期权、期货及其他衍生产品课件1金融工程学
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1.23
1. Oil: An Arbitrage Opportunity?
Suppose that: - The spot price of oil is US$19 - The quoted 1-year futures price of oil is US$25 - The 1-year US$ interest rate is 5% per annum - The storage costs of oil are 2% per annum Is there an arbitrage opportunity?
1.16
上海期货交易所 http://www.shfe.com.cn/ 大连商品交易所 http://www.dce.com.cn/portal/template/index.html 郑州商品交易所 http://www.czce.com.cn/portal/index.htm 渤海商品交易所 http://www.boce.cn/web/index.jsp 中国金融期货交易所 http://www.cffex.com.cn/
1.8
Forward Price
The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities
http://www.bis.org/publ/rpfxf10t.pdf
1.6
Ways Derivatives are Used
To hedge risks To speculate (take a view on the future direction of the market) To lock in an arbitrage profit To change the nature of a liability To change the nature of an investment without incurring the costs of selling one portfolio and buying another
1.18
1. Gold: An Arbitrage Opportunity?
Suppose that: The spot price of gold is US$300 The 1-year forward price of gold is US$340 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
1.6253
1.6192 1.6100
1.11
Example (page 4)
ቤተ መጻሕፍቲ ባይዱ
On June 3, 2003 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.6100 This obligates the corporation to pay $1,610,000 for £1 million on December 3, 2003 What are the possible outcomes?
OTC Exchange
Jun-01
Jun-02
Jun-03
Jun-04
Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market
金融工程
(美)salih n. neftci(著) | 陈典发(译) | 人民邮电出版社
1.1
Introduction
Chapter 1
1.2
The Nature of Derivatives
A derivative（衍生产品） is an instrument whose value depends on the values of other more basic underlying variables
1.14
Futures Contracts (page 6)
Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange
1.19
Borrow $300 at 5% for one year Buy one ounce of gold Enter into a short forward contract to sell the gold for $340 in one year 340-300-300×5%=$25
1.10
Foreign Exchange Quotes for GBP June 3, 2003 (See page 4)
Bid 1.6281 Offer 1.6285
Spot
1-month forward
3-month forward 6-month forward
1.6248
1.6187 1.6094
1.21
Sell the gold for $300 per ounce Invest the proceeds at 5% Enter into a long forward contract to repurchase the gold in one year for $300 per ounce
1.3
Examples of Derivatives
• Futures Contracts（期货合约） • Forward Contracts（远期合约） • Swaps（互换） • Options（期权）
1.4
Derivatives Markets
Exchange traded（场内交易）
1.22
The Forward Price of Gold
If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r )T where r is the 1-year (domestic currency) riskfree rate of interest. In our examples, S = 300, T = 1, and r =0.05 so that F = 300(1+0.05) = 315
1.9
Terminology
The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position
1.15
Exchanges Trading Futures
Chicago Board of Trade（芝加哥期货交易所） Chicago Mercantile Exchange（芝加哥商品交易
所）
LIFFE (London)（伦敦国际金融期货和期权交易所） Eurex (Europe)（欧洲期权和期货交易所） BM&F (Sao Paulo, Brazil) TIFFE (Tokyo)（日本东京国际金融期货交易所） and many more (see list at end of book)
1.5
Over-the-counter (OTC)（场外交易）
Size of OTC and Exchange Markets
(Figure 1.1, Page 3)
240 Size of Market ($ 220 trillion) 200 180 160 140 120 100 80 60 40 20 0 Jun-98 Jun-99 Jun-00
1.24
2. Oil: Another Arbitrage Opportunity?
Suppose that: - The spot price of oil is US$19 - The quoted 1-year futures price of oil is US$16 - The 1-year US$ interest rate is 5% per annum - The storage costs of oil are 2% per annum Is there an arbitrage opportunity?
1.7
Forward Contracts
Forward contracts are similar to futures except that they trade in the over-thecounter market Forward contracts are particularly popular on currencies and interest rates
Traditionally exchanges have used the openoutcry system, but increasingly they are switching to electronic trading Contracts are standard there is virtually no credit risk A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers Contracts can be non-standard and there is some small amount of credit risk
1.20
2. Gold: Another Arbitrage Opportunity?
Suppose that: - The spot price of gold is US$300 - The 1-year forward price of gold is US$300 - The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
1.12
Profit from a Long Forward Position
Profit
K
Price of Underlying at Maturity, ST
ST K
1.13
Profit from a Short Forward Position
Profit
K ST
K
Price of Underlying at Maturity, ST
1.17
Examples of Futures Contracts
Agreement to: buy 100 oz. of gold @ US$400/oz. in December (NYMEX) （纽约商品交易所） sell £62,500 @ 1.5000 US$/£ in March (CME)（芝加哥商品交易所） sell 1,000 bbl. of oil @ US$20/bbl. in April (NYMEX)
1. Oil: An Arbitrage Opportunity?
Suppose that: - The spot price of oil is US$19 - The quoted 1-year futures price of oil is US$25 - The 1-year US$ interest rate is 5% per annum - The storage costs of oil are 2% per annum Is there an arbitrage opportunity?
