Ch 5: Options and Other Derivatives Flashcards
Options: In the money
when the strike price can be exercised at profit
options: at the money
when the strike price is the same as the current market price
Option: out of the money
when the strike price is at a loss at the time
European type options
Exercise at the End (only at Expiry)
American type options
Exercise Anytime prior to expiration
Intrinsic value of premium
Profit available to the option holder if it were immediately exercised (ie diff between the mkt value of the underlying instrument and the strike price)
Time Value of option
- Chance that the option will move into the money
- Decreases as the option approaches expiry (less likelihood that underlying instrument will move
- Premiums will increase in volatile markets as there is increased likelihood that an option will be exercised
Cap
- interest rate option transaction. Caps the level of interest rate on a floating rate borrowing
- cap = strip of consecutive options over BBSW sold as a package
- protects from rising rates, therefore equivalent to a call on the interest rate (if rates go up buyer receives payment)
- can also be considered a put on bank bills (right to sell BB at predetermined price)
++ call on rates vs put on securities: can be confusing, therefore use cap, floor etc
Floor
- protects buyer from a fall in interest rates (places a floor on interest rate received
Collar
- Borrower (investor) simultaneously purchases (sells) a cap and sells (purchases) a floor.
- ## usually structured as zero cost collar (premium of sold option offsets exactly the premium from the bought option
Swaption
- define
- payer swaption
- receiver swaption
- option over an interest rate swap
- payer swaption: buyer would pay fixed rate if exercised
- receiver swaption: buyer would receive fixed rate if exercised
Black Scholes assumptions (6)
- stock pays no dividends during options life
- European exercise terms are used - ie only exercise at expiry. (American options are more valuable)
- Markets are efficient
- Transaction costs and taxes are zero
- Interest rates remain constant and known (risk free rate)
- Returns are log normally distributed
Black Scholes in original form
- cannot ….
- Black Model accounts for this by…
- cannot be used for bonds or fixed interest securities because of pull to par problem (known value at maturity, therefore violates the random probability distribution of price
- uses forward price of bond, therefore assumes forward price at option maturity is log normally distributed (compare to Black Scholes where spot price is log normally distributed over life of option)
Binomial model
- tree of stock prices moving forward from present to expiration.
- at each step assume stock price moves up or down by an amount calculated using volatility and time to expiration
Monte Carlo option model
- method of estimating a value by the random generation of numbers and statistical principles (in particular, confidence intervals)
Interest rate option specific models:
- Hull- while model
- Brace Gatarek Musiela (BGM)
Hull- while model
- assumes interest rates normally distributed and exhibit mean reversion. Modelled on evolution of an instantaneous interest rate
Brace Gatarek Musiela (BGM)
- aka Libor Market Model (LMM).
- assumes that forward 3-mth interest rates along the yield curve are log normally distributed and correlated
Implied volatility vs historic volatility
Implied volatility
- measure of the expected magnitude of change in prices. If vol is high, premium is high
- reflection of the expected probability distribution of the underlying
- expected outcomes of future events, holidays, put/call skew, market sentiment
Historic volatility
- what the underlying security has already done
Delta
- calc
- define
- value of put, value of call
- deep in the money option:
- hedge ratio
Calculation:
Delta = changer in premium / change in mkt price
Define: sensitivity of option premium to changes in the price of the underlying
Value of put: negative delta (value of option decreases as underlying market price increases)
Value of call: positive delta (value of option increases as underlying market increases)
Deep in the money option: put = delta of -100% and for a call; +100%. There is no time value, only intrinsic value.
Deep out of the money = 0% delta
At the money: approx. +50% for calls and -50% for puts
Delta also known as hedge ratio - by selling (buying) amount of underlying equal to the delta, can instantaneously hedge changes in the option value against movements in the underlying market
Delta varies between +/- 100
Gamma
- Gamma = rate of change of delta
- if using delta as a hedge ratio, gamma indicates how rapidly the hedge must be adjusted as the market moves
- Gamma is the 1st derivative of delta, and therefore the 2nd derivative of the option price with respect to underlying market
Theta
- Theta = changes in time to maturity
- Theta = change in premium / change in time to expiry
- time decay
Vega
- amount that the price of an option changes compared to a 1% change in volatility
- increase in volatility increases the value of all options; whether puts or calls; whether in, at or out of the money
Exchange Traded Options
Options on 90 day bank bills
- 1m face value
- in the money options are automatically exercised at expiry unless abandoned
- options available up to 8 quarter months ahead, quoted in yield %pa in multiples of 0.005% = premium.
- strike / exercise prices set at intervals of 0.125%
- expiry 12.30pm on first Friday 1 week prior to settlement day for underlying futures
Exchange Traded Options:
Options on 3 and 10 year Treasury bond futures
- in the money options are automatically exercised at expiry unless abandoned
- $100,000 face value, coupon 6%
- up to 2 quarter months ahead.
