Why Derivatives Texts Use Undiscounted Option Prices

Summary

The document asks why some derivatives references express option prices on an undiscounted basis. It contrasts a density formula using the strike derivative of an undiscounted call price with the version using discounted prices, which includes a discount-factor adjustment. It also compares two forms of put-call parity: one using future values of options and one using discounted values.

These examples show how discounting conventions affect the form of pricing identities and derivatives with respect to strike. The document does not answer whether markets quote options undiscounted or explain the practical benefits of that convention. It is therefore a prompt for investigating consistent units and numeraire choices in option pricing, rather than a worked derivation or trading method. The cited references are mentioned but their details are not included, so the claims cannot be assessed further from this text alone.

Key ideas

• Discounting conventions change how option-pricing identities are written.
• The document contrasts strike derivatives of discounted and undiscounted call prices.
• Put-call parity can be expressed using future option values or discounted values.
• The text leaves open whether market quotes use undiscounted prices and why.

Tags

# What is the use of undiscounted Futures/Option Prices


# What is the use of undiscounted Futures/Option Prices












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?

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