“ RISK MANAGEMENT APPLICATIONS OF OPTION STRATEGIES ” 2.2 Risk Management Strategies with Options and the Underlying An investor can exposure without selling the underlying through: C
Trang 1“ RISK MANAGEMENT APPLICATIONS OF OPTION STRATEGIES ”
2.2 Risk Management Strategies with Options and the Underlying
An investor can exposure without selling the underlying through:
Covered call
Protective put
IR = Interest Rate
NP = Notional Principal
2.2.1 Covered Calls
Long stock + short call
Appropriate when stock price neither nor in near future
Limited upside potential & downside protection
Reduces both overall risk & the expected return
=−0, −
= −
the X, lower the option premium
2.2.2 Protective Puts
Long stock + long put
Provide protection against in value (similar to insurance)
Requires upfront option cost
Appropriate when an investor expects a in value of the stock in near future
= + 0, −
Profit =−− &
Max loss =+ −
Break even = +
2.3 Money Spreads
another identical option but either with different X or different time to expiration
Trang 22.3.1 Bull Spreads
Buying a call with a lower X & selling another with X
future
Similar to covered call it provides protection against downside risk
& limited upside potential
Where & are option premiums for the lower X & higher X respectively
= Value of long call - value of short call
Profit ==+
Max profit = −−+
Max loss = −
Breakeven = +−
Bull Put Spread
Buys a put with a lower X & sells an identical put with a higher X
Cash inflows at initiation of the position
Identical to the sale of bear put spread
Profit occurs when both put options expires out-of-the money
Bear Put Spread
Long position in a put with X & short position in a put with a X
= − Where
P2 = put premium on higher X
= value of long put - value of short put
Profit = − +
Max profit = −− +
Max loss = −
Breakeven = − +
2.3.2 Bear Spreads
Bear Call Spread
Investor sells a call with a lower X & buys an otherwise identical call with a higher X
Investor will earn net premium when both call options expire out-of-the money
Identical to the sale of a bull call spread
Trang 3Long Butterfly Spread
Long bull call spread + short bull call spread
Require cash outlay at initiation because bull spread purchased by an investor is expensive than a bull spread sold
relative to market expectations
=0, − − 20, − + 0, −
= − 2+
Two breakeven points
+− 2+
2.3.3 Butterfly Spreads
Short Butterfly Spread
Selling the calls with & & buying two calls with
relatively high compared to market expectations
Long Butterfly Spread (using puts)
Long bear put spread + short bear put spread
Cost of < <
Long Butterfly Spread (using puts)
Selling the puts with & & buying two puts with
Max profit = + − 2
If correctly priced, butterfly spread using calls will provide the same result as butterfly using puts
2.4.1 Collars
Strategy in which cost of buying put option can be reduced by selling a call option
Provide downside protection at the expense of giving up upside potential
Put X & call X results is in both the upside & downside potential
Quite similar to bull spread with respect to cap on gains & a floor on loss but
no underlying holdings in bull spread
=+ 0, − − 0, −
2.4 Combinations of calls and Puts
Trang 4Long Straddle
Buying at-the-money put & a call with same X on same underlying &
expiration
Costly strategy
=0, − + 0, −
Breakeven ± +
2.4.2 Straddle
Short Straddle
Selling a put & a call with same X on the same underlying with the same expiration
Preferable when neutral view about volatility
Unlimited loss potential
This strategy gains when both the options expires out-of-the money
Variation of Straddle
Adding cal (put) to a straddle is known as strap (strip)
Long strangle ⇒ variation of the straddle (buying put &
calls with different (X)
Short strangle ⇒ selling the put & call with different X
2.4.3 Box Spread
Bull spread + bear spread
Long Box Spread
Long call with & short cal with + long put with & short put with
If options are correctly priced, the box spread payoff is always RF (riskless strategy)
PV of the payoff discounted at RF should be equal to initial outlay