- quoted in yield %pa in multiples of 0.005% = premium.
- strike / exercise prices set at intervals of 0.1%
- expiry 12.30pm on business day before the last day of trading in the underlying futures contract.
Exchange Traded Options
Serial options on 3- and 10 - year Treasury bond futures
- listed in non-financial quarter months, with 2 serial option months listed at a time
- quoted in yield %pa in multiples of 0.005% = premium.
- premiums payable on trade date
- expiry 12.30pm on business day before the last th day of the serial option money or next business day at noon on the last day of trading in the underlying contract.
Exchange Traded Options
Intraday options on 3 & 10 year Treasury bond futures
- Put: right to sell a specified 3 or 10 year bond futures contract at a specified rate at 4.10pm on the day of the trade.
- in the money options are automatically exercised at expiry
- Options are only available on the futures contract for the nearest quarter month
- quoted in yield %pa in multiples of 0.005% = premium.
- premiums payable on trade date
- strike / exercise prices set at intervals of 0.01%pa yield
- settlement price is the weighted average of traded prices executed in the underlying futures contract between 4.15 and 4.25pm calculated to 3 and rounded to 2dp
Exchange Traded Options
Overnight options on 3 & 10 year Treasury bond futures
- Put: right to sell a specified 3 or 10 year bond futures contract at a specified rate at 8.40am on the day following the night trade.
- in the money options are automatically exercised at expiry
- Options are only available on the futures contract for the nearest quarter month
- quoted in yield %pa in multiples of 0.005% = premium.
- premiums payable on trade date
- strike / exercise prices set at intervals of 0.01%pa yield
- Expiration = cessation of each ASX Trade 24 session. settlement price is the weighted average of traded prices executed in the underlying futures contract between 8.30am and 8.40am on the business day immediately following, calculated to 3 and rounded to 2dp
Exotic derivatives
- illiquid, highly leveraged
- usually take vanilla derivatives and add several mathematical conditions
eg - barrier options (payment only occurs if a reference rate or index threshold is (or is not) exceeded during period
- look back option: payment is based on max or min level reached by underlying instrument before maturity
- event-run derivative: derivative may change from a put to a call, increase in leverage or terminate if a particular event happens during its life
- spread option: underlying index is the spread between the yield of two interest rate products or services
Financial engineering
- combination of derivative products and blending with other financial market instruments (eg debt instrument with option component)
Credit derivatives
- facilitates transfer of credit risk between 2 counterparties
- contracts negotiated under ISDA documentation
Main types of credit derivatives
- CDS
- credit linked notes
- total (rate of) return swaps
- credit swap options
CDS
- unfunded notional instrument.
- transfers credit risk on defined reference entity from protection buyer to protection seller in exchange for fixed rate payment payable by the buyer
CDS: key terms
reference entity:
reference obligation:
credit events:
Settlement method:
Obligations:
Deliverable obligations
reference entity:
- entity that the buyer is seeking protection for default from
reference obligation:
- sets the seniority of the credit exposure being transferred
credit events:
- specific legal default risks, defined under ISDA
Settlement method:
- physical or cash
Obligations:
- debt (or other financial) obligations of the reference entity that are subject to credit events under CDS
Deliverable obligations
- comprise a specific set of obligations which the buyer can physically deliver to the seller
Credit linked note
- structured, funded cash security
- issued by a protection buyer to the protection seller against the default risk on a specified reference entity
- Basic terms of CLN are identical to those of CDS
- redemption calculation: at par if no credit event; depends on the occurrence of a defined credit event. Coupon payments during life of note are priced relative to the credit risk of the reference entity
- issuer may be bank, SPV or trust
- CLNs look like bonds. They provide access to credit risk that is not generally available in cash market
Total Rate of Return Swap
- creates synthetic long position for an investor on an underlying reference security
- receiver has the total economic returns and benefits of the underlying reference entity, including cashflows and cap gain/loss. Receiver accepts all of the credit risk and the market risk of the security without actually purchasing it.
- Receiver pays a spread over the relevant benchmark to cover balance sheet and other costs
- unfunded (it is a swap)
Credit Spread option
- bilateral financial contract
- references a credit spread
Calculate option delta
Delta = (change in premium) / (change in underlying)
Cash settled swaption
Physical settled swaption
Cash settled swaption:
- all existing hedges remain in place and the buyer receives a payment equal equivalent to expiry value of option (diff betw strike and mkt if in the money).
Physically settled swaption
- buyer of the swaption receives (pays) fixed on the swap
Theta calcs
ensure that theta is ADDED to an option premium.
eg calculate theta for number of days as a percentage, then add to the premium
