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odemann
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Joined: March 18th, 2010, 7:53 pm

(Time) Spread Option

April 28th, 2012, 1:12 pm

Hi all, I am trying to better understand the Kirk formulae and the resulting Greeks.I understand that beeing long the (time) spread option gives me a short correlation position, but also is driven by the vola spread of the two underlyings.When I now calculate my deltas I have 2 which are not the same i.e. I sometimes buy 1 unit of X and sell 1.5 units of Y. This would seem to leave me slightly short overall and I turn a spread option hedge into a partially outright position.Can you explain why it makes sense to hedge more units of one underlying and create a net long/short across the forward curve agains a spread option?Thank you very much in advance.
Last edited by odemann on April 28th, 2012, 10:00 pm, edited 1 time in total.
 
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animeshsaxena
Posts: 18
Joined: June 19th, 2008, 2:56 pm

(Time) Spread Option

April 29th, 2012, 10:57 am

I am assuming spread = outperformance option.So payoff is Max[A-B,0]simplify this to B x Max[A/B-1,0]Now treat A/B as a single asset which will have a volatility ofsigmaA/B^2 = sigmaA^2 + sigmaB^2 - 2 correlation(A,B) sigmaA sigmaB (From Ito's)Max[A/B-1,0] is your black scholes formula with asset as A/B (let's say time t) instead of a stock, but the price is in B's unit...which I can convert to dollars by using B(t)(which is $ price) x Price of blackscholes payoff of Max[A/B-1,0] Similarly think of hedging in two steps1. Hedge with A in terms of B2. Hedge B in terms of dollar (or any currency) - (similar to a quanto actually....)Quantities might be different but finally A * change in price / change in A + B * change in price / change in B = Priceabove equality should hold. Or intuitively think in these termsA is at 130 and B = 2 or very small valuethen your price is Max[130 - 20,0] is mostly dependent on volatility of A and not on volatility of B. And if B's volatility is very small it might behave like a call option ITM with strike 20. Of course this is a very very crude example. But it's another way of seeing why quantity of A,B might be different in hedging.
 
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tw
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Joined: May 10th, 2002, 3:30 pm

(Time) Spread Option

May 10th, 2012, 8:23 pm

QuoteOriginally posted by: odemannHi all, I am trying to better understand the Kirk formulae and the resulting Greeks.I understand that beeing long the (time) spread option gives me a short correlation position, but also is driven by the vola spread of the two underlyings.When I now calculate my deltas I have 2 which are not the same i.e. I sometimes buy 1 unit of X and sell 1.5 units of Y. This would seem to leave me slightly short overall and I turn a spread option hedge into a partially outright position.Can you explain why it makes sense to hedge more units of one underlying and create a net long/short across the forward curve agains a spread option?Thank you very much in advance.Is the option worth more when one price is 10 and the other is 5, or when one price is 100 and the other is 95? 1000 and 995?If so, does it not make sense to make the hedges have a net overall short?