# Replication in Derivatives

Hi,

I am struggling with this concept of Replication. Can someone explain to me in layman terms?

In layman’s terms, replication is four fives for a twenty: they behave exactly the same (they’re each worth twenty dollars), but they look completely different (one is four pieces of paper, the other is one piece of paper).

You’re familiar with replication in put-call parity: a portfolio comprising a share of stock and a put option on that stock replicates a portfolio comprising a call option on that stock and a risk-free bond. (To be clear on the details: the strike price on the put and the strike price on the call have to be the same as the par value on bond, and the expiration of the put and the expiration of the call have to be the same as the maturity of the bond.) Under all circumstances (i.e., all possible prices of the stock on the date that the options expire and the bond matures), these two portfolios will have the same value as each other.

Similarly, a portfolio comprising a long call option on a stock and a short put option on that same stock (with the same expiration and strike price) replicates a long position in a forward contract on that same stock with the same expiration and price as the options. Under all circumstances (i.e., all possible prices of the underlying stock on the date the the options expire and the forward contract matures), these two portfolios will have the same value as each other.

Other examples of replication are that a swap can be replicated with a series of FRAs, and an FRA can be replicates with a pair of interest rate options: one call and one put.

Thanks so much…so replication will ensure that the 2 portfolios will have the same value as the other…this will help in exploiting arbitrage, is it? also, cash & carry arbitrage is a type of a replicating strategy?

Exactly.

Yes.

The price of a forward or futures contract (on an underlying asset that has no cash flows, storage costs, or convenience yield, to keep things simple) should be the spot price of the underlying increased at the risk-free rate. This replicates a risk-free bond.

Magician - wanted to also say thanks to you…I used to follow AF for my doubts in L1…And your explanation indeed made concepts easier to understand…

My pleasure.

One more question…Difference between Price and Value of a forward…Can I say that Price is what is specified in the contract, while Value is the profit or loss on the contract?

Yes, and yes.

While pricing forwards, why do we subtract benefits and add the costs?

Because we don’t receive the benefits of ownership when we’re merely long a forward contract and we don’t incur the costs when we’re merely long a forward contract.

When you enter into the long position in a forward contract, you have, in essence, already bought the underlying asset; you simply haven’t taken delivery or paid yet. If you already essentially own the asset, then you should receive all of the benefits of ownership and incur all of the costs of ownership. Because there is no natural way to cause that, it’s done _ artificially _, by adjusting the forward price.

Oh wow…thanks so much for the simple explanation you are amazing …

You’re quite welcome.

In put call parity, the idea is to have similar payoffs, right? So, is it that we are indifferent to any of the portfolios, Stock + Put or Bond + Call?

Or is it that we should invest in both? I find this concept very abstract :(.

There . . . that’s better.

Yup.

From CFAI text - Risk-neutral investors are willing to engage in risky investments for which they expect to earn only the risk-free rate. Thus, they do not expect to earn a premium for bearing risk.

Why would a risk neutral investor expect to earn only the risk-free rate? And is a risk neutral investor only a theoretical concept?

anyone?

Risk-neutral means, in essence, risk-immune (or, perhaps better, risk-ignorant).

If you don’t care about risk, then a risky investment is the same as a risk-free investment.

Thanks Magician…By the way, what is your actual name?

Check the link in my signature.

Impressive profile!!!