Understanding Derivatives Markets and Risk Management

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CORPORATE
FINANCIAL
THEORY
Lecture 11
Risk Management
Risk Management
Lloyds of London
Ship building
1840s Midwest USA farmers
1848 Chicago Board of Trade (CBOT) for grain
1874 Chicago Produce Exchange for butter/eggs
1919 Chicago Mercantile Exchange (CME)
Jet Fuel
Land options
History of Derivatives
 
 
Derivatives
Insurance
Risk Management
Lloyds
Ship Building
Jet Fuel
Cost Predictability
Revenue Certainty
Stocks (
example
)
Bonds
Indices
Commodities (
examples for metal and ag.
)
Currencies
Weather
Carbon emissions
Radio bandwidth
Underlying Assets
Futures
Options / Warrant
Future options
Swaps
Mortgage backed securities
Forward Rate Agreement
Convertible bonds
Real options
Derivative Instruments
OTC vs. Exchanges
Eurex (E-X)
Chicago Board Options Exchange (CBOE)
Chicago Mercantile Exchange (CME)
Chicago Board of Trade (CBOT)
New York Mercantile Exchange (NYMEX)
Hong Kong Futures Exchange (HKFE)
Derivative Markets
Source: Bank for International Settlements
https://stats.bis.org/statx/srs/tseries/OTC_DERIV/H:A:A:B:5J:
A:5J:A:TO1:TO1:A:A:3:C?t=D5.1&p=20172&x=DER_RISK.3
.CL_MARKET_RISK.J:T:E:B:D:U&o=w:20121.20172,s:stc,t:
Derivatives%20risk%20category
Notational outstanding of OTC derivatives ($ trillion)
 
Derivative Markets
Source: Bank for International Settlements
Exchange Options on OTC derivatives Q2 2022 = $53,925 billion
Derivative Markets
Source: Bank for International Settlements
https://stats.bis.org/statx/srs/tseries/OTC_DERIV/H:A:A:B:5J:A:5J:A:TO1:TO1:A:A:3:C?t=D
5.1&p=20172&x=DER_RISK.3.CL_MARKET_RISK.J:T:E:B:D:U&o=w:20121.20172,s:stc,t:
Derivatives%20risk%20category
Derivative Markets
Source: WFE/IOMA Derivatives Market Survey 2021
Derivative Markets
Source: WFE/IOMA Derivatives Market Survey 2021
Derivative Markets
Source: WFE/IOMA Derivatives Market Survey 2021
Derivative Markets
Source: WFE/IOMA Derivatives Market Survey 2018
Derivative Markets
undefined
Source: WFE/IOMA Derivatives Market Survey 2021
Arbitrage
Speculation
Hedging
Derivative Uses
Derivatives are financial instruments whose price and value derive
from the value of the underlying assets or other variables (ISDA)
Derivatives are a “zero sum game”
Example: Insurance
Derivatives Definition
 
 
Derivatives & Options
Historical Topics (Internal to the Corp)
1 - Capital Budgeting (
Investment
)
2 - Capital Structure (
Financing
)
Today
We are leaving Internal Corporate Finance
We are going to Wall St & “Capital Markets”
Options - financial and corporate
Options are a type of derivative
 
 
Options
 
 
Options
Terminology
Derivatives
 - Any financial instrument that is derived from another. (e.g.. options,
warrants, futures, swaps, etc.)
Option
 - Gives the holder the right to buy or sell a security at a specified price
during a specified period of time.
Call Option
 - The right to 
buy 
a security at a specified price within a specified
time.
Put Option
 - The right to 
sell 
a security at a specified price within a specified time.
Option Premium
 - The price paid for the option, above the price of the underlying
security.
Intrinsic Value
 - Diff between the strike price and the stock price
Time Premium
 - Value of option above the intrinsic value
 
 
Options
Terminology
Exercise Price
 - (Striking Price) The price at which you buy or sell the security.
Expiration Date
 - The last date on which the option can be exercised.
American Option
 - Can be exercised at any time prior to and including the
expiration date.
European Option
 - Can be exercised only on the expiration date.
All options “usually” act like European options because you make more money
if you sell the option before expiration (vs. exercising it).
                        3  vs. 70-68=2
 
 
Option Value
The value of an option at expiration is a function of the stock price and the exercise price.
 
