Derivatives and Risk Management (11.6.24) Flashcards
Put Call Partiy
Stock price + put premiuxm = call premium + strike price/(1+r)^T
Synthetic long forward position
Long call + short put (same strike and maturity)
Synthetic short forward position
Short call + long put (same strike, maturity)
Delta
The relationship between option price and underlying price; shows how much an option price will change for a small change in the stock
Gamma
A numerical measure of how sensitive an option’s delta (the sensitivity of the derivative’s price) is to a change in the value of the underlying
Vega
The change in a given derivative instrument for a given small change in volatility, holding everything else constant
Theta
The change in a derivative instrument for a given small change in calendar time
Position delta
the overall/portfolio delta
cash secured delta
an option strategy involving the writing of a put option and simultaneously depositing an amount of money equal to the exercise price into a designated account (also called fiduciary put)
How are spreads classified
1) Market sentiment
2) Direction of the initial cash flows
Bull spread
An option strategy that becomes more valuable when the price of underlying asset rises; requires buying one option and writing another with a higher exercise price
bear spread
an option strategy that becomes more valuable when the price of the underlying asset declines;
long put + short put, on different strikes
Debit spread
when the spread requires a cash payment by the investor; effectively long because the long option value exceeds the short option value
credit spread
when the spread initially results in a cash inflow to the investor; effectively short because the short option value exceeds the long option value
Long straddle
option combination in which one buys both puts and calls with the same exercise price and same expiration date on the same underlying asset
Short straddle
short put + short call, both with same strike
When would you use a straddle
when you expect volatility but don’t know which direction
Collar
long stock + long put (exercise below current price) + short call (exercise above current price)
When would you use a collar
protect gains that has long-term potential but are concerned about short-term volatility; limits both potential gains and losses
Calendar spread
a strategy in which one sells an option and buys the same type of option but with different expiration dates, on the same underlying asset and with the same strike
Implied volatility
Standard deviation that causes an option pricing model (BSM) to give the current option price
Realized volaility
Historical volatility, the square root of the realized variance of returns, which is a measure of the range of past price outcomes for the underlying asset
Annual Standard deviation %
StD monthly % * sq (252/21)
Volatility smile
the u-shaped plot (of implied volatility (y axis) against strike (x axis) for options on the same underlying with the same expiration) that occurs when the implied volatilities priced into both OTM puts and calls trade at a premium to implied volatilities of ATM options
Volatility skew
The skewed plot (of implied volatility (y axis) against strike price (x axis) for options on the same underlying with the same expiration) that occurs when the implied volatility increases for OTM puts and decreases for OTM calls, as the strike price moves away from the current price
Risk reversal
a strategy used to profit from the existence of an implied volatility skew and from changes in its shape over time. A combination of long (short) calls and short (long) puts on the same underlying with the same expiration is a long (short) risk reversal
Term structure of volatility
The plot of implied volatility (y axis) against option maturity (x axis) for options with the same strike price on the same underlying. Typically, implied volatility is not constant across different maturities - rather, it is often in contango, long-term options implied volatilities are higher than near-term ones
Implied Volatility surface
a 3-dimensional plot, for put and call options on the same underlying asset, of days to expiration (x axis), option strike prices (y axis), and implied volatilities (z axis). It simultaneously shows the volatility skew (or smile) and the term structure of implied volatility
Interest rate Swap
OTC contract between two parties that agree to exchange cash flows on specified payment dates - one based on a variable interest rate and the other based on a fixed rate - determined at the time the swap is initiated
Swap tenor
when the swap is agreed to expire
Basis risk
Spread risk, or the difference between the market performance of the asset and the derivative instrument used to hedge it
basis = bond - futures
Forward rate agreement
