provide a way to enter the up and down commands needed in order to
calculate the option price.
Question 2
Current stock price (S0)
Stock price up 8%
St
Explain the similarities and the differences between ABS and ABS CDO.
Similarities
Differences
structured asset-backed security
ABS CDOs encompass the MBS markets
ABS CDO is an ABS issued by a SPV
ABS assets encompass loan, receivable, and credit payment
1. You are converting the currency in the middle May not in June. But why do we use June 2015 futures instead of May 2015 futures?
2. What is the contract size of EUR/USD futures contract?
3. How many futures contract do you have to buy or short to hedge
Arbitrage Opportunity Requirements
1. no negative net cash flows
2. at least 1 postive net cash flows
10.4 Put-Call Parity
c + K *exp(-r*T) = p + S0
(Eq 10.6)
Objective: Check the put-call parity, and find strategy with arbitrage opportunity.
Table 10.3
S
Example 1.2 Hedging with options (pg 13)
Objective: Protection against MSFT price decline in 2 months
Current MSFT price
$28.00
Put expiration month
2 months from now
Put exercise price
$27.50
Cost of 1 put option
$1
Possible Stock prices in 2 1000 Stocks
In chapter 9, we will learn how to calculate the option payoff and option profit at the expiration.
Call payoff
=max(S - K, 0)
Call profit
=max(S - K,0) - c
Put payoff
=max(K - S, 0)
Put profit
=max(K - S,0)- p
Profit = payoff - initial cost
Example 9.1
K
Homework 3
Q1. The 6-month, 12-month, 18-month, and 24-month interest rates are 2.00%, 2.25%, 2.50%,
and 2.75% with continuous compounding.
Solution
a. Calculate the present value of $100 in 2 years.
Present Value =
=
=
=
$100*e-0.0275*2
$100*e-0.055
$100
Explain the similarities and the differences between ABS and ABS CDO.
The following are similarities and the differences between ABS and ABS CDO:
Similarities
ABS and ABS CDO both are colletaralized securities.
Both ABS and ABS CDO are used to sell the po