Créer un site internet

Questions and Answers

Q1. Prove that the price of a call option is a convex function of the strike price. 

 

Answer: 

To prove the call option is a convex function of the strike price we consider the price as a function of strike, and prove that a line joining any 2 points on the graph of this function lies on or above the graph. 

This is a necessary and sufficient property of convex functions. 

 

For K1 < K2:   Convex function    for all Thetaaa

 

With this in mind, consider a ptf long Thetaacall options struck at K1, long (1-Thetaa) struck at K2 and short one option struck at ThetaaK1 + (1-Thetaa)K2.

Since the final payoff is convex in strike, the above equation holds at the expiry of the options. Therefore our ptf has non-negative value at expiry. 

By no-arbitrage considerations, this implies that the ptf must be of non-negative value at all times before expiry, and hence that the equation above hold at these times and we have proved the convexity of the call option price.  

Add a comment

 

The NEW website is OUT! 

Go have a look at https://www.derivativesacademy.com.

You will find the content in the 'Derivatives Academy' section in a book format. 
The full content is not yet available as I am rewriting it and improving it.

You can try the Exotic Derivatives pricer under the 'Derivatives Pricer' section (
https://www.derivativesacademy.com/derivatives-pricer/). I will speed up the page soon as I forgot to compress some images.
Each application allows you to price differents products and contains links towards the correct section of the book. 
You will then be able to get practical and theoretical knowledge quite easily.

I teach quite often using the pricer. You can get so much information and answers to your questions thanks to it.

Take advantage of it as much as you can to hone your knowledge!

If you are looking for junior opportunities in the field of market finance. Register yourself on the website. It's free!

If you have any questions, do not hesitate to contact me on info@derivativesacademy.com.