 
Option Value
The value of an option at expiration is a function of the stock price and the exercise price.
Example - Option values given a exercise price of $85
 
 
Options
CBOE Success
1 - Creation of a central options market place.
2 - Creation of Clearing Corp - the guarantor of all trades.
3 - Standardized expiration dates - 3rd Friday
4 - Created a secondary market
 
 
Option Value
 
Components of the Option Price
1 - Underlying stock price
2 - Striking or Exercise price
3 - Volatility of the stock returns (standard deviation of annual returns)
4 - Time to option expiration
5 - Time value of money (discount rate)
 
 
Black-Scholes Option Pricing Model
Black-Scholes Option Pricing Model
Option Value
 
 
O
C
- Call Option Price
P
 
 - Stock Price
N(d
1
)
 - Cumulative normal density  function of (d
1
)
PV(EX) 
 - Present Value of Strike or Exercise price
N(d
2
) 
- Cumulative normal density function of (d
2
)
r
 - discount rate (90 day comm paper rate or risk free rate)
t
 - time to maturity of option (as % of year)
v
 - volatility - annualized standard deviation of daily returns
Black-Scholes Option Pricing Model
 
 
Put - Call Parity
Put Price = Call + EX - P - Carrying Cost + Div.
or
Put =  Call + EX(e
-rt
)– P
s 
- Carrying Cost + Div.
Carrying cost = r x EX x t
 
 
Put - Call Parity
Example
 
ABC is selling at $41 a share.  A six month May 40 Call is
selling for $4.00. If a May $ .50 dividend is expected and
r=10%, what is the put price?
O
P
 = O
C
 + EX - P - Carrying Cost + Div.
O
P
  
=
 
4  +  40 -  41  -  (.10x 40 x .50) + .50
O
P
 =
 
3  -  2  +  .5
O
p
 =  $1.50
 
 
Warrants & Convertibles
Review Topics (not going over in class)
Warrant - a call option with a longer time to expiration.
Value a warrant as an option, plus factor in dividends
and dilution.
Convertible - Bond with the option to exchange it for
stock.  Value as a regular bond + a call option.
Won’t require detailed valuation - general concept on
valuation + new option calc and old bond calc.
 
 
Option Strategies
Option Strategies are viewed via charts.
How do you chart an option?
Stock Price
Profit
Loss
 
 
Long Stock   Bought stock @ Ps = 100
Option Strategies
 
 
Option Strategies
Long Call   Bought Call @ Oc = 3 S=27 Ps=30
 
 
Option Strategies
Short Call  Sold Call @ Oc = 3 S=27 Ps=30
 
 
Option Strategies
Long Put = Buy Put @ Op = 2 S=15 Ps=13
 
 
Option Strategies
Short Put = Sell Put @ Op = 2 S=15 Ps=13
 
 
Option Strategies
Synthetic Stock = Short Put & Long Call @
Oc = 1.50  Op=1.50 S=27 Ps=27
P
/
L
P
s
2
7
3
0
2
4
-
1
.
5
0
+
1
.
5
0
 
 
Option Strategies
Synthetic Stock = Short Put & Long Call @
Oc = 1.50  Op=1.50 S=27 Ps=27
P
/
L
P
s
2
7
3
0
2
4
-
1
.
5
0
+
1
.
5
0
 
 
Option Strategies
Synthetic Stock = Short Put & Long Call @
Oc = 1.50  Op=1.50 S=27 Ps=27
 
 
Option Strategies
Why?
1 - Reduce risk - butterfly spread
2 - Gamble - reverse straddle
3 - Arbitrage - as in synthetics
Arbitrage - If the price of a synthetic stock is different
than the price of the actual stock, an opportunity for
profit exists.
Recall discussion on Real Options
Dilution
Expanding the binomial model to allow more possible price changes
         1 step
  
       2 steps
  
     4 steps
 
    (2 outcomes)
  
  (3 outcomes)
  
 (5 outcomes)
     
etc. etc.
  
