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Chapter 1
Introductions To Futures And Options
What is a future ?
An agreement to buy or sell a standards quantity of a specified asset on a fixed future date at a price agreed today.
What is a contract ?
Exchange traded futures are traded in standardized parcels known as contracts.
What are delivery days ?
Delivery of futures takes place on specified dates known as delivery days, when buyer exchange money for goods with sellers.
What is a tick ?
The smallest permitted price movement in a future contract found in the contract specification.
What the purpose of a tick ?
It avoids potentially huge numbers of trading prices.
What is a tick value ?
Futures contract fixed size (standardized parcel) times the smallest price movement = tick value. 100 x 5p = 5 GBP
What is a hedger ?
The hedger is someone seeking to reduce risk.
What is a speculator ?
The speculator is a risk-taker seeking large profits.
What is an arbitrageur ?
The arbitrageur seeks riskless profits from exploiting market inefficiencies.
Future profit/loss (formula)
Future profit/loss = ticks x tick value x contracts
long position
A transaction in which a future is purchased to open a position ('going long of the future').
short position
A transaction in which a future is sold to open a position ('going short').
Long Future risk
almost unlimited - the maximum loss would occur if the future fell to zero.
Long Future reward
unlimited - the futures price could rise to infinity.
Short Future risk
unlimited
Short Future reward
limited, but large - the future can only fall to zero.
Short Hedge
protects against a price fall
Long Hedge
protects against a price rise
What is an option ?
A contract that gives the right, but not the obligation, to buy or sell an asset at a given price on or before a given date.
What is a call option ?
The right to buy an option is called a call option.
What is a put option ?
The right to sell an option is called a put option.
What is the holder ?
The person buying the option is known as the holder (he has the rights to buy or sell).
What is the writer ?
The person selling an option is known as a writer.
What is the total cost of an option ?
The total cost of an option is called the premium.
What determines the premium ?
The premium is determined by factors including the stock price, strike price and time remaining until expiration.
What is exercising ?
When options holders wish to take up their rights under the contract, they are said to exercise the contract.
What is the exercise price ?
The price at which an options contract gives the right to buy (call) or sell (put) is known as the exercise price or strike price.
What is an other word for the strike price ?
The exercise price.
What is the expiry date ?
The date on which an option comes to the end of its life is known as its expiry date.
What exercise styles exist ?
American, Bermudan and European style options.
What is an American style option ?
Can be exercised by the holder at any time after the option has been purchased.
What is an Bermudan style option ?
Can be be exercised only on predetermined dates, usually every month.
What is an European style option ?
Can be exercised by the holder only on its expiry date.
What are the basic strategies ?
Long Call, Long Put, Short Call, Short Put
What is a uncovered Call/Put ?
A Short Call/Put when you don't owe the underlying asset.
What is a covered Call/Put ?
A Short Call/Put when you owe the underlying asset.
Long Call (buying a Call) - risk
limited - the investor's risks are limited to the premium he pays for the options.
Long Call (buying a Call) - reward
unlimited - contract gives the right to buy at fixed price, this right becomes more valuable as the asset price rises above exercise price.
Short Call (selling a Call) - risk
unlimited - the writer has to deliver at fixed price and underlying asset price could rise to infinity
Short Call (selling a Call) - reward
limited - the maximum profit the writer can make is the premium he receives.
Long Put (buying a Put) - risk
limited - to the premium paid
Long Put (buying a Put) - reward
limited - maximum profit will arise if the asset price falls to zero
Short Put (selling a Put) - risk
limited - the writer has obligation to buy the asset at a fixed price, the maximum loss will be the exercise price less the premium received.
Short Put (selling a Put) - reward
limited - the maximum profit the writer can make is the premium he receives.
Long Call (buying a Call) - motive
directional, very bullish (market direction and volatility)
Short Call (selling a Call) - motive
directional, bearish to neutral (market direction and volatility)
Long Put (buying a Put) - motive
directional, very bearish, motivation is to profit from a fall in the asset's price (market direction and volatility)
Short Put (selling a Put) - motive
directional, bullish to neutral (market direction and volatility)
Chapter 4
Basic Pricing Of Futures And Options
Simple Basis (formula)
Basis = Cash price - Futures price
What's an other term for Simple Basis ?
