Derivatives Flashcards
Pricing
vs
Valuation
Pricing generally takes place at initiation
Valuation value is determined at any given time following initiation
Fair value of a future =
Cash price + cost of carry
Ie cost of buying and holding until delivery at a future date.
Forward PRICE =
given spot and rf
Forward price given dividend =
PV dividend =
Forward VALUE =
Forward = Spot x (1+r)^T
Forward = Spot - PV dividend x (1+r) ^t
PV Dividend = Dividend / (1 + rf)^n/365
ie if prepricing the forward at day 100 and there is a dividend day 110 you discount 1+rf ^10/365 and subtract this from Spot from ON DAY 100!
Forward VALUE = (Forward PRICE on day 100 - Forward PRICE on day 0) / (1+rf)^remaining t
How often are gold futures marked to market?
Forward value =
Gold futures are marked to market daily
Forward value = Current stock price day 100 - PV of cash flows remaining - PV of original forward
3% Effective Annual Rate into continuous compound =
1.03 LN = 2.9559%
2 x 3 FRA means what?
FRA 2 x 3
Contract expires in two months.
Loan is settled in 3 months
FRA given
90 day LIBOR = 3.5%
180 day LIBOR = 3.9%
1 + (Rlong x n/360) / 1+(Rshort x n/360) - 1 = 1.065%
Reannualise = 0.01056 x (360/difference) = 4.26%
Difference = 180 - 90 = 90
Future price =
CTD Future =
cheapest to deliver future
Future price = CTD Future / Conversion factor
CTD Future = (Future price - PV of CF Until expiry) x 1 + rf^T
Forward currency =
Forward currency = Spot x (1+Rprice)^t / (1+Rbase)^t
e.g. t = 180/365
Interest rate swap =
Value at initiation
Value at initiation of a swap is always zero.
It is a series of call and put options equal to the swap rate.
Swap Fixed Rate SFR =
Discount factor =
LIBOR 90 days 4%
SFR = [(1- final discount factor) / sum of discount factors] x no settlement periods PER YEAR
Discount factor = 1 / 1 + (LIBOR x n/360)
1 / 1 + (0.04 x 90/360) = 0.9901
LIBOR 90 days 4%
Pay fixed receive floating is the same as =
Pay fixed = issuing a fixed coupon bond
Receive floating = Long FRN
Currency swaps are fixed or floating or a combination of both?
Currency swaps can be a combination of fixed and fixed, fixed and floating or floating and floating.
FRA payments are made on ‘notional principal amount’ when is this exchanged?
Almost always at the start of a contract but occasionally at the end.
Value of equity swap =
Step 1:
equity value = End value / start value x notional value = Ansa
Step 2:
Bond = (swap payment x sum of discount factors) + (1 x final discount factor) x notional value = Ansb
Step 3
Swap value today = Equity Ansa - Bond Ansb
Indices swap
FTSE d0 = 4000, FTSE d90 = 4200
S&P d0 = 12600, S&P d90 = 12900
Notional = £50m
Market value of swap =
Market value of swap = (Return from receiver leg - return on payer leg) x notional value
(12,900/12,600) - (4,200/4,000) x £50m = £1.309m
Binomial tree - Probability of an up/down move.
Probability of an UP move =
UP = (1 + Rf - D) / U - D
Down = 1 - Up
Black-Scholes-Merton option model =
Underlying assets follow a brownian motion process which change smoothly.
Interest rate is annualised continuously compounded.
Normally distributed Rf rate is KNOWN and CONSTANT
Options are European
Volatility is KNOWN and CONSTANT
BSM Long call C0 =
C0 = (S x N(d1)) - (e^-rfT x X x N(d2))
Nd1 = Buy stock Nd2 = Subtract = sell zero coupon bond
Spot = 20 rf = 4% Exercise price = 17 Nd1 = 0.64 Nd2 = 0.522
call = [20 x 0.64] - [(-0.04 x 1) 2nd LN x 17 x 0.522]
Note MINUS rf x T
BSM Long Put =
P0 = (e^rfT x X x N(-d2)) - (S0 x N(-d1))
N(-d2) = Buy zero coupon bond N(-d1) = Sell stock
What is the black model?
The model value European forwards and futures.
Call = e^-rfT x [Ft x Nd1 - X x Nd2] Put = e^-rfT x [X x 1 - Nd2] - f x T x [1-Nd1]
Individual interest rate call options =
Long cap plus short floor with same interest rate =
Portfolio of long interest rate put options =
Individual interest rate call options = cap
Long cap plus short floor with same interest rate = pay fixed, receive floating interest rate swap
Portfolio of long interest rate put options = long floor
What is a swaption?
Swaptions gives the holder the right to enter into an interest rate swap fixed and floating. A series of annuity cash flows.
Payer swaption
Receiver swaption
Payer swaption = fixed rate payer, equivalent to a long put on a bond. More valuable as rates rise.
Receiver swaption = fixed rate receiver
Delta =
No of calls to sell =
Delta = Change in option price / Change in share price
Delta = (no shares x 1) + (No call options x delta of call options)
No of calls to sell = Portfolio delta aka no shares / Delta of call option
Increase in interest rates
Call options
Put options
Increase in interest rates
Call options
Put options
Increase in interest rates
Call options = increase
Put options = decrease
Increase in interest rates
Call options = increase
Put options = increase
What is Gamma
Long options
Short options
Positive or negative and how to correct them
highest when
Gamma is rate of change of delta
Long options = Positive Gamma correct with a short call
Short options = Negative Gamma correct with a long call
Highest when at-the-money.
Vega =
Theta =
Vega is a volatility measure. Always positive value and exactly the same for puts and calls
Theta is a measure of time decay. Both puts and calls have NEGATIVE Theta which increases as expiry approaches.
Rho =
Positive Rho =
Positive Gamma =
Rho shows options prices changes to a change in the Risk Free rate. Positively related to calls and negatively to puts.
Positive Rho = long call and short put
Positive Gamma = long call and long put
If you think implied vol is greater than the market =
If you think implied vol is less than the market =
If you think implied vol is greater than the market Buy the put option
If you think implied vol is less than the market sell the call option.
