Options Flashcards
Market Value of Equity
MVE = LC(k=k)
Market value of Debt
MVD = Enterprise value - MVE
Interest rate of debt
PV debt = Face value of debt/(1+r)^T
Breakeven rate
Breakeven = S +C or -P
SPKC
S+P=PV(K)+C
Binary Call
BC = Payoff * N(d2) * e^(-rcc*t)
BMS Call option
C = SN(d1) - PV(K)N(d2)
BMS d1
d1 = (ln(S/K) + T(r+sd^2/2)) / (sd(T)^0.5)
BMS d2
d2 = d1 - sd*(T)^0.5
Sd 1 year
SD 1 year = (SD6month^2 *2)^0.5
rcc
1+r = e^(rcc*t) | r for period t
u
u = e^ (sd*(T/N)^1/2)
d
d = 1/u
R
R = (e^rcc / 1+r)^(T/N)
probability u
p_u = (R-d)/(u-d)
Cu (risk neutral)
Cu = (Cuupu + Cudpd) / R
Cd (risk neutral)
Cd = (Cudpu + Cddpd) / R
C (risk neutral)
C = (pu^2Cuu + 2pupdCud + pd^2*Cdd) / R^2
△u
△u = (Cuu-Cud) / (u*S * (u-d))
Bu
Bu = (Cuu - △u*uuS) / R
Cu (Dynamic replication)
Cu = △u*uS + Bu
△d
△d = (Cud-Cdd) / (d*S * (u-d))
Bd
Bd = (Cdd - △d*ddS) / R
Cd (Dynamic replication)
Cd = △d*dS + Bd
△
△ = (Cu-Cd) / (S * (u-d))
B
B = (Cu - △*uS) / R
C (dynamic replication)
C = △*S + B
Synthetic call option
C = △*S - B
Synthetic put option
P = B - △*S
New S (BMS)
S = S - Dividend/e^(rcc*T) | T - of the dividend
