# 12. Options

## Table of Contents

## 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:

- Buy $H$ shares of the underlying asset
- 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.