financial benefit due to the fact that the up-front disbursement investment cost (cash
outflow) becomes smaller in present value terms.
If volatility is zero or if all possible payoffs at expiry are above the strike price, the
insurance component is obviously worth zero, and thus it is optimal to defer the exercise of
the option as long as the interest savings exceeds the lost payouts. For example at the UP
node of the event tree, the value of the cash outflow deferment is equal to 14.4 (480$ times
the exogenous interest rate of 0.03), whereas the payout is equal to 40. Thus the benefit of
exercising exceeds the cost and the option is rationally exercised.
In order to illustrate the decision process on whether to exercise or not it is useful to
compare node t0 and node “C”. In fact, at these two nodes the NPV and the payout are the
same; still, as we will see, in the latter case it is optimal to exercise the option while in the
former it is not. In our example, the rate of interest is kept constant over the event tree,
hence the cash postponement component is exogenously given and the same at both nodes
(see Figure 5 and 6). Equally, the lost payout is the same by construction. All the difference
is thus given to the reversibility-protection component. In particular, at node t0 the
reversibility component is higher because the array of possible outcomes (payoffs at expiry
prices) is much greater than those which can be reached from the node “C”: hence the value
of the insurance against “bad” states of nature is much greater. At node “C” the range
possible final payoffs decreases substantially since, as time elapses, some final outcomes
can no longer be reached and the rate of change of prices at t2 (± 10%) is much smaller than
at t0 (+60%; -20%). In a continuous time setting this is equivalent to saying that the total
variance falls with time because the time horizon becomes shorter and the variance per unit
of time decreases. In conclusion the optimal strategy is not exercise at t0 but to exercise at
“C”.
17 The value of the payoff obtained by exercising the option is usually called the intrinsic value of the option.
16
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