The Breeden-Litzenberger formula says any probability density can be recovered from call prices. Its converse — any payoff function can be replicated by a strip of calls and puts — is the spanning formula. This model-free replication result is the backbone of variance swap theory: the log contract (which pays ) can be replicated by a specific strip of out-of-the-money calls and puts, and the cost of that strip equals the fair variance strike of the variance swap.
Learning objectives. By the end of this note you should be able to:
- state the spanning formula and apply it to replicate a general European payoff;
- derive the static replication formula for the log contract;
- explain why the replication is model-free and what "model-free" means here.
In this lesson
- 1.1 The spanning formula
- 1.2 The log contract
- 1.3 Connection to variance
Before you start
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