Question

(Derivatives & Risk Management - BOPM: Binomial Options Pricing Model)

-What is the significance of delta to the BOPM?

- -How does it (delta) relate to the concept of a replicating portfolio and why is that important?

(Derivatives & Risk Management - BOPM - Binomial Options Pricing)

-Explain the no-arbitrage approach to valuing options with the Binomial options pricing model.

--Explain why the no-arbitrage condition must exist for a call. In other words, explain what it means for a call to be over-priced or under-priced relative to the BOPM.

-Explain the risk neutral pricing approach to valuing options with the BOPM.

Answer 1

1)Significance of delta in BOPM: The delta holds important significance in BOPM

• Delta in BOPM is defined as price of the derivatves to price of the underlying asset
• Delta used in BOPM is discreet analog
• Delta of derivatives on underlying asset is the sum of its individual deltas
• Delta of long stock is 1

How does it (delta) relate to the concept of a replicating portfolio and why is that important?

In replicating portfolio the main reason to create portfolio is to use combination risk free lending and underlying asset to create same cashflow as option being value so the number of shares bought and sold represents option delta so it is important in replicating portfolio

Call= lending +buying of stocks

Put= selling short on underlying asset +lending

• With respect to stock price delta is first option of derivative
• Graph of stock price vs option price wont be straight

Explain the no-arbitrage approach to valuing options with the Binomial options pricing model.

No arbitrage apporch in BOPM valuation simply means that all risk free investments earn the risk free rate of return there is no investment opprtunities with no investment and postive return

In no arbitrage approch in BOPM we have to create a portfolio with two assets regardless of underlying price goes up however net return of the portfolio is always same.

Explain the risk neutral pricing approach to valuing options with the BOPM:

Neutral pricing approch in BOPM is useful when we only need to know the price of the replication portfolio however not the whole holding

Risk neutral pricing is unique probablity measure that is equivalent to physical probablity and risk neutral pricing indifferent between sure thing and risky bets with an expected payoff equal to value of sure thing.