Derivatives Flashcards
Forward price of an equity
= (S0 - PVD) x (1 + Rf)^T
= [S0 x (1 + Rf)^T] - FVD
Value of long forward contract
= Spot price - PV(forward price)
= St - FP/(1+Rf)^(T-t)
Value of forward on coupon-paying bonds
(St - PVC) - FP/[(1+Rf)^(T-t)]
Put-call parity
call + PV(ZCB) = put + stock
Risk-neutral probability of an up move
(1 + Rf - D)/(U - D)
Size of a down-move
1/(size of up move)
Option’s delta
(Up-value of call - Down-value of call)/(Up-value of stock - Down-value of stock)
units in shares/option
Assumptions of Black-Scholes
- Price of underlying asset follows a lognormal distribution
- Risk-free rate and volatility are constant and known
- Markets are frictionless
- Underlying asset has no cash flow
- Options are European style
Delta-neutral hedge
Combination of long stock and short calls to hedge value of portfolio
of options needed = # of shares hedged/delta
What is delta and how are call and put options affected?
Change in option price as asset price changes
- positive for calls: option value increases as underlying increases
- negative for puts: option value decreases as underlying increases
What is vega and how does call and put options affected?
Change in option price as volatility changes
- positive for calls and puts
What is rho and how does call and put options affected?
Change in option price as risk free rate changes
- positive for calls
- negative for puts
What is theta and how are call and put options affected?
Change in option price with the passage of time
- as calls and puts approach maturity (passage of time increases), option value decreases, except for deep in-the-money put options
What is gamma and how does it affect dynamic hedging?
Change in delta as the price of the underlying changes
Hedges that use high gamma options (ATM options) will require frequent rebalancing
Value of plain vanilla swap
(1 - Zn)/(Z1 + Z2 +…+ Zn)
Use calls and puts to describe the position of a cap buyer
- long call on LIBOR
- long put on bond prices
Use calls and puts to describe the position of a floor buyer
- long put on LIBOR
- long call on bond prices
Value of currency forward
St/(1+Rfc)^(T-t) - FT/(1+Rdc)^(T-t)
What are Eurodollar futures?
- Similar to forward rate agreements
- Based on 90-day LIBOR
- Calculated as 100 minus annualized LIBOR
Normal backwardation
Futures prices are expected to be less than expected future spot prices (hedging activity by sellers)
Normal contango
Futures prices are expected to be greater than expected future spot prices (hedging activity by buyers)
Delta for call option
= 1 - delta of put option
= Δoption price/Δstock price
Backwardation
Futures price < spot price
Contango
Futures price > spot price