Crude Basis
What does 'x GBP under futures' mean ?
basis is negative
What does 'x GBP over futures' mean ?
basis is positive
market is in contango
futures prices higher than cash prices
market is in backwardation
futures prices lower than cash prices
market is at a premium
negative carry market, futures prices higher than cash prices (contango market)
market is at a discount
positive carry market, futures prices lower than cash prices (backwardation market)
Theoretical Basis (formula)
Theoretical Basis = Cash Price - Fair Value
Value Basis (formula)
Value Basis = Fair Value - Future
Basis is weakening
Basis becomes more negative or less positive
Basis is strengthening
Basis becomes less negative or more positive
Basis is narrowing
Basis moves nearer to zero, Narrowing is either weakening or strengthening
Basis is widening
Basis moves away from zero, Widening is either weakening or strengthening
A hedger faces what type of risk ?
A hedger faces basis risk. It emerges when cash prices move further than futures prices, i.e. a change in basis.
What does the Fair Value of a future mean ?
This is the price at which Investors are indifferent as to whether buy or sell the underlying asset or the future.
What is arbitrage ?
Traders (arbitrageurs) seek to make riskless profits from exploiting mispricings between markets
Cash and Carry Arbitrage
Sell Futures and Buy Underlying Asset (future is expensive relative to fair value)
Reverse Cash and Carry Arbitrage
Buy Futures and Sell Underlying Asset (future is cheap relative to fair value)
Arbitrage Channel
Is an area either side of the fair value within arbitrage will not take place. It is created by exchange fees, taxes and bid/offer spreads.
Convergence
Futures Price and Cash Price will converge towards the cash price at moment of delivery as cost of carry will be nil.
Which factors affect the price of an option
VA TE EP V IR D - Value of underlying asset, Time to expiry, Exercise price, Volatility, Interest rates, Dividends.
What are the components of the option premium ?
Premium = Intrinsic value + Time value
What does in-the-money mean ?
An option that has an intrinsic value.
What does out-of-the-money mean ?
An option that has only time value.
What does at-the-money mean ?
The option exercise price that is nearest to the current underlying price.
How does time decay affect holders and writers ?
Holders are hurt by time decay, writers are helped by time decay.
Impact of volatility on option premiums ?
If volatility rises (falls), call and put premiums increase (decrease).
Conversion of Volatility (monthly, weekly, daily)
monthly volatility = annual volatility / sqrt(12), weekly volatility = ann. Vol. / sqrt(52), daily vol. = ann. vol. / sqrt(256)
Types of volatility
Future Volatility, Historic Volatility, Forecast Volatility, Implied Volatility.
Future Volatility
Volatility that will exist in the future.
Historic Volatility
A measure of how historically variable an asset has been in the past.
Forecast Volatility
The expected future volatility of an asset.
Implied Volatility
A measure of volatility derived from current option prices.
How does the changes in interest rates affect options (Physicals) ?
For options on physicals: rate rises => call (put) premiums rise (fall).
How does the changes in interest rates affect options (futures PPI) ?
For options on futures (premium paid immediately): rate rise => call and put premium falls.
How does the changes in interest rates affect options (futures PM) ?
For options on futures (premium is margined): rate rise => no influence.
Option price upper boundary ?
c <= S, C <= S, P <= X, p <= X * e^(-rt)
Option price lower boundary (at expiry) ?
c = max(S - X, 0), C = max(S - X, 0), p = max(X - S, 0), P = max(X - S, 0)
Option price lower boundary (before expiry - European options) ?
c >= max(S - X * e^(-rt), 0), p >= max(X*e^(-rt) - S, 0)
Option price lower boundary (before expiry - American options) ?
C >= max(S - X, 0), P >= max(X - S, 0)
Option price lower boundary (before expiry - American options - non-dividend paying stock) ?
C >= max(S - X * e^(-rt), 0)
Option price lower boundary (before expiry - dividend paying stock) ?
c >= max(S - D - X*e^(-rt), 0), C >= max(S - X, 0)
Put/Call Parity (definition)
Purchasing a future gives the same position as buying a call and selling a put with the same strike price (synthetic long position).
