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:

  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.

C. Put Call Parity

D. Black-Scholes Option Pricing