or as was said earlierQuoteOriginally posted by: pcaspersprobably it is aiming at the put call parity call - put = Share - Strike x DiscountFactor(Expiry) - DividendsNpvand the question was misstated

All Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.

QuoteOriginally posted by: AnalyticalVegaAll Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.Nice thinking, thanks for reply.Can we put it in another way,such as AAA pays a constant dividend each season indicating that it is a very mature company whose stock price will be very stable. So the volatility of the stock is very low. And given a not too short t (several years), put can be worthless.best,

QuoteOriginally posted by: FinatosQuoteOriginally posted by: AnalyticalVegaAll Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.Nice thinking, thanks for reply.Can we put it in another way,such as AAA pays a constant dividend each season indicating that it is a very mature company whose stock price will be very stable. So the volatility of the stock is very low. And given a not too short t (several years), put can be worthless.best,my reply is one word: Leptokurtosis

QuoteOriginally posted by: FinatosQuoteOriginally posted by: AnalyticalVegaAll Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.Nice thinking, thanks for reply.Can we put it in another way,such as AAA pays a constant dividend each season indicating that it is a very mature company whose stock price will be very stable. So the volatility of the stock is very low. And given a not too short t (several years), put can be worthless.there's a difference between being worth very little and being worth zero, and the question as initially posed required the put to be worth zero.

QuoteOriginally posted by: ppauperQuoteOriginally posted by: FinatosQuoteOriginally posted by: AnalyticalVegaAll Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.Nice thinking, thanks for reply.Can we put it in another way,such as AAA pays a constant dividend each season indicating that it is a very mature company whose stock price will be very stable. So the volatility of the stock is very low. And given a not too short t (several years), put can be worthless.there's a difference between being worth very little and being worth zero, and the question as initially posed required the put to be worth zero.I know, but since it is a put, this can be. Because put can have negative time value. That's why I say time can dominate volatility, even there is a little volatility in there. There should be a point where the time value of money and the effect of volatility cancel each other making the time value=0.Thanks for reply.best,

QuoteOriginally posted by: FinatosI know, but since it is a put, this can be. Because put can have negative time value. That's why I say time can dominate volatility, even there is a little volatility in there. There should be a point where the time value of money and the effect of volatility cancel each other making the time value=0.Thanks for reply.best,No. As long as there is a positive probability that your put will be in the money at expiry, it has a positive value today. The fact that theta of the option is negative is a different thing, you are mixing things up here.

QuoteOriginally posted by: pcaspersQuoteOriginally posted by: FinatosI know, but since it is a put, this can be. Because put can have negative time value. That's why I say time can dominate volatility, even there is a little volatility in there. There should be a point where the time value of money and the effect of volatility cancel each other making the time value=0.Thanks for reply.best,No. As long as there is a positive probability that your put will be in the money at expiry, it has a positive value today. The fact that theta of the option is negative is a different thing, you are mixing things up here.The time value of money embedded in the option is a different concept with theta. theta is a dynamic concept while what I am talking about is how much a put's value is contributed by the time value of money which is a static concept. (i.e.negative theta does not means the positive or negative time value). But what you said is reasonable, since ATM or OTM will not be exercised so that it has no time value of money needed to be considered.Thanks for the reminder.best,

QuoteOriginally posted by: ppauperQuoteOriginally posted by: FinatosQuoteOriginally posted by: AnalyticalVegaAll Cash buyout of the company AAA. The stock converts to cash and the volatility of cash is zero. So the two portfolios could be equal without any dividends in this one scenario.Nice thinking, thanks for reply.Can we put it in another way,such as AAA pays a constant dividend each season indicating that it is a very mature company whose stock price will be very stable. So the volatility of the stock is very low. And given a not too short t (several years), put can be worthless.there's a difference between being worth very little and being worth zero, and the question as initially posed required the put to be worth zero.Yes you are correct, ATM option can not be worthless before maturity.