Profit & Max profit = −−−+ −
No breakeven & max loss
Short box is also possible with opposite positions
Benefits of box spread:
To exploit an arbitrage opportunity
Does not require a volatility estimate
Hold lower transaction costs
Trang 53 INTEREST RATE OPTION STRATEGIES
IR call & put options are used to protect against IR
IR call option pay-off = N.P × Max (0, underlying rate at expiration –exercise rate)
× Days in underlying rate/360
180 day LIBOR can be used as the underlying rate & underlying days could
be 180, 182 183 etc
Rate is determined on the day when option expires & payment is made m days later
IR put option pay-off =NP × Max (0, X – underlying rate at expiration) × days in underlying rate/360
3.1 Using Interest Rate Calls with Borrowing
Used by borrowers to manage IR risk on floating rate loans
Consider the following factors:
Option expiration date is the same as when loan starts
Option pay-offs must occur at the time when borrower makes IR payments
on loan
3.2 Using Interest Rate Puts with Lending
Used by lender to manage IR risk on floating rate loans
3.3 Using an Interest Rate Cap with a Floating-Rate Loan
Interest rate cap ⇒combination of IR call options
Each option in a cap is called a caplet
Each caplet has same X but its own expiration date
Cap seller makes payments if IR < strike rate
Payoff is determined on its expiration date but made on the next payment date
Cap pay-off = NP × (0, LIBOR on previous reset date – X) X days in settlement period / 360
Effective interest = interest due on the loan – caplet pay-off
3.4 Using an Interest Rate Floor with a Floating-Rate Loan
Floorlet pay-off = NP X (0,X –LIBOR on previous reset date) × days in settlement period/360
Effective interest = interest received on the loan + floorlet pay-off
Trang 63.5 Using an Interest Rate Collar with a Floating-Rate Loan
Combination of a long (short) position in a cap & a short (long) position in a floor
The borrower (lender) can buy a cap (floor) to protect against rising (falling) IR &
sell the floor (cap) to finance the premium paid to buy a cap
Initial cost of the hedge can be by call exercise rate & floor exercise rate
Cost can also be by having NP for the cap & NP for the floor
Borrower will benefit when IR & will be hurt when IR within the collar
4 OPTION PORTFOLIO RISK MANAGEMENT STRATEGIES
Dealers provide liquidity to the market & take risk by trading in options
Dealers use different hedging strategies to avoid risk
If a dealer has sold a call, he can hedge his/her risk by:
Buying an identical call option
Buying a put with same X & expiration, buying the asset & selling a bond (static hedge)
Using delta hedging
Size of the long position in underlying to offset the risk associated with short position in option = -1/ delta
Three complicating issues in delta hedging:
Delta is an approximate for small changes only
Delta changes with the change in the price of the underlying & or time
Small amount of imprecision due to rounding the no of unit of underlying
4.1 Delta Hedging an Option over Time
priced ∆ or with the passage of time
Delta of in-the-money (out-of-the money) call option will () towards 1 (0) near expiration
Delta hedges are most difficult to maintain for-at-the-money option & /or near expiration
Hedging Using Non-Identical Option
=
= −∆
∆
= +
Where
& = quantity of each option that hedges the value of one of the options in
a portfolio
& = price of option 1&2
desired quantity of option 1 relative to option 2:
Trang 74.2 Gamma and the Risk of Delta
=
Larger the gamma greater will be the risk
Gamma is largest for at-the-money options & /or near expiration
4.3 Vega and Volatility Risk
! =
At-the-money option has greater sensitivity to ∆ in volatility
Volatility is unobservable, so it is difficult to estimate Vega
Delta is required to manage Vega risk jointly with delta & gamma
5 FINAL COMMENTS
Major difference b/w equity & bond option strategies are that bond options must expire before the bond mature
Bullish (bearish) investor buys puts (calls) on IR
Bullish (bearish) equity or bond investors buy calls (puts)