收藏家 J‘s Collection

Plain Vanilla 利率互换
Fixed Rate Payment = (Swap FR – LIBOR(t-1)) × T/360 × NP
FR= Fixed rate
T=期限
NP=notional principal

Equity Swaps: individual stock, stock portfolio, stock index.

Riskmanagement using  options

Covered Calls
Write a call option on stock you own. writer相信股价会跌或者保持不变；loss因premium减少；缺点：writer要在potencial premium的上方交易股票。

Protective Put
Buy a put on stock you own. 像保险

行权时间对Option Price影响 表格见课本
权证期限对价格影响，时间越长，价格越高

Put-Call Parity
Fiduciary Call=  C+X/(1+RFR)^T
Riskless Bond with face value = X
Call Option with exercise price = X,
S<=X,payoff=X(call 失效);  S>X,payoff =S

Protective Put = S + P,   S<=X,payoff=X;  S>X,payoff =S

No-arbitrage condition
Protective put = Fiduciary call
stock + put = call + X/(1+RFR)^T
S+P=C+X/(1+RFR)^T

现金流的影响
PVCF折现现金流
调整公式S-PVCF+P=C+X/(1+RFR)^T

利率影响，I涨，C涨，P跌
换成C=S+P-X/(1+RFR)^T
P=C-S+X/(1+RFR)^T

波动性影响，波动性增加，C增加，P增加，因为波动增加，增加upside potential without downside risk

Swap Market互换市场  :Interest Rate, Currency, Equity
特点：
1.不需要预付款
2.没有二级市场交易
3.多数无监管
4.违约风险是首要考虑
5.多数参与者是大机构
6.私下协议
7.难转换或终止
fixed和floating的互换

互换终止：
Notional Principal 用于计算periodic payments
Floating rate: 通常是US，LIBOR
Tenor:时限 ,展期
Settlement Dates:结算日
Mutual termination 双方同意
Offsetting contract 对冲
Resale 转卖
Swaption – right to enter into a swap

Currency Swap货币互换
4种情况，Fix-Float，Fix-Fix，Float-Fix，Float-Float
开始时Notional amount exchanged
Interest payment，结算日互相付利息

Plain Vanilla interest rate swaps
开始不付notional amount, 只付利息差价Fix-Float

American options: 到期日前任意时间行权
European options: 到期日行权，容易分析

所有属性一样，美式权证价值>欧式，因为美式较灵活

Call option
In the money, S > X , S-X>0
At the money, S = X, S-X=0
Out of the money, S<X, S-X<0

Put option相反

Option Value=intrinsic value + time value
intrinsic value Call : max[0,s-x] , Put : max[0, x-s]

Expiration Day Value
Call : max[0,s-x] , Put : max[0, x-s] ，stock
Call : max[0,(s-x)×multiplier] , Put : max[0, (x-s)×multiplier] ， index
Call : max[0,(LIBOR-strike rate)×notional amt] , Put : max[0, (strike rate-LIBOR)×notional amt] ，interest rate

Trading:
exchange-traded ,Regulated ,standardized,liquid; back by OCC for CBOE trades
OTC, currency, swap, equity options, largely unregulated, custom options contracts.

Types of options
Equity, stock index, bonds, interest rates, currency, Commodity options,options on future

Option, right, interest rate 没义务，所以最低是0，
FRA, obligation, reference rate(LIBOR)，有负

Interest Rate Caps & Floors
Caps : 一系列的call option(caplets),保护floating rate borrower，不受上涨影响
each caplet payoff, Max[0,(floating rate - cap rate)×notional ]
Floors:一系列put option(floorlets), 保护Lenders不受下降rates影响
each caplet payoff, Max[0,(floor rate - floating rate)×notional ]

interest rate Collars
浮动利率borrowers，long cap，short floor to pay for cap,上下限限制

St， t时刻的股价，X， 行权价，T 行权时间，ct 欧式权证Call price行权前价格，Ct美式权证行权前价格，pt欧式权证行权前价格，Pt美式

所有权证最小价值大于等于0， Call options C0 c0都小于S0，Put options美式 P0<X,  欧式p0<X/(1+RFR)^T计算折现

一大堆式子见课本

FRA:
Floating rate > Fixed rate, long 得钱，short给钱
Floating rate < Fixed rate, long 给钱，short得钱
Default risk is present at settlement
FRA formula 见课本
FRA Notation：每月30天转换。
1 × 4 FRA on LIBOR，30天期限，90天LIBOR
2 × 8 FRA on LIBOR,  60天期限，180天LIBOR

