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I got this question from the last exercise of chapter 2 from "paul wilmott introduces quantitative finance" book. Appreciate your help.

Taken from chapter 2 of PWIQF

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  • $\begingroup$ I gave you the link to the solution below - if this answers your question it would be great if you could upvote and accept the answer - Thank you :-) $\endgroup$ – vonjd Jan 20 '15 at 11:28
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Let's think about it like this:

$V(E,T) = \int_E^{\infty} (x-E)^{+} \rho (x) dx$

Then $\frac{\partial C}{\partial E} = \int^\infty_E \rho(x) dx$

and $\frac{\partial^2 C}{\partial K^2} = \rho(K)$

Ill leave you to interpret these quantities. Hint, what is the defintion of the value of a contingent claim?

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You can find the solution here:
http://www.wiley.com/legacy/wileychi/pwiqf2/supp/c02.pdf

For all solutions see my answer here: https://quant.stackexchange.com/a/16061/12

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