Why Options Remain Distinct Risks Despite Theoretical Replication

# Why are options studied separately from a portfolio of stocks and bonds?


# Why are options studied separately from a portfolio of stocks and bonds?












I have just started studying finance and stochastic calculus so apologies if this question is too naive.

I was first introduced to stocks and bonds as risk and riskless investment assets. Then a new idea is introduced, that of a call option. At first sight, this seems like a new independent investment product, and that you wouldn't be able to create such a portfolio using stocks and bonds only.

But now to calculate the price of this call option, we assume no-arbitrage in our model (Binomial and Black Scholes are the two I have studied so far) and hedge using the stocks and bonds. In other words, just using stocks and bonds we create a portfolio that is the same as a call option. This was surprising to me in a nice way.

But at the same time, it has left me confused. If I could achieve such a portfolio using stocks/bonds then why are call options studied separately?

In fact, it seems to me like introducing call options as an additional investment asset class adds to your "risk dimension". In the sense that, when someone sells a call option, they need to hedge against this risk. So why should someone sell a call option, instead of shorting some stocks or bonds? I agree that options risk will still exist implicitly, but introducing them as a separate asset class just adds to the risk dimension that I would need to hedge.

Also, are there any other merits of options that stocks/bonds alone cannot provide, perhaps in the real world?

## Answer by user34971 (score 12, accepted)

https://quant.stackexchange.com/a/68276

"But at the same time, it has left me confused. If I could achieve such a portfolio using stocks/bonds then why are call options studied separately?"

Good question! The short answer: because it turns out options cannot be synthesized using stocks and bonds only, except in the highly idealized case of Black-Scholes which assumes constant volatility, constant interest rates, infinite liquidity, no transaction costs to name but a few sources of replication "slippage".

Hence options should really be regarded as a new source of risk, even perhaps a different asset class.

The uses of options are speculation and/or taking a view without the need to buy the underlying security, but for a large part also hedging the risk of other (more complex) options such as options embedded in structured notes and life insurance guarantees, and to create bespoke investment vehicles that address investors needs for particular risk profiles.

## Answer by D Stanley (score 5)

https://quant.stackexchange.com/a/68277

Yes, conceptually, you can replicate options with stocks and bonds, but why would you when options are readily available?

Put another way, you can replicate a Coke with the right amount of sugar, water, flavorings, etc., but why would you do that when you can just buy a bottle. How easy are those ingredients to get individually (and in the minute quantities that you need)?

It's impractical to replicate an option exactly with the right about of stocks and bonds. That replication is great for creating pricing models, but is not practical to do in reality.