Foreign Exchange by Adam S. Iqbal

Author:Adam S. Iqbal
Language: eng
Format: epub
ISBN: 9783030935559
Publisher: Springer International Publishing

The price of the unit call spread is therefore

Next, take the limit as becomes infinitesimally small. As we decrease , the payoff converges to the profile shown in Fig. 4.6. In the limit as , the payoff of the unit call spread converges to that of the digital. The price of the digital payoff is therefore given by

(4.8)

which follows from the definition of a (calculus) derivative (see Appendix C.1). This is Eq. 4.7, as required.

Practical Extraction of the Q distribution (Optional)

This feature box details how the investor may extract the Q distribution from the prices of vanilla options. The discussion presented here is targeted at readers with some familiarity with the so-called volatility smile in FX options and the terminology relating to delta space. Readers without prior exposure in this area may consult Iqbal (2018) for a full treatment.

I denote the volatility of the at-the-money-forward (ATMF) option by , the 25 delta risk reversal by , and the 25 delta butterfly by . Finally, I impose a simple quadratic form for the volatility smile of

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.