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Martinghoul
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Joined: July 18th, 2006, 5:49 am

Dumb/interesting Black-Scholes question

July 19th, 2007, 7:53 pm

My question is quite possibly stoopid, but here goes...In a simple Black-Scholes world, for a simple option, if I am trying to compute E[max(BSDelta(t))], where T < t < 0 with T as time to expiry. What kind of a function of t, do you expect this thing to be? It should be a simple thing, but somehow I can't wrap my head around it... Can this be expressed analytically, or do you have to monte-carlo the bugger?Gracias in advance...
Last edited by Martinghoul on July 18th, 2007, 10:00 pm, edited 1 time in total.
 
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Antonio
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Dumb/interesting Black-Scholes question

July 20th, 2007, 9:00 am

I don't really see the point : BSDelta(t) is a deterministic function of time and the other Black-Scholes parameter, so there is no point in considering the expectation. As BSDelta=N(d1), yu simply need to find the maximum of d1, which is a function of t.Or am I missing something ?
 
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Rez
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Joined: May 28th, 2003, 9:27 pm

Dumb/interesting Black-Scholes question

July 20th, 2007, 11:43 am

Antonio:BSDelta also depends on the current price S_t. As this will change with time the delta will also change.dk:do you have the joint distribution of the maximum price and the time it occurs? Then you could integrate and get delta.KyriakosQuoteOriginally posted by: AntonioI don't really see the point : BSDelta(t) is a deterministic function of time and the other Black-Scholes parameter, so there is no point in considering the expectation. As BSDelta=N(d1), yu simply need to find the maximum of d1, which is a function of t.Or am I missing something ?
 
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Martinghoul
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Joined: July 18th, 2006, 5:49 am

Dumb/interesting Black-Scholes question

July 20th, 2007, 4:57 pm

Antonio, the point here is that the t in question is not the time to expiry of the option (T), but rather the time elapsed since inception of the option. Thus, T > t >0 (sorry for a stupid typo in my original post)... So, and it's the same thing, I am looking for an expression for MAX(moneyness(t))...