B/S is for pricing...
European options
Can use P/C parity if you have a B/S european call price and need
to figure out the price of a european put
FACT: Never exercise early on an American _____ on a non dividend paying stock
call
-use B/S because it acts like a euro call
when pricing american FX calls..
you can't use B/S
if the spot price changes by a "little bit
the call (put) price will change by delta "little bits
link between puts and the equity portfolio
beta/delta
y=mx+b can be written as
y-yo=m(x-xo)
where xo and yo are any point on the line
create a 3 asset portfolio equal to a long forward with
long call, short put and a bond with a face value of (k-0Ft)
P/C/F and P/C parity only work for
european options
if P-C>B
-buy +B (now)
-sell +P (sell put with strike=k)
-Buy +C (buy call now with strike=k)
if delta is positive
we want to lend delta units of denominator (foreign) currency
if B is negative
we want to buy B units of numerator ($) currency
in a binomial tree Ct up
max(0,u*St-k)
in a binomial tree Ct down
max(0,d*St-k)
to do a binomial tree for puts a calls first you need to
find the evolution of the spot and then overlay the call values
for the evolution of the spot you move
left to right
for the evolution of the call you move
right to left
American call/put binomial tree you need to measure
max(dead,alive)
final nodes stay the same
Cu dead
max(0,Su-k)
C alive is
what was determined in the evolution of the spot
in order to find Co
need to calculate based on the new Cu and Cd, then compare to the previous Co (euro) to determine if you need to early exercise
annualized volatility of spot rate returns
8-20%
short underlying position
CF exit= --oFt--bexit
where bexit is the beta at the time of the exit
basis risk does not affect
speculators
what is a CALL option
it gives the owner the right but not the obligation to BUY a specific asset at a specific time
what is a PUT option
it gives the owner the right but not the obligation to SELL a specific asset at a specific time
can you have a negative intrinsic value?
NO-it is 0
when IV=0 and So doesn't =k
it is out of the money
when IV>0
it is in the money
IVt call
max(0, St-k)
IVt put
max(0,k-St)
a call option with the right to buy $/pound is the same as
a put with the right to sell pound/$
profit LC
max(0,St-k)-Po call
profit SC
max(0,St-k)+Po call
profit LP
max(0,k-St)-Po put
profit SP
max(0,k-St)+Po put
if you are bullish
you think St will increase
if you are bearish
you think St will decrease
Bullish
long cal
non-bullish
short call
bearish
long put
non bearish
short put
ways to hedge a long underlying position
long put or a short future
returns are distributed
normal
prices are distributed
lognormal
dealers buy at
bid
dealers sell at
ask
customers buy at
ask
customers sell at
bid
bid=yen/$
we sell $
we buy yen
ask-yen/$
we buy $
we sell yen
when bid/ask quotes are flipped
bid becomes ask and ask becomes bid
if you are due to PAY foreign currency then
you are SHORT the foreign currency and LONG the domestic currency
if you are due to RECEIVE foreign currency then
you are LONG the foreign currency and SHORT the domestic currency
profit of a short foward contract
(oFt-St)*Quantity
in cash settlement
a single CF is paid in NUMERATOR terms
option quotes: if forward prices are quoated as X/y and X<Y
then ADD forward points to spot quotes
option quotes: if forward prices are quoated as X/y and X>Y
then SUBTRACT forward points to spot quotes
if F>S then the
the denominator currency is trading at a forward premium and the numerator currency forward discount
if F<S then
the numerator currency is trading at a forward premium and the denominator currency forward discount
forward premium(discount)
#NAME?
when it comes to volatility, we are discussing volatiltiy of
the % change of FX rates (typically % change of spot rates)
when you buy(sell) a futures contract to inititae a position, you are contracting to buy(sell) the
denominator currency and therefore contracting to sell(buy) the numerator currency
Basis-t
spott--tFT
CF1
+0FT-b1