Skip to main content
3 votes

How to prove the value of a European Call Option is convex on the underlying’s price?

Proposition. If $f:A\rightarrow\mathbb{R}$ and $g:A\rightarrow\mathbb{R}$ are convex functions defined on convex subset $A$ of $\mathbb{R}^n$, then $\max(f,g):A\rightarrow\mathbb{R}$, defined as $\max(...
Amit's user avatar
  • 8,966
3 votes
Accepted

How to prove the value of a European Call Option is convex on the underlying’s price?

I know nothing about finance so please do not be too harsh. Let's sell 1 call option with underlying price $\alpha S_a + (1-\alpha) S_b$ and strike price $K$. This means that I need to pay $$ \max\{\...
tdm's user avatar
  • 12.4k

Only top scored, non community-wiki answers of a minimum length are eligible