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Quantitative Finance · Glossary

What is Complete market?

Definition 1.13 Derivatives and Volatility · Chapter 1 — No Arbitrage and the Fundamental Theorems

A complete market is one in which every contingent claim has a replicating self-financing strategy. In the one-period finite model, the market is complete if and only if DD has rank SS.

The trinomial market: two assets, three states. The two equations q_u+q_m+q_d=0.98 and 120q_u+100q_m+80q_d=100 leave one degree of freedom, a segment of state-price vectors whose end points each give one state a zero price. Illustrative numbers.
Figure 1.2. The trinomial market: two assets, three states. The two equations qu+qm+qd=0.98q_u+q_m+q_d=0.98 and 120qu+100qm+80qd=100120q_u+100q_m+80q_d=100 leave one degree of freedom, a segment of state-price vectors whose end points each give one state a zero price. Illustrative numbers.
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