Put/Call Parity (formula - Non-dividend paying stock - ConDis)
C - P = S - K * e^(-rt)
Put/Call Parity (formula - Non-dividend paying stock - DisDis)
C - P = S - K / (1 + rt)
Put/Call Parity (formula - Dividend paying stock - ConDis)
C - P = S - D - K * e^(-rt)
Put/Call Parity (formula - Dividend paying stock - DisDis)
C - P = S - D - K / (1 + rt)
Put/Call Parity (formula - Stock Index Options - ConDis)
C - P = S * e^(-dt) - K * e^(-rt) (S = cash price of index, d = annual rate continuous dividend yield)
Put/Call Parity (formula - Stock Index Options - DisDis)
C - P = S / (1 + dt) - K / (1 + rt) (S = cash price of index)
Put/Call Parity (formula - Currency Options - ConDis)
C - P = S * e^(-ft) - K * e^(-rt) (S = spot price of currency, f = interest earned on currency)
Put/Call Parity (formula - Currency Options - DisDis)
C - P = S / (1 + ft) - K / (1 + rt) (S = spot price of currency)
Put/Call Parity (formula - Futures - premium margined)
C - P = S - K (C = call price, P = put price, S = stock price, K = exercise price)
Put/Call Parity (formula - Futures - Premium paid upfront - ConDis)
C - P = S * e^(rt) - K * e^(-rt) (S = price of the future)
Put/Call Parity (formula - Futures - Premium paid upfront - DisDis)
C - P = S / (1 + rt) - K / (1 + rt) (S = price of the future)
Convexity Arbitrage
If options with different strikes, but on the same asset are not priced along the curved line, then there is an arbitrage opportunity.
Convexity Arbitrage (how to check for)
1) construct a long butterfly (buy 1 x call, sell 2 x+n call, buy 1 x+m call, where n<m)
Chapter 5
Strategies
directional trades
bullish or bearish
volatility trades
Investors do not know which direction the market may move, but have opinions as to its likely variability.
arbitrage trades
Investors have no interest in market direction or volatility, but seek to make riskless or near riskless profits, by exploiting mis-pricings between options and the underlying assets.
spreads
Trades that involve positions exclusively in either calls or puts.
combinations
Trades in which calls and puts are used together.
spreads (categories)
vertical, horizontal and diagonal
horizontal spread
same exercise price, different expiry
vertical spread
different exercise price, same expiry
diagonal spread
different exercise price, different expiry
bull spread (motivation)
directional, moderately bullish
bear spread (motivation)
directional, moderately bearish
synthetic long (motivation)
directional, very bullish
synthetic short (motivation)
directional, very bearish
synthetic long call (motivation)
directional, bullish but with limited downside risk
synthetic short call/covered put (motivation)
directional, bearish-neutral, subject to exercise price
synthetic short put/covered call (motivation)
directional, bullish-neutral, subject to strike
synthetic long put (motivation)
directional, bearish
diagonal spread (motivation)
directional - bullish if constructed with calls, bearish if constructed with puts
cylinder (motivation)
directional - moderately bullish, but with desire for downside protection
long straddle (motivation)
volatility - undertaken to exploit increasing variability
short straddle (motivation)
volatility - undertaken to exploit decreasing variability
long strangle (motivation)
volatility - expect large increase in market variability
short strangle (motivation)
volatility - expect large decrease in market variability
short butterfly (motivation)
volatility - undertaken to exploit increasing variability
long butterfly (motivation)
volatility - undertaken to exploit reducing variability
ratio back spread (motivation)
volatility expected to rise, directional bias bullish when constructed with calls, bearish with puts
ratio spread (motivation)
volatility expected to fall, directional bias bearish when constructed with calls, bullish with puts
horizontal spread (motivation)
volatility, undertaken to take advantage of static market
conversion (motivation)
arbitrage - employed to exploit mis-pricing between options and futures/stock. Conversion used when synthetic short is expensive and the underlying is relatively cheap.
reversals (motivation)
arbitrage - employed to exploit mis-pricing between options and futures/stock. Reversal used when synthetic long is cheap and the underlying is relatively expensive.
box (motivation)
arbitrage - employed to exploit mis-pricing between synthetic long position at one strike and a synthetic short at another. Similar to conversion/reversal but with lover risk, as no underlying position established.
