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 in an economy.
We denote it by B (t; T ) and it is the p
BUFN 761 FUTURES CONTRACTS AND OPTIONS FALL 2012 Instructor: Dr. Dilip B. Madan, VMH 4409, 405-2127 email: dmadan@rhsmith.umd.edu Time and Location: M 2.00-5.35 in DC C2 O ce Hours: Monday 10.00-11.00 Tuesday 10.00-11.00
Textbook: Derivative Securities by
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 may hedge an option eectively by holding the option delta
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 Scholes formula is for an asset with no intermediate
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 earning a continuously compounded interest rate of r wi
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 of .nancial contracts, for example options of all strike
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
P@
t=1 T
1
k2A
where
P = notional principal
!
St
xt = log
St 1
St = Market Pri
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 The details for the tree construction dier from what we
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 there is no early
exercise for an American call option.
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
p(S (t); t :; K; T ) = c(S (t); t; K; T )+KB (t; T ) S
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 ] for some maturity T:
We may partition this time interva
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 from which we shall build the Black Merton Scholes opt
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 exact contract in other markets.
For long forward stock o
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 agreed upon today say t < T:
Forward prices like discount c
BUFN761 Derivative Securities Problem set 4.
Prof. Julien Cujean
MS sec 0501/0502/0503/0504 Spring 2017
Due Date: March 1
For Exercises 1-3, suppose that:
i) there is:
a non-dividend-paying stock with current value S0 , the returns of which
have volatili