Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 25
Real Options
Options, Futures, Derivatives / April 30, 2008
1
Real Options
We can try to use our knowledge of derivatives to help value real objects, such as buildings, land, and equipment. Often there are options embedded in these investment o
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 18
Stochastic Models & Numerical Methods
Options, Futures, Derivatives / April 7, 2008
1
Alternatives to BlackScholes
We can generalize the underlying stochastic process of the asset to try to better capture the behavior of both the asset and any
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 20
Martingales & Interest Rate Derivatives
Options, Futures, Derivatives / April 16, 2008
1
Market Price of Risk
If f is the price of a derivative dependent only on and t with
df = dt + dz f r = (1) The parameter is called the market price of risk
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 15
Credit Derivatives & Exotic Options
Options, Futures, Derivatives / March 26, 2008
1
Credit Derivatives
Credit derivatives allow companies to trade credit risks in the same way that they trade market
risks.
Companies can enter into credit deriv
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 23
Interest Rate Derivatives: Short Rates
Options, Futures, Derivatives / April 23, 2008
1
Blacks Model
Consider a European call option on a variable whose value is V  which does not have to be the price of a traded security. Dene
T : Time to mat
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Final Review Spring 2008
Options, Futures, Derivatives / 11/05/2007
back to start
1
Financial instruments used in derivative transactions
I. Forwards
II. Futures
III. Swaps
IV. Options
Options, Futures, Derivatives / 11/05/2007
back to start
2
Forward Con
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 14
Credit Derivatives
Options, Futures, Derivatives / March 24, 2008
1
Credit Derivatives
Credit derivatives allow companies to trade credit risks in the same way that they trade market
risks.
Companies can enter into credit derivative contracts t
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 22
Interest Rate Derivatives
Options, Futures, Derivatives / April 21, 2008
1
Blacks Model
Consider a European call option on a variable whose value is V  which does not have to be the price of a traded security. Dene
T : Time to maturity of the
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 24
Real Options
Options, Futures, Derivatives / April 28, 2008
1
Real Options
We can try to use our knowledge of derivatives to help value real objects, such as buildings, land, and equipment. Often there are options embedded in these investment o
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 20
Martingales & Interest Rate Derivatives
Options, Futures, Derivatives / April 14, 2008
1
Martingales
So far we have valued options by assuming a riskneutral valuation that is found by rst assuming the interest rate is constant and then
calcul
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 19
Numerical Methods & Martingales
Options, Futures, Derivatives / April 9, 2008
1
Monte Carlo Simulation and American Options
We discuss two approaches to trying to value pathdependent options using a MonteCarlo based method. LeaseSquares Appr
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 13
Midterm Review
Options, Futures, Derivatives / March 10, 2008
1
Derivation of BlackScholesMerton Dierential Equation
We are now in position to derive the BlackScholes or BlackScholesMerton dierential equation.
We build the model via a risk
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 12
Credit Risk & Credit Derivatives
Options, Futures, Derivatives / March 8, 2008
1
Historical Default Probabilities
We can consider the historical default rates of the certain class of corporate bonds:
Options, Futures, Derivatives / March 8, 200
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 17
Exotic Options, Stochastic Models & Numerical Methods
Options, Futures, Derivatives / April 3, 2008
1
Compound Options
Compound options are options on options. There are four main kinds
call on a call At time T1 the holder of the compound opti
Mathematics of Options, Futures, and Derivative Securities II
MATH 5076

Spring 2014
Lecture 16
Exotic Options
Options, Futures, Derivatives / March 31, 2008
1
Exotic Options
American and European options are known as plain vanilla options. Recently there have developed nonstandard exotic options that have become parts of portfolios. May