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Derivative, RISK, American option vs European option, Spot market,…

- - - - The right to buy the underlying asset
    - - The right to sell the underlying asset
- - - - aka how many call for 1 stock
    - - discount rate = e^ (r x t)
        r = discreate rate, t = time
  - - - 1- p = % of portfolio going down
- - - - ST<X or X>ST
        
        Π = X-𝑆0 - P
        
        Min Profit/Max los
      - ST> X or X<ST
        
        Π = 𝑆𝑇 - 𝑆0 -P
        
        Max profit
        
        Breakeven Π = 0
        ST=S0+P
  - - - Long a Stock
        +S
      - Short a CALL
        -C
      - Payoff
        
        Π = 𝑆𝑇 - 𝑆0 -Max(0, 𝑆𝑇 - X) + C
        
        ST>X
        In the money
        
        Π =X+C-S0
        
        Max profit
        
        ST< X
        Max =0
        
        Π =ST-S0+C
        
        Max loss/Min profit, ST =0
        Π =C-S0
      - Protect again stock price falling
        Bearish
  - - - Profit equation
        
        CALL held to expiration
        Π = 𝑁𝐶[Max(0, 𝑆𝑇 - X) - C]
        
        Buyer of 1 call
        NC= 1
        +C
        
        Π = Max(0, 𝑆𝑇 - X) - C
        
        If ST>X
        =>In the money
        
        Π= ST-X-C
        
        1 more item...
        
        ST<X
        ST-X max = 0
        
        Π= -C
        Max loss
        
        Seller of 1 call
        NC = -1
        -C
        
        Π = -Max(0, 𝑆𝑇 - X) + C
        
        If ST>X
        Π=C-ST+X
        
        Breakeven Π =0
        ST= X+C
        
        ST<X
        Π =C
        
        Max gain
        
        puts held to expiration
        Π =𝑁𝑃[Max(0,X - 𝑆𝑇) - P]
        
        buyer of one put
        𝑁𝑃 = 1
        +P
        
        Π = Max(0,X - ST) - P
        
        ST<X =>In the money
        
        Π=X-ST-P
        
        1 more item...
        
        ST>X -> Max = 0
        
        Π=-P
        
        1 more item...
        
        seller of one put
        𝑁𝑃 = -1
        -P
        
        Π = -Max(0,X - ST) + P
        
        ST<X
        
        Π= -X+ST +P
        
        1 more item...
        
        ST>X => Max =0
        
        Π=P
        
        1 more item...
        
        STOCK
        Π = 𝑁𝑆[𝑆𝑇 - 𝑆0 ]
        
        buyer of one share
        (𝑁𝑆 = 1)
        +S
        
        Π = 𝑆𝑇 - 𝑆0
        
        Max loss = -S0
        
        short seller of one share
        𝑁𝑆 = -1
        -S
        
        Π = - 𝑆𝑇 + 𝑆0
        
        Max gain = S0
        Max loss = infinitive
  - - - 𝑃 = 𝐶 − 𝑆0 + 𝑋𝑒^(−𝑟𝑇)
        
        Π = 𝑁𝑆 𝑆𝑇 − 𝑆0 + 𝑁𝐶 [𝑀𝑎𝑥 0, 𝑆𝑇 − 𝑋 − 𝐶]
        
        ST>X
        In the money
        
        ST< X
        Max =0
      - Long CALL
        +C
      - Short S
        -S
  - - - Limits up and downside potential
        Good for arbitrage if one option is overprice relative to another
        
        Π = Max(0, 𝑆𝑇 - X1) - C1 - Max(0, 𝑆𝑇 - X2) + C2
        
        ST> X1>X2
        in the money
        
        Π = X2- X1- C1+C2
        
        ST<X1<X2
        Max = 0
        All out of the money
        
        Π = -C1 +C2
        
        X1<ST<X2
        MAX2=0
        
        Π = 𝑆𝑇 - X1 - C1 + C2
    - - Benefit from speculation of a stock price fall, but with limited up /
        downward potential
        
        Π = -Max(0, 𝑆𝑇 - X1) + C1 + Max(0, 𝑆𝑇 - X2) - C2
        
        ST>X1>X2
        All, in the money
        
        Π =X1 + C1 - X2 - C2
        
        X1<ST<X2
        
        Π = 𝑆𝑇 - X1 - C1 + C2
        
        ST<X2<X1
        All, out of the money
        
        Π = C1 - C2
    - - Speculate that large stock price movements are unlikely
    - - Π = -Max(0,X1 - ST) + P1 + Max(0,X2 - ST) - P2
        
        ST < X1 < X2
        
        Π = X2-X1+P1- P2
        
        MAX PROFIT
        
        X1 < ST < X2
        
        Π =P1 + X2 - ST - P2 if
        
        Breakeven Π =0
        ST = P1-P2+X2
        
        X1 < X2 < ST
        
        Π = P1 - P2
        
        Max loss
    - - Π = ST - S0 + Max(0,X1 - ST) - P1 - Max(0,ST - X2) + C2
        
        ST < X1 < X2
        
        Π= X1 - S0 - P1 + C2
        
        X1 < ST < X2
        
        Π= ST - S0 - P1 + C2
        
        X1 < X2 < S
        
        Π=X2 - S0 - P1 + C2
    - - Benefit from volatility and time value decay
    - - Straddle
        +C +P
        
