Derivatives formula Flashcards

mari
Terms Definitions
Question
Answer
(d/dx) tanu
u'sec^2u
(d/dx) cosu
-u'sinu
(d/dx) cu
cu'
(d/dx) cotu
-u'csc^2u
(d/dx) lnu
u'/u
(d/dx) secu
u'(secu tanu)
Simple Interest (formula)
i1 = D0 * r
Short Call (Key Formulae)
MaRi: unlimited, MaRe: premium received, BEaex: exercise price + premium.
horizontal spread (Key Formulae)
MaRi: net initial debit, MaRe: indeterminate, subject to relative changes in premiums, BEaex: indeterminate, subject to relative changes in premiums.
BPV (formula)
BPV = Modified duration * Dirty Price of Bond * 0.01 / 100
Volatility (formula)
σ = sqrt( sum((r - ř)^2) / n)
Flat Yield (formula)
Y = Gross Coupon / Market Price
box (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
conversion (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
Terminal value simple interest (formula)
D1 = D0 * (1+r)
Future profit/loss (formula)
Future profit/loss = ticks x tick value x contracts
Long Put (Key Formulae)
MaRi: premium paid, MaRe: exercise price - premium, BEaex: exercise price + premium.
Value Basis (formula)
Value Basis = Fair Value - Future
Futures Price CTD (formula)
Futures Price = (Price of deliverable bond + Finance cost - Bond Income) / Price Factor
Theoretical Basis (formula)
Theoretical Basis = Cash Price - Fair Value
DDM (formula)
Value of Stock = Dividend per share / (Discount Rate - Dividend growth rate)
Invoice amount (formula)
Invoice Amount = Price of future * Price Factor + Accrued Interest
short butterfly (Key Formulae)
MaRi: difference between one set of strikes less initial credit, MaRe: net initial credit, BEaex: lower strike + credit, higher strike - credit
Hedging Non-CTD (formula)
Number of contracts = ( Nominal Value of Portfolio / Nominal Value of future ) * Price factor of CTD * ( BPV hedge bond / BPV CTD )
Volatility of 2 securities (formula)
σa+b = sqrt(pa^2*σa^2 + pb^2*σb^2 + 2pa*pb*σa*σb*cor(ab)), p = proportion of funds invested in each security, cor = correlation between the returns on two securities.
Short Put (Key Formulae)
MaRi: exercise price - premium, MaRe: premium received, BEaex: exercise price - premium.
cylinder (Key Formulae)
MaRi: limited, cap set by put, MaRe: limited, floor set by call, BEaex: stock price +/- net initial debit/credit.
synthetic short call/covered put (Key Formulae)
MaRi: unlimited, MaRe: initial value of stock/future - exercise price + put premium, BEaex: initial value of stock/future + put premium.
synthetic long call (Key Formulae)
MaRi: initial value of stock/future - exercise price + put premium, MaRe: unlimited, BEaex: initial value of stock/future + put premium.
Greeks on dividend paying stock (formula)
Delta Call: N(d1), Delta Put: -N(-d1)
synthetic long put (Key Formulae)
MaRi: exercise price - initial value of stock/future + call premium, MaRe: initial value of stock/future - call premium, BEaex: initial value of stock/future - call premium.
Greeks on future options premium upfront (formula)
Delta Call: e^(-rt)*N(d1), Delta Put: -e^(rt)*N(-d1)
Theoretical Futures Price CTD (formula)
Fair Price = (Dirty Price + (Dirty Price * Finance Rate * Days in the holding period / 365) - Interest paid and accrued) / Price Factor
Fair Value (bond future formula)
Fair Value = Futures Price * Price Factor
Hedging Non-CTD (formula using GRY)
Number of contracts = ( Nominal value of hedge bond / Nominal value of future ) * ( Price factor of CTD / Price of CTD ) * ( Duration bond / Duration CTD ) * ( 1 + GRY of CTD ) / ( 1 + GRY of hedge bond ) )
Weighted average portfolio (formula)
( Holding_1 * Price_1 * Beta_1 + ... + Holding_n * Price_n * Beta_n ) / (Holding_1 * Price_1 + ... + Holding_n * Price_n )
long strangle (Key Formulae - call strike > put strike)
MaRi: limited to premiums, MaRe: unlimited, BEaex: upside: higher strike + premium, downside: lower strike - premium.
Binomial Expression (formula)
P(r) = n! / (r! * (n - r)! * p^r * (1 - p)^(n - r)
Black Scholes (formula call on futures/forwards)
C = F * e^(-rt) * N(d1) - X * e^(-rt) * N(d2), F = the future/forward price
Put/Call Parity (formula - Currency Options - ConDis)
C - P = S * e^(-ft) - K * e^(-rt) (S = spot price of currency, f = interest earned on currency)
Put/Call Parity (formula - Stock Index Options - ConDis)
C - P = S * e^(-dt) - K * e^(-rt) (S = cash price of index, d = annual rate continuous dividend yield)
Binomial Model (formula probability upmove - equity index option)
p = (e^(rt - yt) - d) / (u - d), y = dividend yield
Black Scholes (formula d1 of call on a currency)
d1 = (ln(S/X) + (rd - rf + 0.5 * σ^2) * t) / (σ * sqrt(t))
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