Please enable JavaScript.
Coggle requires JavaScript to display documents.
READING 33: RISK MANAGEMENT APPLICATION OF OPTION STRATEGIES (DELTA…
READING 33: RISK MANAGEMENT APPLICATION OF OPTION STRATEGIES
COVERED CALL
investor believes that the asset price remain unchanged over the short term.
=>
Buy a asset
Sell a call
Profit = - Max(0, S(T) - X) + Co+ S(T) - So
Max profit = Co+ X - So
Max loss = So-Co
BEP = So-Co
https://bit.ly/3cpV2WX
PROTECTIVE PUT
Investor want to buy insurance for his portfolio
=>
Buy an asset
Buy a put
Profit = Max (0, X- S(T)) -Po + S(T)-So
Max profit = Unlimited
Max loss= So-X+Po
BEP = So+Po
https://bit.ly/2VBIEwh
SPREAD STRATEGIES
BEAR SREAD USING PUTS
Investor expects the asset price will go down
with limited downside & expects a limited profit and loss
=>
Buy a put at high X price, X(H)
Sell a put a low X price, X(L)
Profit = Max[0, X(H)- S(t)] -Max[0, X(L)- S(t)] -Po(H)+ Po(L)
Max profit = X(H) - X(L)-Po (H) + Po(L)
Max loss = Po(H)-Po(L) (i.e. - beginning net premium)
BEP = X(H)-Po(H)+Po(L)
BEAR SPREAD USING CALLS
Investor expects the asset price will go down
with limited downside & expects a limited profit and loss
=>
Sell a call at low X price , X(L)
Buy a call at high X price , X (H).
Profit= - Max [0, S(T)-X(L)] + Max[0, S(T)-X(H)] +Co(L) -Co(H)
Max Profit = Co(L)-Co(H) (i.e. beginning net premium)
Max Loss= X(L)- X(H) +Co(L)- Co(H)
BEP= X(L)+Co(L)-Co(H)
https://cutt.ly/At7IJRB
BULL SPREAD USING CALLS
Investor expects the asset price will go up, but not above a certain level & expect a limited profit and loss
=>
Buy a call at low X price, i.e X (L)
Sell a call at high X price, i.e. X(H)
Profit = Max [0, S(t)- X(L)] - Max [0, S(t)- X(H)] -Co (L) + Co(H)
Max profit = X(H) - X(L) -Co (L) + Co (H).
Max Loss= Co(L)- Co(H) (i.e. - beginning net premium)
BEP= X(L)+ Co(L) -Co (H)
http://lnnk.in/ftaA
BUTTERFLY SPREAD WITH CALLS
Investor expects the asset price will STAY NEAR A PRICE LEVEL & expects a limited profit and loss
=>
Buy a call at Low X price , X(L)
Sell 02 calls at medium X price, X(M)
Buy a call at high X price, X(H)
2X(M) = X(L)+ X(H) , ie. equidistant part
Profit= Max[0, S(T)-X(L)] - 2*Max [0, S(T)-X(M)]+ Max[0, S(T)-X(H)] - Co(L)+2Co(M)-Co(H)
Max profit = X(M) - X(L) - Co(L)+2Co(M)-Co(H)
Max Loss= Co(L)-2Co(M)+-Co(H) (i.e. - beginning net premium)
BEP (
lower band
) = X(L) + Co(L)-2Co(M)+C0(H)
or BEP
(upper band
) = 2
X(M)-X(L) -Co(L)+2Co(M)-Co(H) = 2
X(M)- BEP(lower band)
https://cutt.ly/Zt7GSb7
BUTTERFLY SPREAD WITH PUTS
Investor expects the asset price will STAY NEAR A PRICE LEVEL & expects a limited profit and loss
=>
Buy a put at Low X price , X(L)
Sell 02 puts at medium X price, X(M)
Buy a put at high X price, X(H)
2X(M) = X(L)+ X(H) , ie. equidistant part
Profit= Max[0, X(L)-S(T)] - 2*Max [0, X(M)-S(T)]+ Max[0, X(H)-S(T)] - Co(L)+2Co(M)-Co(H)
Max profit = X(L)- X(M) - Co(L)+2Co(M)-Co(H)
Max Loss= Co(L)-2Co(M)+-Co(H) (i.e. - beginning net premium)
BEP (
upper band
) = X(L) - Co(L)+2Co(M)-Co(H)
or BEP
(lower band
) = 2
X(M)-X(L) +Co(L)-2Co(M)+Co(H) = 2
X(M)- BEP(upper band)
TRADDLE
You expect a large stock price move, but you are unsure of the direction
=>
Buy a call, same X price, expiration
Buy a put, same X price, expiration
Profit = Max (0, S(t)-X) + Max(0, X-S(t)) -Co-Po
Max Profit = S(t)- X -Co-Po (unlimited)
Max Loss= Co+Po
BEP = X+Co+Po or X-Po-Co
https://cutt.ly/Zt5XKqf
COLLAR
