Internal markets

The IR is the next point of attention. 


We recall from delta-hedging procedure that we were using a cash account, where we received/were charged an IR r, continuously compounded, meaning every day we would receive/pay interest. 

This is a source of uncertainty.

One can expect that the interest received for cash is lower than the interest to be paid for a loan. 

This typical bid/offer spread in IR market is the first of out problems. 


What's next?


The IRs are not constant. So we don't know in advance what the applicable rate IR is. 

If we have a certain amount on the cash account, we could fix the IR for the lifetime of the option, but only for this fixed volume. 

Because of the dynamic nature of the hedging procedure, the cash on the account will constantly change and a few days later, the conditions in the market might have changed. 


So, the best we can do is fix as much as we can at the start of the procedure, where we have at least an accurate view on the money in the cash account. 

For the future, the trader will use an estimate of the future IR.  


The problem of uncertain IRs in the context of equity derivatives is sometimes handled by the bank by fixing an internal system. 

For the sake of making the point, we will oversimplify. 

Suppose you have 2 different desks in a trading room: 

- the desk that trades options on stocks; 

- the desk that trades IRs. 


This will allow the IR risk to be transferred from one desk to the other. 

The management could decide that an internal system needs to be set up to accommodate for this transfer. 

Therefore mngmt could decide that the equity derivatives desk always receives an IR r-∆r and pays an IR r+∆r.

The spread ∆r could be fixed internally to whatever value is reasonable. 

Often ∆r = 0, as it is usually clear in advance if an activity will be drawing cash or is self-funding. 

That just leaves the determination of r. The fixing of this is harder. 


Taking the overnight IR, which would be the closest match to what we are looking for, leaves out great opportunities. 

A trading house typically has a good view on the value of the cash account as it has built up some history over time. 

Leaving the cash on this account does not make sense.

The equity desk should shift this capital to other desks where it can be invested and managed more wisely. 

One could decide that, for internal purposes, the IR r is taken to be the 6m swap rate, irrespective of option lifetime. 

One could even decide that value of r is fixed once a week and kept constant throughout the week. 


That means that the internal transfer is obligated and, in some cases, the interest desk is forced to take on positions with a loss, at other times it could be a profit. If the volumes coming from the equity derivatives desk are much smaller than the typical volumes they trade, this might not be as bad as it sounds. 

For the equity derivatives desk, it eliminates the burden of following up on IR. 


If the activity is organised this way, it is clear that the equity desk could arbitrage the system. 

If the IR is fixed on Monday and valid until Friday and they are looking into a transaction on Friday, and the IR market has changed a lot, they could decide to keep their IR position open and wait to deposit the cash until next Monday. 

An internal check-up should be installed to prevent one-sided abuse between the internal desks. 


The main conclusionto be drawn from this is that an equity derivatives trader should be less focused on the problem of IR risk, and more on the value of the stock, and, on the volatility. 


In practice, desks don't have a cash account but instead they receive internal funding. 

This funding has become more and more a topic of discussion as the regulator has raised the question if banks have enough capital available to run their business. 

From the cost of hedging argument, it is clear that the cost of funding should be factored into the hedging cost and hence into the price of any derivative. 


Different participants in the market will have different funding rates, depending on the capitalisation and credit rating they have. 

This leads to different internal IRs, but also to different option prices, which they can offer to their clients. 


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