The ‘wriggle parameter’ in derivatives: futures pricing formula takes on new importance

Aside from specialist trading desks, the wriggle parameter is little-known in financial markets. Yet, this part of a derivatives formula now plays a critical role in understanding pricing dynamics at major banks. In this article, we explain the wriggle parameter, why it matters and why clients should watch for its impacts in their dealer pricing. A guest post by Vincent Maury and Natalie Lyons of Societe Generale.

What is it?

The wriggle parameter is shorthand for a part of the derivatives formula for pricing a forward contract; this is the cost of carry that is buried into the future cost. Most people don’t think about either the formula or the cost of carry very often, or they consider the cost of carry as analogous to the risk-free rate. In fact, the cost of carry is an important variable all its own.

The formula for pricing a forward is:

Where

• F = forward rate to be paid at time T
• ex = exponential function (used for calculating compounding interests)
• r = risk free interest rate
• q = cost of carry
• SO = spot price of the asset at time O
• Di = dividend that is guaranteed to be paid at time ti where 0 < ti < T

The q is what we want to focus on. When a dealer takes on a hedge, this is their cost of carry to maintain a position on behalf of a client. It could be an interest rate, operational costs or a number of other variables. In many cases, it is the cost of holding or financing an asset as a hedge. For our purposes, the q in this formula is the repo rate. We, as dealers, need to trade on this rate in order to manage our own risk exposure; this is a central part of running a derivatives desk.

There are two aspects of the q in this formula: the one that clients and dealers see and the one that only dealers see. The difference between the two can represent a wide spread or a narrow spread, and is frequently a point of opacity in the conversation between dealers and clients. The client-side rate is based on a client’s need for a flexible trade: they may want to buy and sell in a short period or change their strategy depending on the investment environment. Clients also want to avoid mark to market or dividend risk: once their pricing is created, they want it set in stone.

From the dealer’s point of view, we must take all of the client’s needs into account plus factor in our own credit risk exposure on the client side. Clients typically do one-sided business that can’t be netted. Clients are much smaller than banks and may not be rated, which keeps our counterparty risk exposures high. This translates into balance sheet expense, which is factored into the cost of carry.

Meanwhile, on the other side, dealers are trading in the interbroker dealer (IBD) market, which has largely different characteristics than a dealer-to-client marketplace. When dealers transact with IBDs, trades are unbreakable and must be held to maturity. If the client trades out of their position, the dealer is still locked in for the duration. Further, any trade has both mark to market and dividend risk; pricing can vary for the length of the trade. One clear benefit for dealers however is that when transacting with IBDs, we have less counterparty risk from netting and improved counterparty ratings than when trading with clients. Still, from the standpoint of valuing the trade, taking a fixed exposure with an IBD compared to a variable exposure with a client creates uncertainty. We need to consider our exposure with IBDs in a very different way than how we calculate balance sheet costs with clients.

The spread between the IBD cost of carry and the client cost of carry creates the wriggle parameter in the futures pricing formula. We start with the IBD cost, which is known and fixed. We then calculate the cost of capital for the uncertainties surrounding the client-side transaction as well as counterparty risk exposure and lack of netting. This of course influences the cost of the transaction in ways both small and large.

How clients should view the wriggle parameter

It is well understood that regulations have created new constraints for bank balance sheets. What was once a readily available resource has become highly constrained across the industry. Clients are already familiar with the basic story and how that has translated generally into pricing.

For clients, the wriggle parameter is a specific opportunity to have a conversation about transparency in pricing with their derivatives dealers. The difference between IDB pricing and client pricing can be spelled out with the outcome of forming a working partnership about the client’s trading strategy, the securities utilised, the term, any netting opportunities and ways to reduce counterparty credit exposure. The wriggle parameter is a real way for clients and dealers alike to manage balance sheet costs in a challenging environment.

Vincent Maury is head of 1D European Major Indices, Societe Generale
Natalie Lyons is Director, Equity Finance, Societe Generale