OTC derivative instrument that is used mainly to hedge a loan expected to be taken out in the near future or to hedge against changes in the level of interest rates in the future
The preferred instrument to hedge bond positions
Fixed income futures, given that their liquidity is high
Principal invoice amount
(futures settlement price/100) * CF * Contract Size
If the basis is negative how would a trader make profit
Buying the basis - purchasing the bond and shorting the futures
basis = bond - futures
If the basis is positive, how would a trade make profit
Selling the basis - sell the bond and buy the futures
basis = bond - futures contract
Hedge Ratio (HR)
Number of fixed-income futures contracts to be sold or purchased
Change in value of the bond portfolio (Delta P) = HR * change in value of the fixed income futures (Delta F)
HR = (Delta P / Delta CTD) * CF
Portfolio’s target basis point value
BPV = MDUR * 0.01% * MV
Basis point value hedge ratio (BPVHR)
- BPV (P) / BPV (CTD) * CF
Cross-currency basis swap
A swap in which notional principals are exchanged because the goal of the transaction is to issue a more favorable funding rate and swap the amount back to the currency of choice
Equity Swap
Derivative contract in which two parties agree to exchange a series of cash flows whereby one party pays a variable series that will be determined by a single stock, a basket of stocks, or an equity index and the other party pays either a variable series determined by a different equity or rate or a fixed series
Disadvantages to equity swaps
1) Require putting up collaterals
2) Relatively illiquid contracts
3) Do not confer voting rights
Advantages of equity swaps
1) When access to a specific market is limited
2) Taxes are levied for owning physical stocks (stamp duty) but not on swaps
3) Custodian fees are high
4) Cost of monitoring the stock position is elevated (corporate actions)
Number of equity futures contracts to buy or sell
NF = ((BT - BS) / BF) * (S/F)
Cash securitization (equitization/cash overlay)
Strategy designed to boost returns by finding ways to “equitize” unintended cash holdings
N(f) = (B(t) / (B(f)) * (S/F)
N(f) = number of futures contracts
B(t) = target beta
B(f) = beta of futures
S = portfolio market value
F = one futures contract value
VIX
“fear index”, measure of investor’s expectations of volatility in the S&P500 over the next 30 days
Payoff at settlement of a variance swap
(variance notional) * (realized variance - variance strike)
variance notional = vega notional / 2 * strike price
Vega Notional
The trade size for a variance swap, which represents the average profit and loss of the variance swap for a 1% change in volatility from the strike
What two things do variance swap traders typically agree on
1) A variance swap trade size expressed in vega notional (not in variance notional)
2) The strike (x), which represents the expected future variance of the underlying, expressed as volatility (not variance)
Variance notional
The notional amount of a variance swap; it equals vega notional divided by two times the volatility strike price
(vega notional) / (2 * strike price)
Rule of thumb for strike of a variance swap
Typically corresponds to the implied volatility of the put that has 90% moneyness (calculated as the option’s strike divided by the current level of the underlying)
Effective federal funds rate (FFE)
The fed funds rate actually transacted between depository institutions, not the Fed’s target federal funds rate
Probability of a change in the federal funds rate
(Effective federal funds rate implied by futures contracts - current federal funds rate) / (federal funds rate assuming a rate hike - current federal funds rate)
How much of the foreign exchange market do spot markets account for
less than 40%
FX Quoting Hierarchy
1) Currency pairs using EUR, EUR base
2) Currency pairs using GBP, other than EUR, GBP base
3) Currency pairs using AUD or NZD, other than EUR and GBP, AUD/NZD base
4) All other currency quotes using USD, USD base
Two forms of hedging costs
Trading costs and opportunity costs
Currency overlay program
Program to manage a portfolio’s currency exposures for the case in which those exposures are managed separately from the management of the portfolio itself
All else equal, the base currency’s real exchange rate should appreciate if there is an upward movement in…
1) Long-run equilibrium real exchange rate
2) Real or nominal interest rates, which should attract foreign capital
3) Expected foreign inflation, which should cause the foreign currency to depreciate
4) Foreign risk premium, which should make foreign assets less attractive compared with the base currency nation’s domestic assets
Carry trade
A trading strategy that involves buying a security and financing it at a rate that is lower than the yield on that security
Forward rate bias
