Reading the great book of Gatheral on Vol Surfaces (link) I can't help but notice that throughout he uses undiscounted option prices (though he obviously never assumed rates to be zero).

See e.g. page 8 where he reviews Dupire's work and derives the pseudo-probability density of the final spot price $S_T$ as $$\phi(K, T; S_0) = \frac{\partial^2 C}{\partial K^2}$$ with $C$ denoting undiscounted option prices. On the other hand, using discounted option prices, and letting $D$ be the discount factor at time $T$, one would obtain $$\phi(K, T; S_0) = \frac{1}{D}\cdot\frac{\partial^2 C}{\partial K^2}$$

Similarly, a Bloomberg reference document states Put-Call Parity (together with subsequent derivations) as $$C-P=F-K$$ with $C,P$ being the future values of European call & put options, and $F$ the forward, as opposed to the standard form (link) which reads $$C-P = D\cdot(F- K)$$

What is the use (or benefit) of doing these derivations with undiscounted prices? Does the market quote prices that way?

  • 2
    $\begingroup$ It is just to simplify notations $\endgroup$ – Ezy Dec 14 '18 at 10:49
  • $\begingroup$ I see. Wouldn't it be quite fiddly/annoying to retrospectively derive everything again with $D$ inserted in all the right places? $\endgroup$ – Phil-ZXX Dec 14 '18 at 10:57
  • $\begingroup$ it would not improve the exposition of ideas imo since the focus here is really about volatilty. $\endgroup$ – Ezy Dec 14 '18 at 11:36
  • $\begingroup$ It's undiscounted as it's about probability, not discounted probability $\endgroup$ – James Spencer-Lavan Dec 14 '18 at 18:40

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