Binomial vs. Black Scholes
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Explore the history of derivatives, the role of derivatives in insurance and risk management, underlying assets, derivative instruments, derivative markets, and the significant notational outstanding of OTC derivatives. Discover key players and exchanges in the derivative markets and the vast scale of options in OTC derivatives as reported by the Bank for International Settlements.


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  1. CORPORATE FINANCIAL THEORY Lecture 11

  2. History of Derivatives Risk Management Lloyds of London Ship building 1840s Midwest USA farmers 1848 Chicago Board of Trade (CBOT) for grain 1874 Chicago Produce Exchange for butter/eggs 1919 Chicago Mercantile Exchange (CME) Jet Fuel Land options

  3. Derivatives Insurance Risk Management Lloyds Ship Building Jet Fuel Cost Predictability Revenue Certainty

  4. Underlying Assets Stocks (example) Bonds Indices Commodities (examples for metal and ag.) Currencies Weather Carbon emissions Radio bandwidth

  5. Derivative Instruments Futures Options / Warrant Future options Swaps Mortgage backed securities Forward Rate Agreement Convertible bonds Real options

  6. Derivative Markets OTC vs. Exchanges Eurex (E-X) Chicago Board Options Exchange (CBOE) Chicago Mercantile Exchange (CME) Chicago Board of Trade (CBOT) New York Mercantile Exchange (NYMEX) Hong Kong Futures Exchange (HKFE)

  7. Derivative Markets Notational outstanding of OTC derivatives ($ trillion) 1600 1400 1200 1000 800 600 400 Source: Bank for International Settlements https://stats.bis.org/statx/srs/tseries/OTC_DERIV/H:A:A:B:5J: A:5J:A:TO1:TO1:A:A:3:C?t=D5.1&p=20172&x=DER_RISK.3 .CL_MARKET_RISK.J:T:E:B:D:U&o=w:20121.20172,s:stc,t: Derivatives%20risk%20category 200 0

  8. Derivative Markets Source: Bank for International Settlements Exchange Options on OTC derivatives Q2 2022 = $53,925 billion

  9. Derivative Markets Source: Bank for International Settlements https://stats.bis.org/statx/srs/tseries/OTC_DERIV/H:A:A:B:5J:A:5J:A:TO1:TO1:A:A:3:C?t=D 5.1&p=20172&x=DER_RISK.3.CL_MARKET_RISK.J:T:E:B:D:U&o=w:20121.20172,s:stc,t: Derivatives%20risk%20category

  10. Derivative Markets Source: WFE/IOMA Derivatives Market Survey 2021

  11. Derivative Markets Source: WFE/IOMA Derivatives Market Survey 2021

  12. Derivative Markets Source: WFE/IOMA Derivatives Market Survey 2021

  13. Derivative Markets Source: WFE/IOMA Derivatives Market Survey 2018

  14. Source: WFE/IOMA Derivatives Market Survey 2021

  15. Derivative Uses Arbitrage Speculation Hedging

  16. Derivatives Definition Derivatives are financial instruments whose price and value derive from the value of the underlying assets or other variables (ISDA) Derivatives are a zero sum game Example: Insurance

  17. Derivatives & Options Historical Topics (Internal to the Corp) 1 - Capital Budgeting (Investment) 2 - Capital Structure (Financing) Today We are leaving Internal Corporate Finance We are going to Wall St & Capital Markets Options - financial and corporate Options are a type of derivative

  18. Options Long Short Call option Right to buy asset Obligation to sell asset Put option Right to sell asset Obligation to buy asset

  19. Options Terminology Derivatives - Any financial instrument that is derived from another. (e.g.. options, warrants, futures, swaps, etc.) Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time. Call Option - The right to buy a security at a specified price within a specified time. Put Option - The right to sell a security at a specified price within a specified time. Option Premium - The price paid for the option, above the price of the underlying security. Intrinsic Value - Diff between the strike price and the stock price Time Premium - Value of option above the intrinsic value