Long Call (Construction)
Opening purchase of a call. Choice of call depends on degree of bullishness. Buy OTM call if bullish, ITM if less so.
Long Put (Construction)
Opening purchase of a put. Choice of put depends on degree of bearishness. Buy OTM put if bearish, ITM if less so.
Short Put (Construction)
Opening sale of a put. Choice of put depends on degree of bullishness. Sell ITM put if very bullish, OTM if less so.
Short Call (Construction)
Opening sale of a call. Choice of call depends on degree of bearishness. Sell ITM call if very bearish, OTM if less so.
bull spread (Construction)
Purchase of low-strike call (put) and sale of high-strike call (put).
bear spread (Construction)
Sale of low-strike call (put) and purchase of high-strike call (put).
synthetic long (Construction)
Purchase of call and sale of put at same strike and with same expiry.
synthetic short (Construction)
Sale of call and purchase of put at same strike an with same expiry.
synthetic long call (Construction)
Long position in stock/future and purchase of put.
synthetic short call/covered put (Construction)
Short position in stock/future and sale of put.
synthetic short put/covered call (Construction)
Long position in stock/future, and sale of call. If call sold is OTM, the trade is bullish. If ATM call is sold, trade is neutral.
synthetic long put (Construction)
Short position in stock/future and purchase of call.
diagonal spread (Construction)
Sale of short-dated call/put and purchase of longer dated and further OTM call/put.
cylinder (Construction)
Sale of call at a high strike and purchase of put at a lower strike, combined with a long position in the underlying.
long straddle (Construction)
Purchase of call and put with same exercise price and expiry.
short straddle (Construction)
Sale of call and put with same exercise price and expiry.
long strangle (Construction)
Purchase of call and put with same expiry, but different strike.
short strangle (Construction)
Sale of call and put with same expiry, but different strike.
short butterfly (Construction)
Sale of low-strike call/put. Purchase of two mid-strike calls/puts. Sale of high-strike call/put.
long butterfly (Construction)
Purchase of low-strike call/put. Sale of two mid-strike calls/puts. Purchase of high-strike call/put.
ratio back spread (Construction Call)
Call: Sale of low-strike call and purchase of two or ore high-strike calls.
ratio back spread (Construction Put)
Put: Sale of high-strike put and purchase of two or ore low-strike puts.
ratio spread (Construction Call)
Purchase of low-strike call and sale of two or more high-strike calls.
ratio spread (Construction Put)
Purchase of high-strike put and sale of two or more low-strike puts.
horizontal spread (Construction)
Sale of short-dated call (put) and purchase of longer dated call (put) with the same strike.
conversion (Construction)
Sell call and buy put with same exercise price and expiry, simultaneously buy underlying stock/future.
reversals (Construction)
Buy call and sell put with same exercise price and expiry, simultaneously sell underlying stock/future.
box (Construction)
Buy call and sell put with same exercise price and expiry. Simultaneously sell call and buy put at different strike. You are long (short) the box if you are synthetically long (short) at the lower strike.
Long Call (Key Formulae)
MaRi: premium paid, MaRe: unlimited, BEaex: exercise price + premium.
Long Put (Key Formulae)
MaRi: premium paid, MaRe: exercise price - premium, BEaex: exercise price + premium.
Short Put (Key Formulae)
MaRi: exercise price - premium, MaRe: premium received, BEaex: exercise price - premium.
Short Call (Key Formulae)
MaRi: unlimited, MaRe: premium received, BEaex: exercise price + premium.
bull spread (Key Formulae calls)
MaRi: net initial debit, MaRe: difference between strikes - initial debt, BEaex: lower strike + initial debit.
bull spread (Key Formulae puts)
MaRi: difference between strikes - initial credit, MaRe: net initial credit, BEaex: higher strike + initial credit.
bear spread (Key Formulae calls)
MaRi: difference between strikes - initial credit, MaRe: net initial credit, BEaex: lower strike + initial credit.
bear spread (Key Formulae puts)
MaRi: net initial debit, MaRe: difference between strikes - initial debit, BEaex: higher strike price - initial debit.