1.16
上海期货交易所 http://www.shfe.com.cn/ 大连商品交易所 http://www.dce.com.cn/portal/template/index.html 郑州商品交易所 http://www.czce.com.cn/portal/index.htm 渤海商品交易所 http://www.boce.cn/web/index.jsp 中国金融期货交易所 http://www.cffex.com.cn/
1.8
Forward Price
The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities
http://www.bis.org/publ/rpfxf10t.pdf
1.6
Ways Derivatives are Used
To hedge risks To speculate (take a view on the future direction of the market) To lock in an arbitrage profit To change the nature of a liability To change the nature of an investment without incurring the costs of selling one portfolio and buying another
1.18
1. Gold: An Arbitrage Opportunity?
Suppose that: The spot price of gold is US$300 The 1-year forward price of gold is US$340 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
1.6253
1.6192 1.6100
1.11
Example (page 4)
ቤተ መጻሕፍቲ ባይዱ
On June 3, 2003 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.6100 This obligates the corporation to pay $1,610,000 for £1 million on December 3, 2003 What are the possible outcomes?
OTC Exchange
Jun-01
Jun-02
Jun-03
Jun-04
Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market
金融工程
(美)salih n. neftci(著) | 陈典发(译) | 人民邮电出版社
1.1
Introduction
Chapter 1
1.2
The Nature of Derivatives
A derivative（衍生产品） is an instrument whose value depends on the values of other more basic underlying variables
1.14
Futures Contracts (page 6)
Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange
1.19
Borrow $300 at 5% for one year Buy one ounce of gold Enter into a short forward contract to sell the gold for $340 in one year 340-300-300×5%=$25
1.10
Foreign Exchange Quotes for GBP June 3, 2003 (See page 4)
Bid 1.6281 Offer 1.6285
Spot
1-month forward
3-month forward 6-month forward
1.6248
1.6187 1.6094
1.21
Sell the gold for $300 per ounce Invest the proceeds at 5% Enter into a long forward contract to repurchase the gold in one year for $300 per ounce
1.3
Examples of Derivatives
• Futures Contracts（期货合约） • Forward Contracts（远期合约） • Swaps（互换） • Options（期权）
1.4
Derivatives Markets
Exchange traded（场内交易）
1.22
The Forward Price of Gold
If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r )T where r is the 1-year (domestic currency) riskfree rate of interest. In our examples, S = 300, T = 1, and r =0.05 so that F = 300(1+0.05) = 315
1.9
Terminology
The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position
1.15
Exchanges Trading Futures
Chicago Board of Trade（芝加哥期货交易所） Chicago Mercantile Exchange（芝加哥商品交易
所）
LIFFE (London)（伦敦国际金融期货和期权交易所） Eurex (Europe)（欧洲期权和期货交易所） BM&F (Sao Paulo, Brazil) TIFFE (Tokyo)（日本东京国际金融期货交易所） and many more (see list at end of book)
1.5
Over-the-counter (OTC)（场外交易）
Size of OTC and Exchange Markets
(Figure 1.1, Page 3)
240 Size of Market ($ 220 trillion) 200 180 160 140 120 100 80 60 40 20 0 Jun-98 Jun-99 Jun-00
1.24
2. Oil: Another Arbitrage Opportunity?
Suppose that: - The spot price of oil is US$19 - The quoted 1-year futures price of oil is US$16 - The 1-year US$ interest rate is 5% per annum - The storage costs of oil are 2% per annum Is there an arbitrage opportunity?
1.7
Forward Contracts
Forward contracts are similar to futures except that they trade in the over-thecounter market Forward contracts are particularly popular on currencies and interest rates
Traditionally exchanges have used the openoutcry system, but increasingly they are switching to electronic trading Contracts are standard there is virtually no credit risk A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers Contracts can be non-standard and there is some small amount of credit risk
1.20
2. Gold: Another Arbitrage Opportunity?
Suppose that: - The spot price of gold is US$300 - The 1-year forward price of gold is US$300 - The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
1.12
Profit from a Long Forward Position
Profit
K
Price of Underlying at Maturity, ST
ST K
1.13
Profit from a Short Forward Position
Profit
K ST
K
Price of Underlying at Maturity, ST
1.17
Examples of Futures Contracts
Agreement to: buy 100 oz. of gold @ US$400/oz. in December (NYMEX) （纽约商品交易所） sell £62,500 @ 1.5000 US$/£ in March (CME)（芝加哥商品交易所） sell 1,000 bbl. of oil @ US$20/bbl. in April (NYMEX)