Handbook of Exchange Rates - FX Options and Volatility Derivatives: An Overview from the Buy-Side Perspective

Handbook of Exchange Rates

24 FX Options and Volatility Derivatives: An Overview from the Buy-Side Perspective24.1 Introduction
24.2 Why Would One Bother with an Option?
0.4 rule of thumb: ATM call = ATM put =
ul price * 0.4 * vol * sqrt(t)

delta = how fast option price changes as UL price changes
gamma = how fast delta changes as UL price changes (always + for options)
vega = how fast option price changes as vol changes

option, in theory, can be replicated by continuously hedging delta, but for latter, during mkt crashes, no one is willing to buy UL and will suffer

gamma hedging (http://investorplace.com/2010/01/long-gamma-position/)
ex.  you're long gamma, ie u own option, since gamma always + for options
1) stock rallies, you get longer delta due to +gamma.  (so u sell the extra delta at a higher price to remain delta neutral)
2) stock drops,  you get shorter delta due to +gamma.  (so u buy the loss delta at a lower price to remain delta neutral)
buy low + sell high = $$$
there's no free lunch.  by owning option, you pay theta everyday.  u'd better hope vol is high so that u can make $ by gamma hedging.

24.3 Market for FX Options
assumptions to make:
expected realized vol
expected skewness
+ive skew - skew to the right - right has longer tail
+ive risk reversal: 2 OTM option - 25 risk reversal is the vol of the 25 delta call less the vol of the 25 delta put. The 25 delta put is the put whose strike has been chosen such that the delta is -25%.  it shows how much demand for upside relative to downside

can't we just use put call parity? no, b/c we have diff strikes
c + x/(1+rfr)^t = p + ul
@t, c + x = p + ul
c ITM
(ul - x) + x = ul
c OTM
x = (x -ul) + ul
expected kurtosis
A high kurtosis distribution - tall and skinny
low one is short w/ fat tails, ie extreme occurrences occur with a probability greater than normal.
expected term structure
PRINCIPAL COMPONENT ANALYSIS shows 3 main components
- // shift - high demand of specific stike/maturity shifts the whole surface
- steepener - changes relative price of short-term and long-term vol
- gull  - changes of relative vol of mid term vs short and long term
or diff strikes?


24.4 Volatility
variance swap - pays the diff b/w future realized variance & a predetermined variance strike

how does gamma affects the spot mkt?
say the mkt implied vol is getting higher than historical vol and the ones expecting it to get back to closer to the historical level will sell options and thus take on -ive gamma position
as UL goes up, u get less delta and have to buy spot to hedge and thus amplify the trend in the mkt.
it only applies when u assume the option buyer aren't gonna hedge.  that's a valid assumption if the buyers, like equity pm, are buying options to insure against their existing spot position, rather than option MM.
so, if we can identify the buyers, we can formulate a trend following strategy?
on the flip side, if implied vol is a lot lower than hist and we expect the implied vol will reverse, we'll buy options and thus hold a +ive gamma position.
as UL goes down, we have less delta and will buy and effectively dampens the spot trend.

black swan strategy
target fat tail risks

24.5 FX Options from the Buy-Side Perspective
corr swap - exchanges the realized correlation into strike corr multiplied by a notional