风险管理与金融衍生品
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Underlying asset put or call
Derivative call or put
Forward Contracts
an agreement to buy or sell at a specified future time a certain amount of an underlying asset at a specified price.
Risk Management
risk management - underlying assets
Method – hedging - using financial derivatives i.e. holds two positions of equal amounts but opposite directions, one in the underlying markets, and the other in the derivatives markets, simultaneously.
Situation II: The stock $66.0 on 8/22.
Strategy A Return =(660-666)/666*100%=-0.9%
Strategy B loss all investment Return = - 100%
Chapter 2
Arbitrage-Free Principle
Investment
At time 0, invest S When t=T,
Payoff = ST S0 Return = (ST S0)/S0
For a risky asset, the return is uncertain, i.e., S is a random variable
Option Pricing
risky asset’s price is a random variable
the price of any option derived from risky asset is also random
the price also depends on time t
Future
VT
Long position
0
K ST
VT ST K
Short position
VT
0
K
ST
VT KST
Futures
same as a forward contract have evolved from standardization of
forward contracts differences –
Purchase a call option to buy £1000,000 with $1,600,000 90 days later. A pays a premium of $64,000 (4%)
Speculator Example
Stock A is $66.6 on April 30, may grow A speculator has 2 plans
there exists a function V ( S , t ) such that
Vt V(St,t) known
VT ((SKTSKT))
call put
How to find out pV(S0,0)?
Types of Traders
Hedger - to invest on both sides to avoid loss Speculator - to take action characterized by
Options
an agreement that the holder can buy from (or sell to) the seller (the buyer) of the option at a specified future time a certain amount of an underlying asset at a specified price. But the holder is under no obligation to exercise the contract.
Hedger Example
In 90 days, A pays B £1000,000 To avoid risk, A has 2 plans
Purchase a forward contract to buy £1000,000 with $1,650,000 90 days later
Financial Derivatives
Many forms of financial derivatives instruments exist in the financial markets. Among them, the 3 most fundamental financial derivatives instruments: Forward contracts Future Options If the underlying assets are stocks, bonds etc., then the corresponding risk management instruments are: stock futures, bond futures, etc..
Option Types
European options - can be exercised only on the expiration date.
American options - can be exercised on or prior to the expiration date.
Other options – Asia option etc.
Total Gain of an Option
PT
Call option
PT
put option
0K p
ST
0
K
ST
PT(STK)p
PT(KST)p
百度文库
[Total gain]= [Gain of the option at expiration]-[Premium]
an agreement to replace a risk by a certainty traded OTC long position - the buyer in a contract short position - the seller in a contract delivery price - the specified price maturity - specified future time
futures are generally traded on an exchange a future contract contains standardized articles the delivery price on a future contract is generally
determined on an exchange, and depends on the market demands
a right, no obligation the holder has to pay premium for this right is a contingent claim
Has a much higher level of leverage
Two Options
A call option - a contract to buy at a
Financial Market
Two Kinds of Assets
Risk free asset
Bond
Risky asset
Stocks Options ….
Portfolio – an investment strategy to hold different assets
A Portfolio
a risk-free asset B n risky assets Si Sit,i1,...n
n
a portfolio B i S i , i1 , i portion of the cor. Asset
,1,...n is called a investment strategy
willing to risk with one's money by frequently buying and selling derivatives (futures, options) for the prospect of gaining from the frequent price changes. Arbitrage - based on observations of the same kind of risky assets, taking advantage of the price differences between markets, the arbitrageur trades simultaneously at different markets to gain riskless instant profits
Risks in Financial Market
asset (stocks, …), interest rate, foreign exchange, credit, commodity, …………
Two attitudes toward risks
Risk aversion Risk seeking
specified future time a certain amount of an underlying asset at a specified price
A put option - a contract to sell at a
specified future time a certain amount of an underlying asset at a specified price. exercise price - the specified price expiration date - the specified date exercise - the action to perform the buying or selling of the asset according to the option contract
on time t, wealth:
n
Vt()t tBt S it it i1
Arbitrage Opportunity
Self-financing - during [0, T] no add or withdraw fund
Arbitrage Opportunity - A self-financing investment,
buys 10,000 shares with $666,000 on April 30
pays a premium of $39,000 USD to purchase a call option to buy 10,000 shares at the strike price $68.0 per share on August 22
liang_jin@mail.tongji.edu.cn
Chapter 1
Risk Management &
Financial Derivative
Risk
Risk - uncertainty of the outcome
bring unexpected gains cause unforeseen losses
Speculator Example cont.
Situation I: The stock $73.0 on 8/22.
