Sunday, June 29, 2014

hockey stick - asymptote

(See also post on fwd price ^ PnL/MTM of a fwd position.)

Assume K = 100. As we get very very close to maturity, the "now-if" graph descends very very close to the linear hockey stick, i.e. the "range of (terminal) possibilities" graph.

10 years before maturity, the "range of (terminal) possibilities" graph is still the same hockey stick turning at 100, but the now-if graph is quite a bit higher than the hockey stick. The real asymptote at this time is the (off-market) fwd contract's now-if graph. This is a straight line crossing X-axis at K * exp(-rT). See http://bigblog.tanbin.com/2013/11/fwd-contract-price-key-points.html

In other words, at time 0, call value >= S - K*exp(-rT)

As maturity nears, not only the now-if smooth curve but also the asymptote both descend to the kinked "terminal" hockey stick.

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http://www.linkedin.com/in/tanbin