# 12. Options

## A. Binomial Model

A short call is an options position is a trading strategy when a trader believes that the price of the asset underlying the option will drop.

• When an investor sells a call option, the transaction is called a short call.

## B. Risk-neutral valuation

The goal is to find the price for an option.

• Therefore we use a binomial model to find the price of the option.

The following portfolio is considered:

1. Buy $H$ shares of the underlying asset
2. Short $1$ call option

Hedge ratio – Tells the how much the payout for the options will change for a dollar change in the stock.

• Risk-neutral probability – is the probability that there would not be any risk in the portfolio.

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