Currency Forward Contract :将来某天的特定汇率

Wrap up forward Markets
long/short positions; Settlement/termination procedures / Eurodollar deposites -LIBOR/Euribor; Equity and bond contracts ; Forward rate agreement ; Currency forward contracts

Futures Markets and Contracts
Futures : exchange-traded; Standardized ; Guaranteed by clearinghouse ; Margin requied ; Regulated
Forwards : Private contracts; Unique contracts ; Default risk present ; No margin ; Little Regulation

Futures的特性：
Contracts specify： Quality & quantity of good ; delivery time ；manner of delivery
Exchange sets: Minimum price fluctuation (tick ); Daily Price limit
Uniformity promotes liquidity

Futures Margin : performance guarantee; clearinghouse sets margins ; future margin 跟asset value低相关性
Securities Markets：50% margin,收借款利息，Fed set margin

Initial margin：定金
Maintennace margin：
Variation Margin：
Settlement Price 收盘价
Contract limits限价
early termination

Four way to terminate:
1.Reversal; 2.delivery ; 3.cash-settlement; 4 exchange for phycical

Types of futures
1.T-bill futures, 1basis point = $25 ,$1M 90-day t-bill
2.Eurodollar future, $1M Eurodollar deposit, 90-day LIBOR, 1basis point=$25

Treasury bond
Maturities  > 15年， Deliverable Contracts , Contract size $100,000
数个deliverable bonds,不同deliverable bonds通过conversion factor转换价值
Long pays invoice price = the Psettle × CF + accrued interest

Stock index, S&P index ; cash settlement, Contract value = $250× future index price

Currency Futures, Trading volume < currency forwards , 单位 USD/FC

Option Market，zero sum  game
Option Buyer， pay premium to buy the right to exercise an option at a future date and price
Option Seller, incur a obligatiion to perform under the option contract terms.

Derivative
Derive its value from the value of another asset or security

Exchange-traded:futures and options; standardized;clearinghouse
over-the-counter:Forwards and swaps; custom instruments; default risk

Forward commitments: a legally binding contract to buy or sell an underlying asset.
通常是custom contact,可以针对equity,index,bond, physical asset, interest rate
Buyer – Long, Seller – Short

Future contact, standardized forward contract
exchange- traded, 活跃的二级市场， Regulated, 有clearinghouse, daily settlement(mark to market)

Swap Contracts: Series of forward contracts
Currencies, equity index, interest rate, fixed rate/floating rate

Options, holder has the right but not the obligation to buy or sell an underlying at a specified price on or before a specified date
Call option, right to buy, seller(writer) has obligation to sell
Put option, right to sell,  seller(writer) has obligation to buy

Purposes of derivatives markets
Provide price information, risk management, reduce transaction cost

Criticism of derivatives markets
Too risky; leverage like gambling

Arbitrage
riskless profit with no investment, when mispriced, continue until supply and demand to effficient levels
Two Arguments: the law of one price, risk free portfolios
Opportunity

Non-Arbitrage Principle
1.金融工具的均衡价格应除去套利机会
2.套利lead to efficient market, 所有的相关信息都反映到资产价格

Forward contracts :双方都有obligation 买或卖，特定的价格，特定的时间；costless
Long：buy;  Short: sell/deliver; both parties remove risk about future prices; both accept default risk; negative side pays the positive site; zero sum game.

参与者
Dealers：banks and nonbank 金融机构， 平衡end-users的long short
Dealer quotes: short和long之间的bid/ask spread是dealer的利润, 同时承担量差的default risk和price risk

End-User：公司，政府机构，非赢利组织，希望锁定风险。

Equity Forward Contract：single stock, portfolio of stock, stock index(notional amount, cash settlement)

Bond Forward Contracts
Settlement date < maturity date

Eurodollar Deposits
美国境外的美元计价的存款，floating rate 基于LIBOR，360 day计算

LIBOR：Compiled in London， Published by British Bankers Association
Euribor(Europe Interbank Offered Rate):Compiled in Frankfurt, Published by the European Central Bank

Floating Rate quotes:30-,90-,180-day LIBOR or Euribor

Forward Rate Agreements
Exchange fixed for floating rate payments: Notional Amount, Fixed rate= forward rate;Floating rate (LIBOR), Long FRA pays fixed rate to short; short FRA pays floating rate to long