The persistent violation of uncovered interest rate parity
uncovered interest rate parity states that forward rates are unbiased predictors of future spot rates, but this is empirically false, so therefore, it is a biased predictor
Return distribution of the carry trade
Pronounced negative skew
Is higher/lower volatility better for the carry trade
lower
Most important Greek traded
Vega
Why do institutional investors prefer forwards over futures when hedging currency trades
1) Futures contracts are standardized, which may not be exactly what they need
2) Futures contracts may not always be available in the currency pair that the PM wants to hedge
3) futures contracts require up-front margin (initial margin), as well as have intra-period cash flow implications
Static Hedge
A hedge that is not sensitive to changes in the price of the asset hedged
Dynamic hedge
A hedge requiring adjustment as the price of the hedged asset changes
Put spread
A type of short risk reversal position used to reduce the upfront cost of buying a protective put
Involves buying an OTM put option and writing another deeper OTM put option
Seagull spread
An extension of the risk reversal foreign exchange option strategy that limits downside risk
Long a protective put and then write both a call and deep OTM put
Knock-in/Knock-out
Features of a vanilla option that is created (or creases to exist) when the spot exchange rate touches a pre-specified level (barrier)
Cross hedge
A hedge involving a hedging instrument that is imperfectly correlated with the asset being hedged; for example, hedging a bond with futures on a non-identical bond
Proxy hedge vs. Cross hedge
Proxy hedge removes the foreign currency risk by hedging it back to the investor’s domestic currency, while a cross hedge moves the currency risk from one foreign currency to another foreign currency
Minimum-variance hedge ratio
A mathematical approach to determining the optimal cross hedging ratio (running a regression)
correlation * (risk of one/risk of other)
2 Considerations when managing emerging market currency exposures
1) Trading costs are higher (thinly traded)
2) Increased likelihood of shit hitting the fan
Non-deliverable forwards
Forward contracts that are cash settled (in the non-controlled currency of the currency pair) rather than physically settled (the controlled currency is neither delivered nor received)
synthetic long put
long call + short shares
theta for short stock + put position
positive
theta for short stock + long call
negative
where does the largest gamma occur
at or near the money
amount of cash exchanged at initiation of a variance swap
0
what does it mean to sell the basis
sell the bond and buy the futures
deriving the probability of a rate move by the FOMC
1) Calculate FFE from contract price: | 100-contract price |
2) (FFE - current contract price)
3) Federal funds rate assuming a rate cut (if contract price is below 100) - current FFE
4) step 2 / step 3
Currency swap - cash flows at inception
two parties pay the notional of the contract they agreed to enter into
Currency swap - periodic cash flows
payments based on floating rate
Currency swap - cash flows at maturity
notional principal in respective currencies
return of domestic currency
R(DC) = (1+R(FC))*(1+R(FX))-1
difference between currency swaps and fx swaps
fx swaps don’t have intermediate cash flows and are typically shorter r
time horizon needed for active currency management
long-term
4 situations that will cause real exchange rate of base currency to appreciate
upward movement in:
1) long-run equilibrium real exchange rate
2) real/nominal interest rates – this attracts foreign capital
3) expected foreign inflation – foreign currency will depreciate
4) foreign risk premium – makes foreign assets less attractive compared to base currency nation’s domestic assets
most significant factor to consider when using futures contracts
margin requirements
delta exposure in straddle
delta neutral
what side of the volatility trade do volatility traders set up as
net-short volatility
most options expire out of the money, and the option writer then gets to keep the option premium without delivery of the underlying
hedgers position themselves how in regards to volatility
long-volatility
they are buying protection from unanticipated price volatility
OTM delta range for put options
0 to -0.5
0 being more OTM
ATM delta for put option
-0.5
OTM delta range for call options
0 to 0.5
0 being more OTM
counterparty risk in futures
virtually zero because they are exchange traded, standardized, and guaranteed by a clearinghouse
total return swap vs equity swap
total return swap includes dividends
disadvantages of equity swaps
1) require putting up collateral
2) illiquid
3) do not confer voting rights (possibly a reason why you would do it)
are VIX options European, American, or Bermuda style
European
