Derivatives Flashcards
Put-Call Parity
1) Formula
2) Variations
3) Put-Call Forward Parity
Put-Call Parity
1) So + Po = Co + pv(X)
1. 1) Long Put: +Po = +Co - So + pv(X)
1. 2) Long Call: +Co = +So + Po - pv(X)
Put-Call Forward Parity
Fo/(1+r)^T + Po = +Co + x/(1+r)^T
Synthetic Long Forward
1) Formula
2) What is it syntheticall replicating?
Synthetic Long Forward
1) +So = +Co - Po + pv(X)
2) Long Call + Short a Put # same strike, expiration
- hedge existing short pos or arbitrage mispricing
* keep Put-Call Parity in your head
So+Po=Co+pv(X)
Synthetic Short Forward
1) Formula
2) What is it syntheticall replicating?
Synthetic Short Forward
1) -So = +Po - Co - pv(X)
2) Long Put and Short a Call
Covered Call
1) Conceptually?
2) Formula
2. 1) Value at expiration
2. 2) Profit at expiration
2. 3) Max Gain
2. 4) Max Loss
2. 5) B/E
Covered Call
1) Long Stock + Short Call
OTM - Yield enhancement or exit at target price
ITM - Position reduction
2) Formula
2. 1) Value at expiration: ST - max(ST-X,0)
2. 2) Profit at expiration: ST - max(ST-X,0) + Co - So
2. 3) Max Gain: (X - So) + Co
2. 4) Max Loss: So - Co
2. 5) B/E: So - Co
Naked Call = don’t own the underlying stock, at risk as if price goes above X, have to buy the stock to deliver if it get’s called
Risk Reversal
1) What is it?
2) Formula?
Risk Reversal
1) Belief that Put Implied Volatility too high relative to Call Implied Volatility
2) RR = Long OTM Call + Short OTM Put
- Long OTM Call (long pos on the base) provides complete downside risk protection
- Short OTM Put limits upside potential from Price appreciation, but reduces cost of hedge
Both have +tve Delta
Passive, Discretionary and Active
Currency Overlay
1) What is it?
2) When can it be used?
Management of currency portfolio can be separated into 2 parts
1) Currency beta = 100% hedge
2) Currency alpha = Currency overlay manager
Currency Overlay Manager
- used when don’t have expertise, hire external currency manager
- can be for passive, discretionary or active
1) Passive - COM implements passive approach to currency hedges
2) Discretionary - COM takes lim. directional views on future currency movements - limited to currency exposures already in the foreign asset portfolio
3) Active - “Foreign exchange as an asset class” - COM not restricted, free to take FX exposures in any currency pair
- Can have
1) foreign-currency asset porflio fully hedged (beta)
2) managing the active FX exposures (alpha)
FX as an asset class (adding as a currency overlay) should add incremental return (alpha) and have min corr with other asset classes and alpha sources in the portfolio
Matched Swap and Mismatched Swap
1) When do you use them?
2) Steps?
Remember - your starting point is that you’ll be long/short a forward contract coming due,
Here, I’m going to assume Eur8m short
Matched Swap - when told MV’s of assets haven’t changed and have no view on forex changes
Steps
- Long Eur8m at spot using Midpoint
- Short Eur8m at forward rate which is Midpoint + points
Mismatched Swap - when told MV’s of assets have changed and expecting changes in forex
Steps
- Long Eur8m at spot using Bid price (weird that it’s bid but make same as short pos)
- Short Eur8m at forward rate which is Bid + points
Difference between Futures and Forward contracts?
Futures
- standardized in terms of settlement dates and contract sizes
- not always available!
- require upfront margin
Forwards
- available for almost every currency pair, settlement date and transaction amount
- do not require upfront margin
Roll Yield and Forward Rate Premiums or Discounts
Roll Yield is whether you’ll expect a return or loss from hedging
Forward Rate Premiums or Discounts
- compare Forward rate to Current Spot rate (this is your Roll Yield)
- Fr > Sr - Forward trading at a premium ((Fr/Sr)-1)
- Fr < Sr - Forward trading at a discount
Rules
- buy at a discount (buy low) - positive roll yield
- sell at a premium (sell high) - positive roll yield
Also
Compare Forecast Spot rate to Current Spot rate to determine prediction in movement of interest rates (FRr/Sr)-1
Look at these two measures together
Volatility Smile
Volatility Skew
A Vol Smile happens when increased demand for OTM Calls = Bullish indicator
- Imp Vol lower for OTM Calls than for ATM Calls and decrease as strike prices rise above the stock price
A Vol Skew reflects the demand for insurance - OTM Puts
- Imp Vol higher for OTM Puts than for ATM Puts, and increases further the strike moves away from the current stock price (aka moving further left on the graph)
- Increase in Imp Vol (on the left) + increase in skew (only left increasing, not right) = bearish signal
Protective Put
1) Conceptually?
2) Formula
2. 1) Value at expiration
2. 2) Profit at expiration
2. 3) Max Gain
2. 4) Max Loss
2. 5) B/E
Protective Put
1) Long Stock + Long Put
2) Formula
2. 1) Value at expiration: ST + max(0,X-ST)
2. 2) Profit at expiration: ST - max(X-ST,0)
2. 3) Max gain: ST - So + Po
2. 4) Max loss: So - X + Po
2. 5) B/E: So + Po
Bull Spreads
Bull Call Spread
Bull Put Spread
Bull Call Spread = Long Call low + Short Call high (debit spread)
Max gain: (Xh - Xl) - debit spread
Max loss: Debit spread
B/E: Xl + Debit spread
Bull Put Spread = Long Put low + Short Put high (credit spread)
Max gain: Credit spread
Max loss: (Xh - Xl) - credit spread
B/E: Xh - credit spread
Bear Spreads
Bear Put Spread
Bear Call Spread
Bear Put Spread = Long Put high + Short Put low (Debit Spread)
Max gain: (Xh-Xl) - debit spread
Max loss: Debit spread
B/E: Xl + debit spread
Bear Call Spread = Long Call high + Short Call low (Credit Spread)
Max gain: Credit Spread
Max loss: Xh - B/E
B/E: Xl + credit spread
Straddles
1) What are we doing here?
2) Long straddle
3) Short straddle
Straddles
- volatility play, only options, no underlying
- combination of Calls and Puts always at same strike price
- same strike typically as close as possible to ATM
Long Straddle = Long Call + Long Put @ same strike price (hoping for Vol!)
Net premium = -C + (-P)
Value at expiration: max(0,ST-X) + max(0,X-ST)
Profit at expiration: Value - net premium
Max gain: unlimited
Max loss: Net premiums
B/E: B/Eh = X + premiums , B/El = X - premiums
Short Straddle = Short Call + Short Put (hoping for no Vol)
Net premium: +C +P
Max gain: net premiums
Max loss: Unlimited
B/E: B/Eh = X + premiums , B/El = X - premiums
Collar
Collar = long stock + covered call + protective put
- already long stock + Short CallH + Long PutL
- Short call to fund the long put
- Zero-cost Collar = premiums paid and received offset
Net premium: +C-P = 0
Value at expiration: ST + max(0,ST-X) + max(0,X-ST)
Profit at expiration: Value - So
Max gain: Xh - So
Max loss: So - Xl
B/E: So
