Saturday, May 10, 2014

Towards expiration, how option greek graphs morph

(A veteran would look at other ways the curves respond to other changes, but I feel the most useful thing for a beginner to internalize is how the curves respond to ... imminent expiration.)

Each curve is a rang-of-possibility curve since the x-axis is the (possible range of) current underlier prices.

-- the forward contract's price
As expiration approaches, ...
the curve moves closer to the (terminal) payout graph -- that straight line crossing at K.

-- the soft hockey-stick i.e. "option price vs current underlier"
As expiration approaches, ...
the curve descends closer to the kinked hockey stick payout diagram

Also the asymptote is the forward contract's price curve, as described above.

-- the delta curve
As expiration approaches, ...
the climb (for the call) becomes more abrupt.

See diagram in http://www.saurabh.com/Site/Writings_files/qf301_greeks_small.pdf

-- the gamma curve
As expiration approaches, ...
the "bell" curve is squeezed towards the center (ATM) so the peak rises, but the 2 tails drop


-- the vega curve
As expiration approaches, ...
the "bell" curve descends, in a parallel shift

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