        You think the stock will move (but don’t know in which direction)
      - Strip
        
        Double bet on Stock going down
        
        down
        +P +P +C
        
        Π = Max(0,ST - X) - C + 2Max(0,X - ST) - 2P (assuming Nc = 1, Np = 2)
        
        ST > X
        PUT out of money
        CALL in the money
        
        Π = ST - X - C - 2P
        
        1 more item...
        
        if ST < X
        PUT IN THE MONEY
        CALL OPUT OF THE MONEY
        
        Π = 2X - 2ST - C - 2P
        
        1 more item...
      - Straps
        
        Double bet on Stock going up
        
        UP
        +C + C +P
- - - - N(0,1)
        
        Mean = 0
    - - Change in Stock price
        
        dS= S(t) - S(t-1)
        
        week 4 page 7
        
        Drift rate (up vs down)
        
        volativity rate
  - - - C = the call option price
      - S = the current stock price
      - x = the strike price
      - r = the risk-free interest rate
        
        e^(-rt) = Expected return periodic
      - t = the time to expiration (in years)
      - N(d1), N(d2) = the cumulative normal distribution function
        
        value between 0 and 1
      - d1 and d2 are intermediate variables calculated as:
        
        d1= [ln(S/X) + (r + [o^2]/2)t ] / [o sqrt(t) ]
        
        d2= [ln(S/X) + (r - [o^2]/2)t ] / [o sqrt(t) ]
        
        OR d2 = d1- [o x sqrt(t)]
      - sigma=o= Standard deviation of log return
    - - European Call option
        
        C = SN(d1) - X[e^(-rt)]N(d2)
        
        component
        
        S =0
        
        Ln(S/X) ->0
        
        d1, d2->0
        
        1 more item...
        
        T=0
        
        r=0
        
        x = 0
        
        Ln(S/X) -> 1
        
        d1, d2 ->1
        
        1 more item...
      - Black Scholes differential equation
      - With Dividend payment
        
        S0 =S0 - D(t) x e^(-rt)
        
        t must be in year
        
        WITH DIVIDEND YEILDS
        
        When dividend accrual continuously
        
        S0=S0- Dt x e^(-rt)
        
        Dt = dividend at time t
        
        Accumulation index - price index = div yield
        
        PSEUDO AMERICAN OPTION
        
        t
        
        Ex Div
        
        T
        
        t= ex Div
        s'
        x = x- div
        
        t = T
        S= S'-PV(Div)
        x = x'
  - - - historical = past information or past volatility
      - Implied volatility
- - - - Expose to DEFAULT RISK
  - - - has standardised terms,
        
        Delivery term
        
        Delivery cycles
      - is traded in an organised exchange, and follows daily settlement procedures where losses from one party are paid to the other.
- - - - Reduce or Alter risk exposure
      - Reason for NOT HEDGING
        
        Hedging can give a misleading impression of the amount of risk reduce
        
        Risk is not reduced or eliminate, it is transferred to another type/style
        
        Hedging eliminates the opportunity to take advantage of favourable market conditions
    - - SHORT
        
        To cover any possible in the fall in price of the underlying
        
        Π = (𝑆𝑇 − 𝑆0) − (𝑓𝑇 − 𝑓0)
      - LONG
        
        To cover any possible in the RISE in the price of the underlying
        
        Π = −𝑆𝑇 + 𝑆0 + (𝑓𝑇 − 𝑓0)
      - Basis
        
        = spot price - futures price
        
        Spot price from the spot market
        
        𝑆𝑇 − 𝑆0
        
        Future from the future market
        
        𝑓𝑇 − 𝑓0
- - - - S has no ceiling
      - If no excercise
        
        Save money by saving EXERCISE price (X)
      - S>X -> in the money
      - S<X out of the money
    - - C = P + S - PV(X)
        
        PV(X) = X - r
      - Condition:
        same strike price
        same expiration
    - - Higher r -> higher C
    - - Higher delta -> higher C,
  - - - S has floor = 0
      - If no exercise
        
        Not earning EXERCISE price (X)
      - S< X -> In the money
      - S>X-> out of the money
    - - Higher r -> lower P
    - - Similar to call
- - - - WHEN HAVE EXPECTATION OF MARKET GOING UP OR DOWN
        
        TAKE POSITION BASED ON THAT ASSUMPTION
- - - - For ex, delta = 7 mean oif Stock price (S) increased for 1$, a call option (C) will go up 70 cent
      - change in call price /SMALL change in stock price
  - - - Positive
        
        Gamma for call = gamme for put
- - - - volatility has the same impact on call and put (POSITIVE)
      - Volatility of call = volatility of put