DERIVATIVES
Introduction
 Cash market strategies are limited
 Long (asset is expected to appreciate)
 Short (asset is expected to depreciate)
 Alternative views
 Appreciation within a range
 Depreciation within a range
 Appreciation outside a range
 Depreciation outside a range
 Appreciation with protection against depreciation
 …..
Derivatives
 Securities whose price is derived from other assets
 Payoff depends on the value of other securities
 Examples
 Futures futures
 VIX futures
 Call options
 Put options
 Digital options
 Collar
 ……..
Option Contract
 Call option gives the buyer the right (not the obligation)
to buy an asset for a certain price before some specified
time
 Put option gives the buyer the right (not the obligation)
sell an asset for a certain price before some specified
time
 Exchange Traded
 Over The Counter (OTC)
Underlying Assets
 Equity
 Commodity
 Foreign Exchange
 Indexes
 S&P
 Volatility VIX
 Futures
 Interest rate





Cap
Floor
Collar
Corridor
Swaps (flat forward)
Payoff Profile & Profit of Long Call
 Payoff of a long Call option at expiration with strike of S
with X the price of underlying = Max ( 0, X –S )
$
payoff
S
Profit & Loss (P&L)
Asset Price
Payoff Profile & Profit of Short Call
 Payoff of a short Call option at expiration with strike of S
with X the price of underlying = Min ( 0, S – X )
$
S
Asset Price
Payoff
Profit & Loss (P&L)
Payoff Profile & Profit of Long Put
 Payoff of a long Put option at expiration with strike of S
with X the price of underlying = Max ( 0, S - X )
$
payoff
S
Asset Price
Profit & Loss (P&L)
Payoff Profile & Profit of Short Put
 Payoff of a short Put option at expiration with strike of S
with X the price of underlying = Min ( 0, X – S )
$
Profit & Loss (P&L)
S
Asset Price
Payoff
Option vs Stock
 Option is a leveraged position in stock
 Stock price=$90
 Premium of one year call with strike of $90 = $10
 Interest rate = 2%
 Funds to invest = $9,000
 Investment Alternatives
 Portfolio A: Buy 100 shares of stock (unlevered position) for
$9,000
 Portfolio B: Buy 900 calls (highly levered position)
 Portfolio C: Purchase 100 calls, invest remaining $8,000 at 2%
Values of Portfolios
 Values of portfolios for different stock price in one year
Portfolio
$85
$90
$95
$100
$105
$110
A)
100 shares
$8500
$9000
$9500
$10,000
$10,500
$11,000
B)
900 Calls
0
0
$4,500
$9,000
$13,500
$18,000
C)
100 Call +
Deposit
$8160
$8160
$8,600
$9,160
$9,660
$10,160
Performance of Portfolios
 Values of portfolios for different stock price in one year
Portfolio
$85
$90
$95
$100
$105
$110
A)
100 shares
-5.56%
0.00%
5.56%
11.11%
16.67%
22.22%
B)
900 Calls
-100%
-100%
-50%
0%
50%
100%
C)
100 Call +
Deposit
-9.33%
-9.33%
-3.78%
1.78%
7.33%
12.89%
Option Strategies
 Combination of options can be used to achieve certain
investment objectives are not available using the cash market
Protective Put

Long Stock, Long Put
Stock
Put Payoff
Performance of Protective Put + Stock

Buying insurance on stock position
Stock
Put Payoff
Covered Call

Long Stock, Short Call
Stock
Short Call Payoff
Performance of Covered Call
 Long Stock, Short Call
Stock
Put Payoff
Long Straddle

Long Call, Long Put with same strike
Long Straddle Payoff

Long Call, Long Put with same strike
Short Straddle

Short Call, Short Put with same strike
Short Straddle Payoff
 Short Call, Short Put with same strike
Long Strangle

Long Call, Long Put with different strikes
Long Strangle Payoff

Long Call, Long Put with different strikes
Short Strangle

Short Call, Short Put with different strikes
Short Straddle Payoff

Short Call, Short Put with different strikes
Collar
 Long Stock, Short Call, Long Put with different strikes
Collar Payoff
 Long Stock, Short Call, Long Put with different strikes
Put-Call-Parity
 C = P + S – PV(X)