_uf.md

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title: Derivative Valuation

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Consider a contract $C$ where the buyer would like to receive the price of stock $S$ at time $T$. The contract seller asks for some amount at time 0 and is obligated to satisfy the contract. This is a very simple case of derivative valuation. The seller can just buy one share of $S$ for $S_0$ at time $0$, then sell it at time $T$ for $S_t$ to fulfill the contract.

A derivative is a (legal) contract: I will give you this at these times if you will give me that at those times. A buyer specifies what cash flows they would like to receive and a seller specifies what cash flows they require in order to enter the contract. Unlike a bond or a stock, there are no physical assets behind a derivative contract. When a company goes bankrupt you can recover some fraction of their remaining assets if you hold a bond or stock. When one counterparty abrogates their obligation in a derivative contract, the other only holds a piece of paper.

Even in our simple example there are a number of transactions required.

$\alpha = (a, i , e)$

$\chi = (\alpha, \alpha')$