On the importance of “arbitrage-free” pricing in finance

The notion of “arbitrage-free” pricing is important not only in Finance 4366, but also in your other finance studies. In Finance 4366, we take it as given that investors are risk averse. However, it turns out that we don’t need to invoke the assumption of risk aversion in order to price risky securities such as options, futures, and other derivatives; all we need to assume is that investors are “greedy” in the sense that they prefer more return to less return, other things equal. Through a variety of trading strategies, we can synthetically replicate any security we want, and do so in such a way that we (in theory anyway) are able to take no risk, incur zero net cost of investment, and yet earn positive returns.

Without question, the notion of arbitrage-free pricing is THE key concept in Finance 4366. However, it is also important in corporate finance. For example, the famous Modigliani-Miller Capital Structure Theorem; i.e., that the value of a firm’s shares is unaffected by how that firm is financed, is based upon this principle. For your personal enjoyment and intellectual edification, I attach a copy of a short (3 page) teaching note which provides a “no-arbitrage” proof based upon a simple numerical example:

The Modigliani-Miller Capital Structure Theorem – A “No-Arbitrage” Proof

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