synthetic long (Key Formulae)
MaRi: exercise price +/- net initial debit/credit, MaRe: unlimited, BEaex: exercise price +/- net initial debit/credit.
synthetic short (Key Formulae)
MaRi: unlimited, MaRe: exercise price -/+ net initial debit/credit, BEaex: exercise price -/+ net initial debit/credit.
synthetic long call (Key Formulae)
MaRi: initial value of stock/future - exercise price + put premium, MaRe: unlimited, BEaex: initial value of stock/future + put premium.
synthetic short call/covered put (Key Formulae)
MaRi: unlimited, MaRe: initial value of stock/future - exercise price + put premium, BEaex: initial value of stock/future + put premium.
synthetic short put/covered call (Key Formulae)
MaRi: initial value of stock/future - call premium, MaRe: exercise price - initial value stock/future + call premium, BEaex: initial value of stock/future - call premium.
synthetic long put (Key Formulae)
MaRi: exercise price - initial value of stock/future + call premium, MaRe: initial value of stock/future - call premium, BEaex: initial value of stock/future - call premium.
diagonal spread (Key Formulae)
MaRi: difference between strikes - initial credit or initial debit, MaRe: at short-dated expiry, limited, BEaex: dependent on relative movements of premium.
cylinder (Key Formulae)
MaRi: limited, cap set by put, MaRe: limited, floor set by call, BEaex: stock price +/- net initial debit/credit.
long straddle (Key Formulae)
MaRi: premiums paid, MaRe: unlimited, BEaex: upside: exercise price + both premiums, downside: exercise price - both premiums.
short straddle (Key Formulae)
MaRi: unlimited, MaRe: limited to premiums, BEaex: upside: exercise price + both premiums, downside: exercise price - both premiums.
long strangle (Key Formulae - call strike > put strike)
MaRi: limited to premiums, MaRe: unlimited, BEaex: upside: higher strike + premium, downside: lower strike - premium.
long strangle (Key Formulae - call strike < put strike)
MaRi: limited to premium - difference between strikes, MaRe: unlimited, BEaex: upside: lower strike + premiums, downside: higher strike - premiums.
short strangle (Key Formulae - call strike > put strike)
MaRi: unlimited, MaRe: premiums received, BEaex: upside: higher strike + premiums, downside: lower strike - premiums.
short strangle (Key Formulae - call strike < put strike)
MaRi: unlimited, MaRe: premiums received - difference between strikes, BEaex: upside: lower strike + premiums, downside: higher strike - premiums.
short butterfly (Key Formulae)
MaRi: difference between one set of strikes less initial credit, MaRe: net initial credit, BEaex: lower strike + credit, higher strike - credit
long butterfly (Key Formulae)
MaRi: net initial debit, MaRe: difference between one set of strikes - initial debit, BEaex: lower strike + debit, higher strike - debit.
ratio back spread (Key Formulae puts)
MaRi: difference between strikes and net initial debit, MaRe: breakeven value, BEaex: lower strike - initial debit - difference between strikes.
ratio spread (Key Formulae calls)
MaRi: unlimited, MaRe: difference between strikes + initial credit, BEaex: higher strike + maximum profit.
horizontal spread (Key Formulae)
MaRi: net initial debit, MaRe: indeterminate, subject to relative changes in premiums, BEaex: indeterminate, subject to relative changes in premiums.
conversion (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
reversals (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
box (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
Long Call (Comment)
Position suffers from time decay.
Long Put (Comment)
Position suffers from time decay.
Short Put (Comment)
Position helped by time decay.
Short Call (Comment)
Position helped by time decay.
bull spread (Comment)
Only moderate exposure to time decay.
bear spread (Comment)
Only moderate exposure to time decay.
synthetic long (Comment)
Will behave like a long futures/physical position.
synthetic short (Comment)
Will behave like a short futures/physical position.
synthetic long call (Comment)
Classic options hedge of long position in underlying, protects downside but allows profit if market advances. More flexible and thus more expensive than short hedge with futures.
synthetic short call/covered put (Comment)
Mirror image of synthetic long call, not a common investment strategy, but premium income can enhance returns in static market.
synthetic short put/covered call (Comment)
Very familiar investment strategy that can enhance returns in static markets, whilst also providing limited protecting against falls. (Protection = call premium).
