READING 33: RISK MANAGEMENT APPLICATION OF OPTION STRATEGIES

COVERED CALL

PROTECTIVE PUT

investor believes that the asset price remain unchanged over the short term.
=>

  1. Buy a asset
  2. Sell a call

Investor want to buy insurance for his portfolio
=>

  1. Buy an asset
  2. Buy a put
  1. Profit = - Max(0, S(T) - X) + Co+ S(T) - So
  2. Max profit = Co+ X - So
  3. Max loss = So-Co
  4. BEP = So-Co

Covered Call
https://bit.ly/3cpV2WX

  1. Profit = Max (0, X- S(T)) -Po + S(T)-So
  2. Max profit = Unlimited
  3. Max loss= So-X+Po
  4. BEP = So+Po

Protective put
https://bit.ly/2VBIEwh

SPREAD STRATEGIES

BEAR SREAD USING PUTS

BEAR SPREAD USING CALLS

BULL SPREAD USING CALLS

Investor expects the asset price will go up, but not above a certain level & expect a limited profit and loss
=>

  1. Buy a call at low X price, i.e X (L)
  2. Sell a call at high X price, i.e. X(H)
  1. Profit = Max [0, S(t)- X(L)] - Max [0, S(t)- X(H)] -Co (L) + Co(H)
  2. Max profit = X(H) - X(L) -Co (L) + Co (H).
  3. Max Loss= Co(L)- Co(H) (i.e. - beginning net premium)
  4. BEP= X(L)+ Co(L) -Co (H)

Bull spread using calls
http://lnnk.in/ftaA

Investor expects the asset price will go down
with limited downside & expects a limited profit and loss
=>

  1. Sell a call at low X price , X(L)
  2. Buy a call at high X price , X (H).
  1. Profit= - Max [0, S(T)-X(L)] + Max[0, S(T)-X(H)] +Co(L) -Co(H)
  2. Max Profit = Co(L)-Co(H) (i.e. beginning net premium)
  3. Max Loss= X(L)- X(H) +Co(L)- Co(H)
  4. BEP= X(L)+Co(L)-Co(H)

Bear spread using calls
https://cutt.ly/At7IJRB

Investor expects the asset price will go down
with limited downside & expects a limited profit and loss
=>

  1. Buy a put at high X price, X(H)
  2. Sell a put a low X price, X(L)
  1. Profit = Max[0, X(H)- S(t)] -Max[0, X(L)- S(t)] -Po(H)+ Po(L)
  2. Max profit = X(H) - X(L)-Po (H) + Po(L)
  3. Max loss = Po(H)-Po(L) (i.e. - beginning net premium)
  4. BEP = X(H)-Po(H)+Po(L)

BUTTERFLY SPREAD WITH CALLS

Investor expects the asset price will STAY NEAR A PRICE LEVEL & expects a limited profit and loss
=>

  1. Buy a call at Low X price , X(L)
  2. Sell 02 calls at medium X price, X(M)
  3. Buy a call at high X price, X(H)
    2X(M) = X(L)+ X(H) , ie. equidistant part
  1. 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)
  2. Max profit = X(M) - X(L) - Co(L)+2Co(M)-Co(H)
  3. Max Loss= Co(L)-2Co(M)+-Co(H) (i.e. - beginning net premium)
  4. BEP (lower band) = X(L) + Co(L)-2Co(M)+C0(H)
    or BEP (upper band) = 2X(M)-X(L) -Co(L)+2Co(M)-Co(H) = 2X(M)- BEP(lower band)

Butterfly spread with calls
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
=>

  1. Buy a put at Low X price , X(L)
  2. Sell 02 puts at medium X price, X(M)
  3. Buy a put at high X price, X(H)
    2X(M) = X(L)+ X(H) , ie. equidistant part
  1. 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)
  2. Max profit = X(L)- X(M) - Co(L)+2Co(M)-Co(H)
  3. Max Loss= Co(L)-2Co(M)+-Co(H) (i.e. - beginning net premium)
  4. BEP (upper band) = X(L) - Co(L)+2Co(M)-Co(H)
    or BEP (lower band) = 2X(M)-X(L) +Co(L)-2Co(M)+Co(H) = 2X(M)- BEP(upper band)

TRADDLE

You expect a large stock price move, but you are unsure of the direction
=>

  1. Buy a call, same X price, expiration
  2. Buy a put, same X price, expiration
  1. Profit = Max (0, S(t)-X) + Max(0, X-S(t)) -Co-Po
  2. Max Profit = S(t)- X -Co-Po (unlimited)
  3. Max Loss= Co+Po
  4. BEP = X+Co+Po or X-Po-Co

Straddle
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
=>

  1. Buy an aset
  2. Buy a Put
  3. Sell a call
  1. Profit = Max [0, X(L)- S(t)] -Max [S(t)-X(H)] + S(t)-So
  2. Max Profit= X(H)-So
  3. Max Loss= So-X(L)
  4. BEP =So

Collar
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)
=>

  1. Buy a bull spread using calls
  2. 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)

Box spread
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

INTEREST RATE FLOORS

  1. 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
  2. The cap is a series of interest rate call options
  1. 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
  2. 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

Delta for long and short calls and put options
https://bit.ly/2Kdm7R4

Steps of delta hedge
Steps to delta hedge
https://bit.ly/3cww8Fe

Discussion

  1. Options that are relatively far form expiration : delta hedging works well
    1. The options were very close to expiration and ATM : poor performance of the delta hedge
    2. Do not delta hedge for ATM options approaching expiration

GAMMA

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