perpetual call - guess how long it would take for IBM to...

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Sheet1 Page 1 A regular perpetual call option should have the same value as the underlying. If we look at Black-Scholes for regular call options, as time gets larger, the value of the exercise price tends towards zero and delta tends toward one. Intuitively, at some point in the future, the call will go ITM (IBM will hit 200) and at the buyer will get paid $1m. However, this option takes the form of a binary option, so we wouldn't charge $1m. If we knew the volatility and risk free rate, we could build a first passage time distribution through 200 and take an expected cash flow/ npv approach. At this point we would want to
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Unformatted text preview: guess how long it would take for IBM to double, given current and projected markets and industry growth assumptions. For example, we could say IBM can hit 200 and the probability is 1 for 10 years, .8 for 8 years, .5 for 5 years, .2 for two years. Then, multiply the probability of the 1M at that time and sum it up. As a crude guess, I would offer 40-50% of the 1M, which takes into account time value of money (6-8% rate), how quickly I think IBM will double (about 10 years), and my level of risk aversion (would charge on the upper end of this spectrum)....
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