- spacemonkey
**Posts:**443**Joined:**

QuoteOriginally posted by: jokeohspacemonkey,why (K2-K1)/K2? how did you derive this?If the stock is less than K1, then the payout of the option is zero and the stock portfolio is worth more.If the stock is worth more than K1 but less than K2, the payout is S-K1 = (1-K1/S)*S and the stock portfolio is (1-K1/K2)*S. Clearly the portfolio is worth more.If S=K2 both are worth the same. As S increases past K2, the portfolio increases but the option payout remains fixed, and so the portfolio dominates in this region as well.This is probably the lowest possible upper bound (under the given constraints, assuming no dividends), but I haven't checked to make sure.I think that this would have been a very good interview question for a front-office quant job.

Last edited by spacemonkey on July 6th, 2006, 10:00 pm, edited 1 time in total.

Geist,I like to play devil's advocate.Let's say the the customer comes back,19 bid for 100,00 contacts. What do you do?I have no idea what I would do? but since you made an offer, I would like to know what you think?on the one hand it seems like you locked in 9 bucks, but on the other hand, who would pay 19 for a 10 dollar vertical if there wasn't something else going on.Anderman

Spacemonkey,I agree with your upper bound portfolios but we have other possibilities.We can trade any portfolio P composed of Alpha Bonds and Beta Stocks verifying P(K2) = K2 - K1 and 0 <= Alpha <= K2 - K1These constraints give Beta = (1 - (K1 + Alpha)/K2).Your Stock portfolio corresponds to Alpha = 0 and your Bond Portfolio to Alpha = K2 - K1.

- spacemonkey
**Posts:**443**Joined:**

QuoteOriginally posted by: JPBSpacemonkey,I agree with your upper bound portfolios but we have other possibilities.We can trade any portfolio P composed of Alpha Bonds and Beta Stocks verifying P(K2) = K2 - K1 and 0 <= Alpha <= K2 - K1These constraints give Beta = (1 - (K1 + Alpha)/K2).Your Stock portfolio corresponds to Alpha = 0 and your Bond Portfolio to Alpha = K2 - K1.True, but alpha = 0 is the lowest of these upper bounds, unless the Stock is > K2 in which case (K2-K1)*Bond is the lowest upper bound.

QuoteOriginally posted by: AndermanGeist,I like to play devil's advocate.Let's say the the customer comes back,19 bid for 100,00 contacts. What do you do?I have no idea what I would do? but since you made an offer, I would like to know what you think?on the one hand it seems like you locked in 9 bucks, but on the other hand, who would pay 19 for a 10 dollar vertical if there wasn't something else going on.AndermanYeah I know where you're coming from. Since I showed a cocky 19 offer I'd be done, but I'd be worried. The degree of worry would be a function of the sophistication of the client. I'd probably be happy paying a couple of cents to learn how a 10c payoff can turn into a liability for the seller that exceeds 10c though...

assuming no divs, rates or anything funny, I'd be 8.4 offered all day...

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