  20. Options Terminology Exercise Price - (Striking Price) The price at which you buy or sell the security. Expiration Date - The last date on which the option can be exercised. American Option - Can be exercised at any time prior to and including the expiration date. European Option - Can be exercised only on the expiration date. All options usually act like European options because you make more money if you sell the option before expiration (vs. exercising it). 3 vs. 70-68=2

  21. Option Value The value of an option at expiration is a function of the stock price and the exercise price.

  22. Option Value The value of an option at expiration is a function of the stock price and the exercise price. Example - Option values given a exercise price of $85 Stock Pric e $60 70 80 90 100 110 Call Value 0 0 0 5 15 25 Put Value 25 15 5 0 0 0

  23. Options CBOE Success 1 - Creation of a central options market place. 2 - Creation of Clearing Corp - the guarantor of all trades. 3 - Standardized expiration dates - 3rd Friday 4 - Created a secondary market

  24. Option Value Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate)

  25. Option Value Black-Scholes Option Pricing Model ) = ( ) ( ) ( OC N d P N d PV EX 1 2

  26. Black-Scholes Option Pricing Model ) = ( ) ( ) ( OC N d P N d PV EX 1 2 OC- Call Option Price P- Stock Price N(d1) - Cumulative normal density function of (d1) PV(EX) - Present Value of Strike or Exercise price N(d2) - Cumulative normal density function of (d2) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns

  27. Put - Call Parity Put Price = Call + EX - P - Carrying Cost + Div. or Put = Call + EX(e-rt) Ps - Carrying Cost + Div. Carrying cost = r x EX x t

  28. Put - Call Parity Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $ .50 dividend is expected and r=10%, what is the put price? OP = OC + EX - P - Carrying Cost + Div. OP=4 + 40 - 41 - (.10x 40 x .50) + .50 OP =3 - 2 + .5 Op = $1.50

  29. Warrants & Convertibles Review Topics (not going over in class) Warrant - a call option with a longer time to expiration. Value a warrant as an option, plus factor in dividends and dilution. Convertible - Bond with the option to exchange it for stock. Value as a regular bond + a call option. Won t require detailed valuation - general concept on valuation + new option calc and old bond calc.

  30. Option Strategies Option Strategies are viewed via charts. How do you chart an option? Profit Stock Price Loss

  31. Option Strategies Long Stock Bought stock @ Ps = 100 +10 P/L Ps 90 100 110 -10

  32. Option Strategies Long Call Bought Call @ Oc = 3 S=27 Ps=30 +6 P/L Ps 36 27 30 -3

  33. Option Strategies Short Call Sold Call @ Oc = 3 S=27 Ps=30 +3 P/L Ps 36 27 30 -6

  34. Option Strategies Long Put = Buy Put @ Op = 2 S=15 Ps=13 +3 P/L Ps 15 10 13 -2

  35. Option Strategies Short Put = Sell Put @ Op = 2 S=15 Ps=13 +2 P/L Ps 15 10 13 -3

  36. Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 +1.50 P/L Ps 30 24 27 -1.50

  37. Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 +1.50 P/L Ps 30 24 27 -1.50

  38. Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 +1.50 P/L Ps 30 24 27 -1.50

  39. Option Strategies Why? 1 - Reduce risk - butterfly spread 2 - Gamble - reverse straddle 3 - Arbitrage - as in synthetics Arbitrage - If the price of a synthetic stock is different than the price of the actual stock, an opportunity for profit exists. Recall discussion on Real Options

  40. Dilution + EX V Nq + = Share price after exercise N Nq 1 = Dilution factor + 1 # of new shares # of outstandin shares g

  41. Binomial vs. Black Scholes Expanding the binomial model to allow more possible price changes 1 step 2 steps (3 outcomes) etc. etc. 4 steps (5 outcomes) (2 outcomes)

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