Tradable Assets in No-Arbitrage Models
Summary
The document explains how mathematical finance uses the idea of a tradable asset when connecting derivative prices to the prices of their underlyings. In the idealized framework described, an asset must be available for continuous, self-financing trading, with instantaneous transactions in unlimited amounts and no transaction costs. These assumptions allow trading strategies in the underlying to replicate derivative payoffs and support no-arbitrage pricing arguments.
The answer emphasizes that these conditions are a mathematical idealization and that real-world tradability is a matter of degree. It illustrates a rough spectrum from bank deposits and index futures through less liquid derivatives to physical property and an irreplaceable landmark. A second answer distinguishes an index from products written on it: the VIX itself is described as non-tradable, while VIX futures and options are tradable. The examples clarify terminology, but the discussion does not develop a formal model for relaxing its idealized assumptions.
Key ideas
- In idealized pricing models, tradability supports self-financing replication of derivative payoffs.
- The mathematical definition assumes continuous access, unlimited quantity, and no transaction costs.
- Real-world tradability varies by asset and is not simply a yes-or-no property.
- An index may be non-tradable even when futures and options referencing it can be traded.
Tags
Full text
# What does tradable asset mean? # What does tradable asset mean? I see a lot of theorems related to tradable assets in quantitative finance text books. What is a tradable asset? What does 'tradable' mean exactly? Does it simply mean the asset can be bought and sold in the market? Any example of non-tradable asset? ## Answer by g g (score 6) https://quant.stackexchange.com/a/16869 The concept of a tradable asset is closely related to the principle of (no-)arbitrage. Much of quant finance is about the connection between the price of a derivative and the price of its underlying. The fundamental reason that there is a connection at all, is the possibility to set up self-financing trading strategies in the underlying(s) which replicate the pay-out of certain derivatives. If you look at the definition of self-financing strategies you will notice that you need to be able to buy and sell the underlying at any time, instantaneously in unlimited quantity, without any transaction costs. So this is a tradable asset within the mathematical theory. Of course this is mathematical fiction and imposes an important restriction on the applicability of mathematical finance to the real world. But from my (limited) experience more realistic assumptions quickly become messy and really difficult. In my opinion being tradable in the real world is not black and white but a gradual thing. So some examples in descending order of tradability: Bank deposits, S&P futures, derivatives on the ABX index , your house(or car or bicycle), the Sistine Chapel. ## Answer by Gabriele Pompa (score 2) https://quant.stackexchange.com/a/16924 An example: Non-tradable asset: VIX index; Tradable assets: VIX Futures, VIX Options
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