The usual goal is for the owner of the underlying asset to buy a protective put and then sell a call to pay for the put
=>
Buy an aset
Buy a Put
Sell a call
Profit = Max [0, X(L)- S(t)] -Max [S(t)-X(H)] + S(t)-So
Max Profit= X(H)-So
Max Loss= So-X(L)
BEP =So
https://cutt.ly/Jt5CC9j
BOX SPREAD STRATEGY
The box spread is a combination of a bull spread (expect limited upside) and a bear spread (expect limited downside) on the same asset, using only two strike prices (X(L) and X(H)
=>
Buy a bull spread using calls
Buy a bear spread using puts
Profit BOX SPREAD
= SUM of Max. profit ( bull spread, bear spread)
= X(H) - X(L) + Po(L) -Co(L) + Co(H)-Po(H)
https://cutt.ly/Ct5VEMv
INTEREST RATE OPTIONS AND EAR
Call Payoff = (NP)
( max(0, LIBOR- strike rate)
(D / 360)
Put Payoff = (NP)
( max(0, strike rate - LIBOR)
(D / 360)
The length of the loan = length of LIBOR . For Libor Yr=360 days
D stands for days in underlying rate. Not maturity of the call
General rule:
The general rule for interest rate options (such as caps and floors) is the interest rate for the payout is set at the expiration of the option but paid at the end of the interest rate period, not when the option expires
Libor uses 360 days in year
EAR uses 365 days in year
EAR = [(Notional principle + Effective dollar interest cost) / net loan amount] ^(365/D) -1
The purpose is to find the percentage (%)
Net loan amount = Notional principle - FV (call premium)
for call
Net loan amount = Notional principle + FV (call premium)
for put
FV (call premium) = call premium
[1+ (Libor + spread)]
(maturity/360)
The purpose is to find the absolute amount ($)
Effective dollar interest cost= borrowing cost w/o call payoff - call payoff
for call
Effective dollar interest cost= lending income w/o put payoff + put payoff
for put
= NP
[1+ (libor@ option expriration+ spread)]
(D/360)-call pay off or + put payoff
INTEREST RATE CAPS, FLOORS, COLLAR
INTEREST RATE CAPS
An interest rate cap is an agreement in which the cap seller agrees to make a payment to the cap buyer when the reference rate exceeds a predetermined called CAP STRIKE / CAP RATE
The cap is a series of interest rate call options
INTEREST RATE FLOORS
An interest rate floor is an agreement in which the seller agrees to pay the buyer when the reference rate falls below a predetermined interest rate called the FLOOR STRIKE or FLOOR RATE
The floor is a series of interest rate put options
Note: we compare the reference rate with the strike rate , NOT (ref. rate + float ) vs. strike rate
INTEREST RATE COLLAR
= long a cap, short a floor or vice versa
DELTA HEDGING
As more demand to buy options than there are sellers
=> Dealers can also serve as a source of supply by being willing to risk capital with a
net short position in options.
Delta hedging allows dealers to hedge the downside risk of short option positions
short a call + long the underlying
short a put + short the underlying
https://bit.ly/2Kdm7R4
Steps of delta hedge
https://bit.ly/3cww8Fe
Discussion
Options that are relatively far form expiration : delta hedging works well
The options were very close to expiration and ATM : poor performance of the delta hedge
Do not delta hedge for ATM options approaching expiration
GAMMA
https://bit.ly/2RRrZnj
VEGA
The most significant additional factor is volatility of the underlying.
Increase volatility
=> increase in value of calls/ puts
=> "immediate loss" to dealer's short options position
