Arbitrage-Free Price Bounds in Incomplete Markets

Summary

The document points readers seeking a theory of option pricing in incomplete markets to a specific textbook chapter. Its premise is that, when markets do not allow every contingent claim to be replicated, an option may not have a unique arbitrage-free price; instead, admissible prices can form an interval.

The response recommends chapter 15 of Tomas Björk’s book on arbitrage theory in continuous time as a reference. It does not explain how to derive the bounds, state the assumptions behind them, or provide examples, so its value is mainly as a pointer for further study rather than a self-contained pricing method.

Key ideas

• Incomplete markets may admit multiple arbitrage-free prices for a claim.
• When a claim cannot be uniquely replicated, its admissible price can be bounded by an interval.
• The document recommends a textbook chapter as a starting point but supplies no derivation or examples.

Tags

# Arbitrage-free prices in incomplete markets


# Arbitrage-free prices in incomplete markets












Hey where I could find theory of option pricing in incomplete markets? I know that there we have not one price, but interval of arbitrage-free prices and I would like to read more about it and I need some references. Can anyone help?

## Answer by tcpedersen (score 4)

https://quant.stackexchange.com/a/61412

Chapter 15 in Arbitrage Theory in Continuous Time by Tomas Björk.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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