Question

Describe how you would replicate a plain vanilla stock call option

using an asset-or-nothing option plus a cash-or-nothing option.

Assume that all three options are on the same underlying and have the same strike prices.

Answer 1

Vanilla Option

A vanilla option is a financial instrument that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price within a given timeframe. A vanilla option is a call or put option that has no special or unusual features. Such options are standardized if traded on an exchange such as the Chicago Board Options Exchange.

Basics of a Vanilla Option

Vanilla options are used by Individuals, companies, and institutional investors to hedge their exposure in a particular asset or to speculate on the price movement of a financial instrument.

If a vanilla option is not the right fit, exotic options such as barrier options, Asian options, and digital options are more customizable. Exotic options have more complex features and are generally traded over the counter; they can be combined into complex structures to reduce the net cost or increase leverage.

Calls and Puts

There are two types of vanilla options: calls and puts. The owner of a call has the right, but not the obligation, to buy the underlying instrument at the strike price. The owner of a put has the right, but not the obligation, to sell the instrument at the strike price. The seller of the option is referred to as its writer. Shorting or writing an option creates an obligation to buy or sell the instrument if the option is exercised by its owner.

Calls and puts both have an expiry date. This puts a time limit on how long the underlying asset has to move.

Vanilla Option Features

Every option has a strike price. If the strike price is better than the price in the underlying market at maturity, the option is deemed "in the money" and can be exercised by its owner. A European style option requires the option be in the money on the expiration date in order for it to be exercised; an American style option can be exercised if it is in the money on or before the expiration date.

The premium is the price paid to own the option. The premium is based on how close the strike is to the price of the underlying (in the money, out of the money, or at the money), the volatility of the underlying asset, and the time until expiration. Higher volatility and a longer maturity increase the premium.

An option gains intrinsic value, or moves into the money, as the underlying surpasses the strike price— above the strike for a call and below the strike for a put.

Asset-or-Nothing Put Option

An asset-or-nothing put option provides a fixed payoff if the price of the underlying asset is below the strike price on the option's expiration date. If instead it is above the strike price, then the option expires worthless.

Asset-or-nothing put options are a type of binary option, which are also known as "digital options." They are so named because their success or failure is based on a yes-or-no (binary) proposition.

Unlike regular put options, asset-or-nothing put options do not pay the difference between the strike price and market price of the underlying asset. In fact, asset-or-nothing put options do not allow the option holder to take a position in the underlying asset at all. Instead, they simply provide a fixed payout if the market price is below the strike price at the time of expiration.

Most asset-or-nothing put options are traded outside of the United States, and are usually structured as European options. Unlike American-style options, European options can only be exercised on their maturity date. Although some binary options do allow execution before the expiration date, this typically reduces the payout received.

strike prices.

The strike price of an option is the price at which a put or call option can be exercised. It is also known as the exercise price. Picking the strike price is one of two key decisions (the other being time to expiration) an investor or trader must make when selecting a specific option. The strike price has an enormous bearing on how your option trade will play out.

ssume that you have identified the stock on which you want to make an options trade. Your next step is to choose an options strategy, such as buying a call or writing a put. Then, the two most important considerations in determining the strike price are your risk tolerance and your desired risk-reward payoff.