Question

The delta of an option is the ratio of the change in the price of the option to the chnage in the price of the underlying asset. Therefore delta is

A. the quantity of underlying stock units necessary to create a riskless portfolio
B. a known quantity that is uniformative with regard to the riskiness of the option
C. the number of derivatives necessary to create a riskless portfolio
D. a quantity that must remain constant in theh case of a multi-step tree in order to be able to compute the price of the option

Answer 1

Delta is the ratio of the price change in an option to the price change in the underlying asset and reflects the hedge ratio necessary for riskless portfolio construction, not a constant quantity or the number of derivatives needed for a risk-free portfolio.

Step-by-step explanation:

The delta of an option is commonly understood in finance as the ratio of the change in the price of the option to the change in the price of the underlying asset. Delta is used in mathematical finance and options trading to describe the amount an option's price is expected to move for every one point change in the underlying asset.

Contrary to the options presented to categorize delta, this term in the context of options trading reflects the sensitivity of an option's price to a change in the price of the asset, and it can be represented symbolically as Δ.

Here, option A would be the most relevant interpretation of delta in a financial context. It suggests delta can represent the number of shares of the underlying stock needed to hedge or create a riskless portfolio - often referred to as 'delta hedging'.

Delta, however, is not a constant quantity; it varies as the price of the underlying asset changes and as time to expiration approaches, refuting options B, C, and D.