Notesale: Turn your study into money

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Concepts
Derivative

Derivative markets and instruments
Derivative : security that derives from value / return of another asset or security
Options and future contracts : exchange-traded derivatives
Forwards and swaps : traded in OTC markets (dealer market with no central location), each contract with a counterparty → expose to default risk

Forward commitment / Contingent Forward commitment : legal binding promise to perform some action in the future (including forward, future, and swaps)
claim
Contingent claim : Claim that depends on a particular event (including option)
Forward contracts

Forward contract : obligate 1 party to buy, and another to sell, a specific asset at a specific price (forward price), on a specific date in the future
Party agree to buy the asset : has a long forward position (the long)
Party agree to sell / deliver the asset : has a short forward position (the short)
Deliverable forward contract : settle by the short delivering the underlying asset to the long
Cash-settled forward contract (contracts for differences / non-deliverable forwards) : 1 party pays cash to the other based on the difference between the forward price and market price of
the underlying asset

Future contracts

Future contract : forward contract that is standardised and exchange-traded
Clearinghouse : Each futures exchange has 1 clearinghouse
...
Exchange members are prohibited to trade
outside of the limits

Swaps

Swaps : agreements to exchange a series of payments on periodic settlement dates over a certain time period
...
g
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The seller of the option (the option writer) is obligated to perform, if the buyer
exercises the option
Call option : right to purchase the underlying asset at a specific price for a specific time period
Put option : right to sell the underlying asset at a specific price for a specific time period
Long call : buyer of a call option - has the right to buy the underlying asset
Short call : writer of a call option - has the obligation to sell the underlying asset
Long put : buyer of a put option - has the right to sell the underlying asset
Short put : writer of a put option - has the obligation to buy the underlying asset
American option : exercise anytime up to and including the contract's expiration date
European option : exercise only at the contract's expiration date

Credit derivatives

Credit derivative : contract that provide bondholder with protection against a downgrade or defaut by the borrower
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g
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Credit default swap : insurance contract against default
2
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Trading by arbitrageurs will continue until they affect supply and demand enough to bring asset prices to efficient levels
1
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Portfolio with certain future payoffs → no risk in inves ng
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futures price

Constant interest rate / interest rate uncorrelate with futures price → Futures price = Forwards price
Positive correlation between interest rates and futures price → Futures price > Forwards price , due to :
- when interest rate is high → ↑ excess margin → ↑ interest on excess margin
- when interest rate is low → ↓ opportuni es cost of deposited margin
Similarly, negative correlation between interest rates and futures price → Futures price < Forwards price

Swaps contracts

Swaps contracts = series of FRAs, in which the first payment is known at initiation, and the rest of the payment is unknown
Unknown payments ≈ off-market FRAs
To replicate a swap with zero value at initiation, sum PV of these FRAs = 0

Moneyness / Exercise value / Time Moneyness : whether the option is in the money or out of the money
value of an option
In the money : immediate exercise → generate posi ve payoff
Out of the money : immediate exercise → generate a loss
At the money : Current price = exercise price → no gain/loss if exercise immediately
*For call option:
- In the money : Current price > Excercise price
- Out of the money : Current price < Exercise price
- At the money : Current price = Exercise price
*For put option :
- In the money : Current price < Exercise price
- Out of the money : Current price > Exercise price
- At the money : Current price = Exercise price
Intrinsic value : maximum of 0 and the amount that the option is in the money
option premium = intrinsic value + time value
When option reach expiraion → me value = 0

Factors that affects the value of an Increase in:
option
1
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Exercise price
3
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Volatility of underlying
5
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Costs of holding the asset
7
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Calculate option payoff @ maturity in both the up move and down move states
2
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Discount this expected value back to PV at risk-free rate
Difference between European and Price of European options = price of American options , unless the right to exercise prior to expiration has positive value
American options
*For call option :
- No CF during the life of the option → no advantage to early exercise → Price of American op ons = price of European op ons
- Asset pays CF during the life of the call option → advantage to exercise the call op on pior to the ex-dividend date (the dividend could be sold @ pre-dividend price, or held to receive
the dividend) → Price of American call op ons > Price of European call op ons
*For put option : when put option is deep in the money → could realise the gain immediately instead of expira on date → Price of American call op ons > Price of European call op ons

Concepts
Call option Profits / Losses

Description
Risk management Applications of Option Strategies
c = $5
X = $50
- Maximum loss for buyer of call option : $5 ; Maximum profit for writer of call option : $5 (at any S ≤ $50)
- Breakeven point for buyer and seller of call option : $55 (c + X)
- Profit potential for buyer of call option : Unlimited (for any S ≥ $55)
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Conversely, potential loss for seller of put option : $45
- At expiration date, buyer of call option will exercise the option when : S < $50
- Long profit = short loss, and vice versa

Covered calls

Covered calls : to enhance income depends upon the chance that the stock price will exceed the exerecise price at which the trader writes the call
S0 = $50
X = $55
c = $4
- S < $50 → call op on expires worthless, writer's loss is offset by premium income = c = $4
- Breakeven price for writer = S0 - c = $50 - $4 = $46

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