You Think You’re Trading Vol...But Are You Even?

Option amateurs underappreciate the role of funding in pricing derivatives. Professional options traders need to be obsessed with funding costs because they are trading for tiny, often sub-penny, margins.

Here’s a simple example to demonstrate the tyrannical effect of funding on pricing:

What is a 1-year American at-the-forward call option on a non-div paying, 20% implied vol, $100 stock worth?

You need to feed the model an interest rate to get an answer. You look at the yield curve and see a 5% rate (making this up) for 1 year. This yields a forward price of $105 (we can hand-wave simple vs compounded rates for this purpose).

Imagine the bid-ask for this call is 40 cents wide $7.80 – $8.20

If you buy on the bid and sell on the offer you make a .40 profit. Easy-peasy.

Now imagine you buy the bid and hedge the position until expiry. What implied vol did you buy?

The first thing to recognize is that you will be shorting the stock to hedge. Assuming it’s easy to borrow, you are still not going to receive a 5% rate on the cash proceeds. Your prime broker needs to earn its margin. If 5% is the risk-free rate, let’s assume they pay you 4.5% on cash balances. Conversely, the prime broker will lend at 5.5% (this is known as the “long rate” and it’s the rate you finance long positions at). If you sell the call on the offer you will need to pay that rate to finance the shares you buy.

Uh oh.

If you buy the call you need to use a 4.5% rate in the model to back out an implied vol and if you sell the call you need to use a 5.5% rate in the model. You can see where this is going.

• If you buy the call on the bid you are paying 20.06% implied vol.
• If you sell the call on the offer you are selling 19.95% implied vol.

(Check the math if you want)

You think you’re trading vol but because of the bid-ask spread on your funding rate, you are basically trading the same implied vol even if you buy the bid and sell the ask. Rho is the sensitivity of the option price for a 1% change in the interest rate. The vega of an option is the sensitivity of its price for a 1-point change in volatility.

The rho of this call option is 46 cents vs a vega of 40 cents.

A 1% difference in funding rate (ie 4.5% vs 5.5%) is an institutional level bid-ask. It can be much worse for retail.

If you are trying to make markets you think you’re trading vol but are you even?

Pricing and carrying longer-dated options is crucially dependent on funding costs and the bid-ask spreads might not even be wide enough to compensate a market maker for their funding spread. Another way of saying this: the market-maker with such a 1% wide funding rate is making a 20% “choice” market in the vol. If the bid-ask was tighter they would be bidding a higher vol than they were offering!

(Again this assumes they hold and manage the position as opposed to spreading the options off by say buying one call and selling another or having the privileged position of just getting ping-ponged on their posted bid-ask all day)