FINC416:
Derivative Securities &
Risk Management
Jay Coughenour
309 Purnell Hall
[email protected]
http:/www.buec.udel.edu/coughenj/
1-1
What is risk management?
Risk management is the process of reducing or
eliminating uncertainty.
Business risk
Options
9-1
Put-Call Parity
From Chapter 3
For European options with the same strike price
and time to expiration the parity relationship is
Call put = PV (forward price strike price)
or
C ( K , T ) P( K , T ) = PV0 ,T ( F0 ,T K ) = e rT ( F0 ,T K )
Int
Some other swap varieties
8-1
Plain vanilla swaps
One leg of swap has a fixed rate or
price, and first payment occurs 1 period
from date of swap initiation
We have considered plain vanilla:
Commodity swaps
Interest rate swaps
Currency swaps
8-2
Other sw
Swaps
8-1
Introduction to Swaps
A swap is a contract calling for an
exchange of payments, on one or more
dates, determined by the difference in
two prices
A swap provides a means to hedge a
stream of risky payments
A single-payment swap is the same thi
Hedging Interest Rate Risk:
FRAs, Eurodollars, & Duration
6-1
Forward Rate Agreements
FRAs are contracts that guarantee a borrowing or
lending rate on a given notional principal amount from
time t1 to time t2. The terms are agreed upon today, t0.
FRAs a
Interest Rate Transformations
6-1
Notation
r0(t1,t2) is the interest rate from time t1 to t2
prevailing at time t0 on a zero coupon bond
r0(0,1) is the current one-year rate
r0(0,2) is the current two-year rate
r0(1,2) is the current one-year forward rat
Natural Gas & Weather Markets
6-1
Natural Gas Market Characteristics
Started trading in 1990
Probably the 2nd most active energy
contract, behind Light Sweet WTI.
Gas is a market with steady production
but large swings in demand
Leads to large and pred
Commodity Forwards:
with some focus on crude oil
6-1
Same concept applies
In general, commodity forward prices
can be found using the same economic
principles used for financial forward
prices:
F0 ,T = S0 e
( r )T
but the details will be different
6-2
F
Equity Index Futures and
Currency Futures
5-1
Commonalities across contracts
Equity and currency contracts are similar
in many respects:
Cash-settled
Priced with underlying paying a continuous
dividend yield:
Therefore, they are priced using the same
equ
Pricing Financial Forwards & Futures
5-1
Outline for today
1. Continuous compounding
2. Pricing Forwards and Futures
3. Review of Assignment for Quiz
5-2
Continuous Compounding
Continuously compounded rates are
used to a great extent with derivatives
Basic Risk Management
4-1
The Producers Perspective
A producer selling a risky commodity has a
natural long position in this commodity
When the price of the commodity , the
firms profit
(assuming costs are fixed)
Some strategies to hedge profit
Selling
Basic Hedging Strategies and
Payoff Replications
3-1
Basic Insurance Strategies
Options can be used to
Buy insurance
Used to insure long positions (floors)
Used to insure short positions (caps)
In both cases you pay a premium to limit losses
Sell insur
2-1
Overview of contracts
2-2
Spot market and Forward
Contracts
S pot Market Transaction
2-3
The purchase/sale of an asset for immediate
delivery.
Both the cash and asset change hands
immediately
The spot price (S) is the price at which this
transaction f
Binomial Option Pricing I
9-1
The problem
Recall
CT = max[0, ST - X]
implies that C is a function of S and X.
The problem:
What is C0?
From above,
C0 = Cte-rt
C0 = max[0, Ste-rt - Xe-rt]
C0 = max[0, S0 - Xe-rt]
implies that C is a function of S, X, r,