synthetic long put (Comment)
Alternative to conventional purchase of put.
diagonal spread (Comment)
Undertaken when short-term view is bearish (calls) or bullish (puts) and subsequently expected to move in opposite direction. As trade involves option with different expiries, it is difficult to estimate potential rewards and breakevens without computer assistance. Point of highest profit at sort-term expiry (at exercise price).
cylinder (Comment)
This is simply a synthetic bull spread. Alternative terms are collar or fence. Can sometimes be done for zero cost: a costless collar.
long straddle (Comment)
Prone to severe time decay if position held near to expiry.
short straddle (Comment)
Benefits from time decay, but beware, unlimited risk.
long strangle (Comment)
Generally a lower cost alternative to a long straddle, which is less prone to time decay, but breakevens further apart.
short strangle (Comment)
Alternative to short straddle, generally breakevens more widely displaced and thus, position is less quickly loss making.
short butterfly (Comment)
Alternative to long straddle/strangle. Less prone to time decay, but at cost of very limited profit.
long butterfly (Comment)
Constructed to be delta neutral. Patently less risky than short straddle/strangle.
ratio back spread (Comment)
Expectation that volatility will rise and that up (call) or down (put) move is likely.
ratio spread (Comment)
Expectation that volatility will decline and that up (call) or down (put) move is unlikely.
horizontal spread (Comment)
Trade exploits the fact that short-dated options will lose time value more quickly than long-dated options. Ideal position is if stock expires at the exercise price by the shorter term expiry.
conversion (Comment)
Strategy rests on violation of put/call parity. In efficient markets, synthetic long/short positions should be in line with the underlying.
reversals (Comment)
Strategy rests on violation of put/call parity.
box (Comment)
Strategy rests on violation of put/call parity. If present value of box differs from the present value of the difference between the strikes, then an arbitrage opportunity exists.
Questions Phase 1
Chapters 1-5
When could it be optimal to exercise a call (put) option early on a dividend paying stock ?
Chapter 6
Financial Mathematics
What is Market Value ?
The market value of a security is the present value of the future expected receipts discounted at the investors required rate of return.
Simple Interest (formula)
i1 = D0 * r
Terminal value simple interest (formula)
D1 = D0 * (1+r)
Terminal value simple interest nth year (formula)
Dn = D0 * (1 + n * r)
Compound Interest (formula)
in = Dn-1 * r
Terminal value compound interest (formula)
Dn = D0 * (1+ r)^n
APR (abbreviation)
annual percentage rate
APR
How much earning over a year based on flat rate and frequency of compounding.
APR (formula)
APR = (1+ r/m)^m - 1
Continuous Compounding
R = e^(r*t) - 1
Present Value
FV / DF
Discount factor at Time n (formula)
DFn = 1 / (1+ r)^n
Chapter 14.1
FRA
What is an FRA ?
A forward rate agreement is a contract between two parties who fix an agreed interest rate for a specified future period on an agreed notional amount.
What is the intention on buying an FRA ?
Buying an FRA will provide compensation when interest rates rise above the FRA contract rate.
What is the intention on selling an FRA ?
Selling an FRA will provide compensation when interest rates fall below the FRA contract rate.
contract amount (FRA)
The notional size of the theoretical loan.
settlement date (FRA)
The starting date of the theoretical loan.
fixing date (FRA)
The date at which the theoretical loan's rate (reference rate) is set.
maturity date (FRA)
The ending date of the theoretical loan.
contract period (FRA)
Difference between maturity and settlement dates.
contract rate (FRA)
Fixed interest rate agreed by the parties at trade date (dealing date).
reference rate (FRA)
Market interest rate for calculating settlement amount.
settlement amount (FRA)
Proceeds of FRA paid to equalize interest for both.
dealing date (FRA)
The date at which the contract rate is agreed and the trade starts.
deferment period (FRA)
Difference between fixing date and value date.
settlement amount (FRA - formula)
((reference rate - contract rate) * contract period/day basis * contract amount) / ( 1 + reference rate * contract period/day basis))
reference rate > contract rate
seller (lender) pays buyer
reference rate < contract rate
buyer (borrower) pays seller