2. Introduction to Forward Contracts and Options (Part 2)
Comparing 3 Types of Long Positions
We have now looked at three different positions that are long with respect to the underlying asset. Each of
these positions has a distinct profit profile.
With a

2. Introduction to Forward Contracts and Options (Part 1)
Forward Contracts
The process of buying or selling a stock (or other asset) consists of the following three events.
1. Buyer and Seller agree to an asset, price and amount.
2. Buyer sends cash to S

8. Swaps and Interest Rate Hedging
Introduction
Most of our semester has been devoted to the study of two basic types of derivative contracts: forward contracts
and European-style options. These two types of derivatives share the following attribute: they

3. Option Trading Strategies and No Arbitrage Pricing
Put-Call Parity Equation for European Options
In this section, we develop a fundamental mathematical result in option pricing theory known as the put-call
parity equation for European options. The equa

4. Risk Management and Hedging (Part 1)
Introduction
In Chapter 3, we studied many stand-alone derivative and option trading strategies such as bull spreads, bear
spreads, straddles, strangles and butterflies. In these strategies, there was no pre-existin

12. Black-Scholes Formula (Derivation and Option Greeks)
N (d2 ): Probability of Call Option Exercise
Let S be the current price of a stock and let ST be the price of that same stock after T years. Next semester,
we will show that if we assume that contin

4. Risk Management and Hedging (Part 2)
Collars and Paylaters
In Part 1, we looked at two extreme approaches to hedging a natural long position. A short forward hedge
preserves the commodity producers current income level but eliminated all additional pro

9. Comparative Option Pricing
European vs American Options
Suppose we own a European call option on an asset at strike price K expiring in T years. The payment of the
premium gives us the right to purchase the underlying asset T years from today.
Now supp

7. Interest Rate Forwards and Futures
U.S. Treasury "Bonds"
The U.S. Treasury issues securities with maturities of 3 months, 6 months, 1 year, 2 years, 3 years, 5 years, 7
years, 10 years, 20 years and 30 years. 3-month, 6-month and 1-year securities make

7. Duration and Convexity
As we saw in some preliminary calculations in the last section, bond prices are sensitive to changes in yield.
Measuring this sensitivity is a vital task when balancing and hedging a fixed income portfolio.
Duration, in various f

5. Forwards, Futures and Currency Transactions
Outright Purchases, Prepaid Forwards and Forwards
Most often, an investor who wants to purchase an asset will pay immediately and take position in 0-3 days. In
the case of a stock or stock index, we will refe

12. Black-Scholes Formula (Introduction)
The Black-Scholes formula calculates prices for European-style options. The formula and the resulting partial
sensitivities are used by most industry participants.
In this chapter, we will learn the formula and see