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Interpreting Strike Derivatives of a Call Option Price

Article Quant Q&A · Author: ensabahnur
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Summary

The document gives a brief hint for a quantitative finance exercise about a European call option’s value as a function of its strike. It writes the price as an integral of the option payoff over a distribution of the underlying value, then relates derivatives with respect to strike to tail probability and the density of that distribution. These relationships connect option prices across strikes to information about the underlying distribution.

The response does not work through the exercise or explain the final interpretation in detail; it prompts the reader to connect the expressions to the definition of a contingent claim. A second answer points to a published solutions document, but the included text does not reproduce its derivation. The excerpt is therefore a compact conceptual clue, with assumptions and notation left implicit, rather than a full pricing treatment.

Key ideas

  • A call value can be represented as the expected positive payoff over the underlying value distribution.
  • The first strike derivative is related to the probability mass above the strike.
  • The second strike derivative recovers the density at the strike under the stated setup.
  • The excerpt offers a hint rather than a complete derivation or interpretation.

Tags

OptionsDerivatives pricingStatistics
Full text
# Anybody knows the answer to this exercise found in PWIQF?


# Anybody knows the answer to this exercise found in PWIQF?












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

## Answer by Drew (score 2)

https://quant.stackexchange.com/a/15269

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?

## Answer by vonjd (score 2)

https://quant.stackexchange.com/a/16062

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.