Solution to Quiz 1
1. The price of a dollar at t, B(t) is using simple interest rate is
B(t) =
1
1 + is t
The continuously compounded rate r has the price at
B(t) = exp( rt):
Hence we must have
exp( r
BMGT 444 Project 1 Fall 2014
Dilip B. Madan
Robert H. Smith School of Business
October 12 2014
The rst project consists of the following 4 questions.
1. Let f (0; t1 ); f (0; t2 ) be forward prices fo
Futures And Options Contracts
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Forward Contracts
A forward contract is an obligation to transact at
a future date T for a price agre
Arbitrage Pricing of Forward
Contracts
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Price of Forward Stock
Forward contract pricing is based when possible on
replicating the ex
Information Content of Option
Prices
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Model Free Results on
Option Prices
We will go on to build a model about stock price
movements
The Stock Price Model
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Modeling Stock Price
Movements
We wish to model the motion of the stock price over
the time interval [0; T ]
Option Price Equalities
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Put Call Parity
The put call parity result for European options on
stocks with no intermediate dividends is
Martingale Probability
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Martingales and No
Arbitrage
Suppose we develop a system for simultaneously quoting on the numerous prices o
Binomial Option Pricing Model
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Call Price on One Period
Tree
Consider the following one period tree for the stock
127:12
100
85:21
T
Pricing American Options
Dilip Madan
Department of Finance
Robert H. Smith School of Business
American Call Options
We have seen as a consequence of call lower bounds
that in the absence of dividends
Hedging at BMS Implied
Volatilities
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Hedging Considerations
Under the BMS assumptions we have seen when deriving the PDE that one ma
Black Merton Scholes Option
Pricing Formula
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Black Merton Scholes
Model
Consider an economy with two assets, a money market account
Pricing Variance Swaps
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Contract Description
The contract pays at the end of day T the sum of
0
T
X x2
t 252
[email protected]
t=1 T
1
k2A
where
P
BUFN761 Derivative Securities Problem set 1.
Prof. Julien Cujean
BMGT444 Spring 2017
Due Date: February 20
For this problem set, suppose that:
i) You are long the non-dividend-paying S&P 500, currentl
BMGT444 Futures and Options Contracts
Solution PS 2.
Prof. Julien Cujean
Spring 2017
For this problem set, suppose that:
i) You can trade 3 stocksA, B, and Ceach of which has current price $100
A is
BMGT444 Futures and Options Contracts Solution
PS 1.
Prof. Julien Cujean
BMGT444 Sec 0101
Spring 2017
For this problem set, suppose that:
i) You are long the non-dividend-paying S&P 500, currently tra
BMGT 444
FUTURES CONTRACTS AND OPTIONS
FALL 2014
Instructor: Prof. Dilip B. Madan, VMH 4409, 405-2127
email: [email protected]
Time and Location: Mon: 7.00pm-9.40pm in VMH 1307
O ce Hours:
Monday
Futures And Options Rate
Conventions
Dilip Madan
Department of Finance
Robert H. Smith School of Business
The Discount Curve
The discount curve is the basic object announcing
the time value of money i
10/20/14 continued
Binomial Option Pricing Model
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Call Price on One Period
Tree
Consider the following one period tree for the stock
10/20/14
The Stock Price Model
Dilip Madan
Department of Finance
Robert H. Smith School of Business
Modeling Stock Price
Movements
we want to model the movements in the stock price
We wish to model th
1. Consider a forward contract on a 1000 dollar face value, 10% coupon
bond with semiannual coupons maturing in two years with a forward delivery
date of 1:75: The yield curve in simple interest rates
Black Merton Scholes Formula
Adjusted for Dividends
Dilip Madan
Department of Finance
Robert H. Smith School of Business
A Fixed Dividend
Suppose we have a xed dividend of d1 at time t1 <
T:
The Black
BMGT444 Futures and Options Contracts Problem
set 2.
Prof. Julien Cujean
Spring 2017
Due Date: March 6
For Exercises 1, 2 and 3, suppose that:
i) You can trade 3 stocksA, B, and Ceach of which has cur