Strategy A Return =(730-666)/666*100%=9.6%
Strategy B Return =(730-680-39)/39*100%=28.2%
Underlying asset put or call
Derivative call or put
Forward Contracts
an agreement to buy or sell at a specified future time a certain amount of an underlying asset at a specified price.
Risk Management
risk management - underlying assets
Method – hedging - using financial derivatives i.e. holds two positions of equal amounts but opposite directions, one in the underlying markets, and the other in the derivatives markets, simultaneously.
Situation II: The stock $66.0 on 8/22.
Strategy A Return =(660-666)/666*100%=-0.9%
Strategy B loss all investment Return = - 100%
Chapter 2
Arbitrage-Free Principle
Investment
At time 0, invest S When t=T,
Payoff = ST S0 Return = (ST S0)/S0
For a risky asset, the return is uncertain, i.e., S is a random variable
Option Pricing
risky asset’s price is a random variable
the price of any option derived from risky asset is also random
the price also depends on time t
Future
VT
Long position
0
K ST
VT ST K
Short position
VT
0
K
ST
VT KST
Futures
same as a forward contract have evolved from standardization of
forward contracts differences –
Purchase a call option to buy £1000,000 with $1,600,000 90 days later. A pays a premium of $64,000 (4%)
Speculator Example
Stock A is $66.6 on April 30, may grow A speculator has 2 plans
there exists a function V ( S , t ) such that
Vt V(St,t) known
VT ((SKTSKT))
call put
How to find out pV(S0,0)?
Types of Traders
Hedger - to invest on both sides to avoid loss Speculator - to take action characterized by
Options
an agreement that the holder can buy from (or sell to) the seller (the buyer) of the option at a specified future time a certain amount of an underlying asset at a specified price. But the holder is under no obligation to exercise the contract.
Hedger Example
In 90 days, A pays B £1000,000 To avoid risk, A has 2 plans
Purchase a forward contract to buy £1000,000 with $1,650,000 90 days later
Financial Derivatives
Many forms of financial derivatives instruments exist in the financial markets. Among them, the 3 most fundamental financial derivatives instruments: Forward contracts Future Options If the underlying assets are stocks, bonds etc., then the corresponding risk management instruments are: stock futures, bond futures, etc..
Option Types
European options - can be exercised only on the expiration date.
American options - can be exercised on or prior to the expiration date.
Other options – Asia option etc.
Total Gain of an Option
PT
Call option
PT
put option
0K p
ST
0
K
ST
PT(STK)p
PT(KST)p
百度文库
[Total gain]= [Gain of the option at expiration]-[Premium]
an agreement to replace a risk by a certainty traded OTC long position - the buyer in a contract short position - the seller in a contract delivery price - the specified price maturity - specified future time
futures are generally traded on an exchange a future contract contains standardized articles the delivery price on a future contract is generally
determined on an exchange, and depends on the market demands
a right, no obligation the holder has to pay premium for this right is a contingent claim
Has a much higher level of leverage
Two Options
A call option - a contract to buy at a
Financial Market
Two Kinds of Assets
Risk free asset
Bond
Risky asset
Stocks Options ….
Portfolio – an investment strategy to hold different assets
A Portfolio
a risk-free asset B n risky assets Si Sit,i1,...n
n
a portfolio B i S i , i1 , i portion of the cor. Asset
,1,...n is called a investment strategy
willing to risk with one's money by frequently buying and selling derivatives (futures, options) for the prospect of gaining from the frequent price changes. Arbitrage - based on observations of the same kind of risky assets, taking advantage of the price differences between markets, the arbitrageur trades simultaneously at different markets to gain riskless instant profits
Risks in Financial Market
asset (stocks, …), interest rate, foreign exchange, credit, commodity, …………
Two attitudes toward risks
Risk aversion Risk seeking
specified future time a certain amount of an underlying asset at a specified price
A put option - a contract to sell at a
specified future time a certain amount of an underlying asset at a specified price. exercise price - the specified price expiration date - the specified date exercise - the action to perform the buying or selling of the asset according to the option contract
on time t, wealth:
n
Vt()t tBt S it it i1
Arbitrage Opportunity
Self-financing - during [0, T] no add or withdraw fund
Arbitrage Opportunity - A self-financing investment,
buys 10,000 shares with $666,000 on April 30
pays a premium of $39,000 USD to purchase a call option to buy 10,000 shares at the strike price $68.0 per share on August 22
liang_jin@mail.tongji.edu.cn
Chapter 1
Risk Management &
Financial Derivative
Risk
Risk - uncertainty of the outcome
bring unexpected gains cause unforeseen losses
Speculator Example cont.
Situation I: The stock $73.0 on 8/22.
Strategy A Return =(730-666)/666*100%=9.6%
Strategy B Return =(730-680-39)/39*100%=28.2%